From 6d9c9d9267511d1843d0cbc6b8590e2f7c2a6005 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Motiejus=20Jak=C5=A1tys?= Date: Wed, 19 May 2021 23:15:44 +0300 Subject: [PATCH] Move to github.com/motiejus/wm --- IV/Dockerfile | 13 - IV/Makefile | 386 --------- IV/README.md | 78 +- IV/aggregate-rivers.sql | 49 -- IV/amalgamate1.png | Bin 13240 -> 0 bytes IV/bib.bib | 262 ------ IV/db | 49 -- IV/extract-and-generate | 11 - IV/gdr2pgsql | 34 - IV/in-container | 23 - IV/init.sql | 33 - IV/layer2img.py | 133 --- IV/mj-msc.tex | 1738 -------------------------------------- IV/notes.txt | 117 --- IV/openmap-wm-bad.png | Bin 66326 -> 0 bytes IV/openmap-wm-good.png | Bin 202357 -> 0 bytes IV/rivers-10.sql | 54 -- IV/rivers-250.sql | 52 -- IV/rivers-50.sql | 54 -- IV/slides-2021-03-29.txt | 90 -- IV/test-rivers.sql | 20 - IV/test.sql | 198 ----- IV/vars.awk | 26 - IV/visuals.sql | 146 ---- IV/vu.pdf | Bin 11905 -> 0 bytes IV/wang125.png | Bin 86831 -> 0 bytes IV/wm.sql | 850 ------------------- 27 files changed, 1 insertion(+), 4415 deletions(-) delete mode 100644 IV/Dockerfile delete mode 100644 IV/Makefile delete mode 100644 IV/aggregate-rivers.sql delete mode 100644 IV/amalgamate1.png delete mode 100644 IV/bib.bib delete mode 100755 IV/db delete mode 100755 IV/extract-and-generate delete mode 100755 IV/gdr2pgsql delete mode 100755 IV/in-container delete mode 100644 IV/init.sql delete mode 100644 IV/layer2img.py delete mode 100644 IV/mj-msc.tex delete mode 100644 IV/notes.txt delete mode 100644 IV/openmap-wm-bad.png delete mode 100644 IV/openmap-wm-good.png delete mode 100644 IV/rivers-10.sql delete mode 100644 IV/rivers-250.sql delete mode 100644 IV/rivers-50.sql delete mode 100644 IV/slides-2021-03-29.txt delete mode 100644 IV/test-rivers.sql delete mode 100644 IV/test.sql delete mode 100644 IV/vars.awk delete mode 100644 IV/visuals.sql delete mode 100644 IV/vu.pdf delete mode 100644 IV/wang125.png delete mode 100644 IV/wm.sql diff --git a/IV/Dockerfile b/IV/Dockerfile deleted file mode 100644 index 6b49cf7..0000000 --- a/IV/Dockerfile +++ /dev/null @@ -1,13 +0,0 @@ -FROM debian:bullseye - -RUN apt-get update && \ - DEBIAN_FRONTEND=noninteractive apt-get install -y \ - texlive-full poppler-utils \ - osm2pgsql postgresql-client \ - python3-pygments python3-geopandas \ - latexmk make \ - docker.io - -COPY layer2img.py /tmp/layer2img.py -RUN python3 /tmp/layer2img.py -o /tmp/foo.pdf && \ - rm /tmp/layer2img.py /tmp/foo.pdf diff --git a/IV/Makefile b/IV/Makefile deleted file mode 100644 index d9e7fa0..0000000 --- a/IV/Makefile +++ /dev/null @@ -1,386 +0,0 @@ -OSM ?= lithuania-latest.osm.pbf -RIVERFILTER = Visinčia|Šalčia|Nemunas -SLIDES = slides-2021-03-29.pdf - -GDB10LT ?= $(wildcard GDB10LT-static-*.zip) - -# Max figure size (in meters) is when it's width is TEXTWIDTH_CM on scale 1:25k -SCALEDWIDTH = $(shell awk '/^TEXTWIDTH_CM/{print 25000/100*$$3}' layer2img.py) - -############################################################################## -# These variables have to come before first use due to how macros are expanded -############################################################################## - -NON_ARCHIVABLES = notes.txt referatui.txt slides-2021-03-29.txt -ARCHIVABLES = $(filter-out $(NON_ARCHIVABLES),$(shell git ls-files .)) - -LISTINGS = aggregate-rivers.sql wm.sql extract-and-generate - -FIGURES = \ - test-figures \ - fig8-definition-of-a-bend \ - fig8-elimination-gen1 \ - fig8-elimination-gen2 \ - fig8-elimination-gen3 \ - fig5-gentle-inflection-before \ - fig5-gentle-inflection-after \ - inflection-1-gentle-inflection-before \ - inflection-1-gentle-inflection-after \ - fig6-selfcrossing \ - selfcrossing-1 \ - isolated-1-exaggerated - -RIVERS = \ - salvis-25k \ - salvis-2x50k \ - salvis-250k-10x \ - salvis-grpk250-2x \ - salvis-dp64-2x50k \ - salvis-vw64-2x50k \ - salvis-dpchaikin64-2x50k \ - salvis-vwchaikin64-2x50k \ - salvis-overlaid-dpchaikin64-2x50k \ - salvis-overlaid-vwchaikin64-2x50k \ - salvis-wm220-10x \ - salvis-wm220-2x \ - salvis-wm-overlaid-250k-zoom \ - salvis-wm220 - -################################################################################ -# FIGURES -################################################################################ -test-figures_1SELECT = wm_figures - -fig8-definition-of-a-bend_1SELECT = wm_debug where name='fig8' AND stage='afigures' AND gen=1 -fig8-definition-of-a-bend_2SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=1 -fig8-definition-of-a-bend_3SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=1 -fig8-definition-of-a-bend_3LINESTYLE = dotted - -fig8-elimination-gen1_1SELECT = wm_debug where name='fig8' AND stage='afigures' AND gen=1 -fig8-elimination-gen1_2SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=1 -fig8-elimination-gen1_3SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=1 -fig8-elimination-gen1_3LINESTYLE = dotted - -fig8-elimination-gen2_1SELECT = wm_debug where name='fig8' AND stage='afigures' AND gen=2 -fig8-elimination-gen2_2SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=2 -fig8-elimination-gen2_3SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=2 -fig8-elimination-gen2_3LINESTYLE = dotted -fig8-elimination-gen3_1SELECT = wm_debug where name='fig8' AND stage='bbends' AND gen=3 -fig8-elimination-gen3_2SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=3 -fig8-elimination-gen3_3SELECT = wm_debug where name='fig8' AND stage='bbends-polygon' AND gen=3 -fig8-elimination-gen3_3LINESTYLE = dotted - -fig5-gentle-inflection-before_WITHDIV = 2 -fig5-gentle-inflection-before_1SELECT = wm_debug where name='fig5' AND stage='afigures' AND gen=1 -fig5-gentle-inflection-before_2SELECT = wm_debug where name='fig5' AND stage='bbends-polygon' AND gen=1 -fig5-gentle-inflection-before_3SELECT = wm_debug where name='fig5' AND stage='bbends-polygon' AND gen=1 -fig5-gentle-inflection-before_3LINESTYLE = dotted -fig5-gentle-inflection-after_WITHDIV = 2 -fig5-gentle-inflection-after_1SELECT = wm_debug where name='fig5' AND stage='cinflections' AND gen=1 -fig5-gentle-inflection-after_2SELECT = wm_debug where name='fig5' AND stage='cinflections-polygon' AND gen=1 -fig5-gentle-inflection-after_3SELECT = wm_debug where name='fig5' AND stage='cinflections-polygon' AND gen=1 -fig5-gentle-inflection-after_3LINESTYLE = dotted - -inflection-1-gentle-inflection-before_WIDTHDIV = 2 -inflection-1-gentle-inflection-before_1SELECT = wm_debug where name='inflection-1' AND stage='afigures' AND gen=1 -inflection-1-gentle-inflection-before_2SELECT = wm_debug where name='inflection-1' AND stage='bbends-polygon' AND gen=1 -inflection-1-gentle-inflection-before_3SELECT = wm_debug where name='inflection-1' AND stage='bbends-polygon' AND gen=1 -inflection-1-gentle-inflection-before_3LINESTYLE = dotted -inflection-1-gentle-inflection-after_WIDTHDIV = 2 -inflection-1-gentle-inflection-after_1SELECT = wm_debug where name='inflection-1' AND stage='cinflections' AND gen=1 -inflection-1-gentle-inflection-after_2SELECT = wm_debug where name='inflection-1' AND stage='cinflections-polygon' AND gen=1 -inflection-1-gentle-inflection-after_3SELECT = wm_debug where name='inflection-1' AND stage='cinflections-polygon' AND gen=1 -inflection-1-gentle-inflection-after_3LINESTYLE = dotted - -fig6-selfcrossing_WIDTHDIV = 2 -fig6-selfcrossing_1SELECT = wm_debug where name='fig6' AND stage='afigures' AND gen=1 -fig6-selfcrossing_1LINESTYLE = dotted -fig6-selfcrossing_2SELECT = wm_debug where name='fig6' AND stage='dcrossings' AND gen=1 -fig6-selfcrossing_3SELECT = wm_visuals where name='fig6-baseline' -fig6-selfcrossing_3COLOR = orange - -selfcrossing-1_WIDTHDIV = 2 -selfcrossing-1_1SELECT = wm_debug where name='selfcrossing-1' AND stage='afigures' AND gen=1 -selfcrossing-1_1LINESTYLE = dotted -selfcrossing-1_2SELECT = wm_debug where name='selfcrossing-1' AND stage='dcrossings' AND gen=1 -selfcrossing-1_3SELECT = wm_visuals where name='selfcrossing-1-baseline' -selfcrossing-1_3COLOR = orange - -isolated-1-exaggerated_WIDTHDIV = 2 -isolated-1-exaggerated_1SELECT = wm_debug where name='isolated-1' AND stage='afigures' AND gen=2 -isolated-1-exaggerated_2SELECT = wm_debug where name='isolated-1' AND stage='afigures' AND gen=1 -isolated-1-exaggerated_1COLOR = orange - -################################################################################ -# 250K -################################################################################ - -salvis-wm220-250k-2x_1SELECT = wm_visuals where name='salvis-wm220' -salvis-wm220-250k-2x_WIDTHDIV = 2 - -salvis-wm220-250k-10x_1SELECT = wm_visuals where name='salvis-wm220' -salvis-wm220-250k-10x_WIDTHDIV = 10 - -salvis-250k-10x_1SELECT = wm_visuals where name='salvis-grpk10' -salvis-250k-10x_WIDTHDIV = 10 - -salvis-wm-overlaid-250k-zoom_1SELECT = wm_visuals where name='salvis-wm220' -salvis-wm-overlaid-250k-zoom_2SELECT = wm_visuals where name='salvis-grpk10' -salvis-wm-overlaid-250k-zoom_1COLOR = orange - -salvis-grpk250-2x_1SELECT = wm_visuals where name='salvis-grpk250' -salvis-grpk250-2x_WIDTHDIV = 2 - -################################################################################ -# 50K -################################################################################ - -label_wm75 = Wang--Müller 1:\numprint{50000} -label_wm220 = Wang--Müller 1:\numprint{250000} -label_vw64 = Visvalingam--Whyatt -label_dp64 = Douglas \& Peucker -label_grpk10 = GRPK 1:\numprint{10000} -label_grpk50 = GRPK 1:\numprint{50000} -label_vwchaikin64 = $(label_vw64) and Chaikin -label_dpchaikin64 = $(label_dp64) and Chaikin -legend_ = lower left -legend_tr = lower right -legend_tl = lower center - -define wm_vwdp50k -RIVERS += salvis-$(1)-$(2)-$(3)-$(4)x50k$(5) -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_1SELECT = wm_visuals where name='salvis-$(1)' -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_1COLOR = orange -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_1LABEL = $(label_$(1)) -$(if $(2), -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_2SELECT = wm_visuals where name='salvis-$(2)' -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_2COLOR = green -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_2LABEL = $(label_$(2)) -,) -$(if $(3), -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_3SELECT = wm_visuals where name='salvis-$(3)' -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_3LINESTYLE = $(6) -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_3LABEL = $(label_$(3)) -,) -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_WIDTHDIV = $(4) -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_QUADRANT = $(5) -salvis-$(1)-$(2)-$(3)-$(4)x50k$(5)_LEGEND = $(legend_$(5)) -endef - -wm_vwdp50kblack = $(call wm_vwdp50k,$(1),$(2),$(3),$(4),$(5)) -wm_vwdp50kdotted = $(call wm_vwdp50k,$(1),$(2),$(3),$(4),$(5),dotted) - -$(foreach x,vw64 dp64 vwchaikin64 dpchaikin64,\ - $(eval $(call wm_vwdp50kdotted,wm75,$(x),grpk10,1,)) \ -) -$(eval $(call wm_vwdp50kblack,wm75,grpk50,grpk10,1)) -$(eval $(call wm_vwdp50kblack,wm75,grpk50,grpk10,1,tr)) -$(eval $(call wm_vwdp50kblack,wm75,grpk50,grpk10,1,tl)) - -$(eval $(call wm_vwdp50kblack,wm75,,grpk10,1)) -$(eval $(call wm_vwdp50kblack,wm75,,grpk10,1,tr)) -$(eval $(call wm_vwdp50kblack,wm75,,grpk10,1,tl)) - -salvis-25k_1SELECT = wm_visuals where name='salvis-grpk10' -salvis-25k_WIDTHDIV = 1 - -salvis-2x50k_1SELECT = wm_visuals where name='salvis-grpk10' -salvis-2x50k_WIDTHDIV = 2 - -salvis-dp64-2x50k_1SELECT = wm_visuals where name='salvis-dp64' -salvis-dp64-2x50k_WIDTHDIV = 2 - -salvis-vw64-2x50k_1SELECT = wm_visuals where name='salvis-vw64' -salvis-vw64-2x50k_WIDTHDIV = 2 - -salvis-dpchaikin64-2x50k_2SELECT = wm_visuals where name='salvis-dpchaikin64' -salvis-dpchaikin64-2x50k_WIDTHDIV = 2 - -salvis-vwchaikin64-2x50k_2SELECT = wm_visuals where name='salvis-vwchaikin64' -salvis-vwchaikin64-2x50k_WIDTHDIV = 2 - -salvis-overlaid-dpchaikin64-2x50k_1SELECT = wm_visuals where name='salvis-dpchaikin64' -salvis-overlaid-dpchaikin64-2x50k_2SELECT = wm_visuals where name='salvis-grpk10' -salvis-overlaid-dpchaikin64-2x50k_1COLOR = orange -salvis-overlaid-dpchaikin64-2x50k_WIDTHDIV = 2 -salvis-overlaid-dpchaikin64-2x50k_QUADRANT = tl - -salvis-overlaid-vwchaikin64-2x50k_1SELECT = wm_visuals where name='salvis-vwchaikin64' -salvis-overlaid-vwchaikin64-2x50k_2SELECT = wm_visuals where name='salvis-grpk10' -salvis-overlaid-vwchaikin64-2x50k_1COLOR = orange -salvis-overlaid-vwchaikin64-2x50k_WIDTHDIV = 2 -salvis-overlaid-vwchaikin64-2x50k_QUADRANT = tl - -salvis-wm220_1SELECT = wm_visuals where name='salvis-wm220' -salvis-wm220_WIDTHDIV = 2 - -define FIG_template -$(1).pdf: layer2img.py Makefile $(2) - python3 ./layer2img.py --outfile=$(1).pdf \ - $$(if $$($(1)_LEGEND),--legend="$$($(1)_LEGEND)") \ - $$(if $$($(1)_WIDTHDIV),--widthdiv=$$($(1)_WIDTHDIV)) \ - $$(if $$($(1)_QUADRANT),--quadrant=$$($(1)_QUADRANT)) \ - $$(foreach i,1 2 3, \ - $$(if $$($(1)_$$(i)LABEL),--g$$(i)-label="$$($(1)_$$(i)LABEL)") \ - $$(if $$($(1)_$$(i)COLOR),--g$$(i)-color="$$($(1)_$$(i)COLOR)") \ - $$(if $$($(1)_$$(i)SELECT),--g$$(i)-select="$$($(1)_$$(i)SELECT)") \ - $$(if $$($(1)_$$(i)LINESTYLE),--g$$(i)-linestyle="$$($(1)_$$(i)LINESTYLE)") \ - ) -endef - -$(foreach fig,$(FIGURES),$(eval $(call FIG_template,$(fig),.faux_test))) -$(foreach fig,$(RIVERS), $(eval $(call FIG_template,$(fig),.faux_visuals))) - -################################# -# The thesis, publishable version -################################# - -mj-msc-full.pdf: mj-msc.pdf version.inc.tex $(ARCHIVABLES) ## Thesis for publishing - cp $< .tmp-$@ - for f in $^; do \ - if [ "$$f" = "$<" ]; then continue; fi; \ - pdfattach .tmp-$@ $$f .tmp2-$@; \ - mv .tmp2-$@ .tmp-$@; \ - done - mv .tmp-$@ $@ - -############################### -# Auxiliary targets for humans -############################### - -.PHONY: test -test: .faux_test ## Unit tests (fast) - -.PHONY: visuals -visuals: .faux_visuals # Generate visuals for paper (fast) - -.PHONY: test-rivers -test-rivers: .faux_test-rivers ## Rivers tests (slow) - -.PHONY: slides -slides: $(SLIDES) - -.PHONY: refresh-rivers -refresh-rivers: refresh-rivers-10.sql refresh-rivers-50.sql refresh-rivers-250.sql ## Refresh river data from national datasets - -########################### -# The report, quick version -########################### - -mj-msc.pdf: mj-msc.tex version.inc.tex vars.inc.tex bib.bib \ - $(LISTINGS) $(addsuffix .pdf,$(FIGURES)) $(addsuffix .pdf,$(RIVERS)) - latexmk -shell-escape -pdf $< - -############################ -# Report's test dependencies -############################ - -.PHONY: allfigs -allfigs: $(addsuffix .pdf,$(FIGURES)) $(addsuffix .pdf,$(RIVERS)) - -.faux_db_pre: db init.sql - bash db start - bash db -f init.sql - touch $@ - -.faux_db: rivers-10.sql rivers-50.sql rivers-250.sql - bash db $(addprefix -f ,$^) - touch $@ -.faux_db: .EXTRA_PREREQS = .faux_db_pre - -.faux_test: test.sql wm.sql .faux_db - bash db -f $< - touch $@ - -.faux_visuals: visuals.sql .faux_test - bash db -v scaledwidth=$(SCALEDWIDTH) -f $< - touch $@ - -.faux_test-rivers: test-rivers.sql wm.sql Makefile .faux_db - bash db -f $< - touch $@ - -################################ -# Report's non-test dependencies -################################ - -REF = $(shell git describe --abbrev=12 --always --dirty) -version.inc.tex: Makefile $(shell git rev-parse --git-dir 2>/dev/null) - TZ=UTC date '+\gdef\VCDescribe{%F (revision $(REF))}%' > $@ - -vars.inc.tex: vars.awk wm.sql Makefile - awk -f $< wm.sql - -############### -# Misc commands -############### - -slides-2021-03-29.pdf: slides-2021-03-29.txt - pandoc -t beamer -i $< -o $@ - -dump-debug_wm.sql.xz: - docker exec -ti wm-mj pg_dump -Uosm osm -t wm_devug | xz -v > $@ - -release.zip: mj-msc.tex mj-msc.bbl version.inc.tex vars.inc.tex \ - $(addsuffix .pdf,$(FIGURES)) $(addsuffix .pdf,$(RIVERS)) \ - $(shell git ls-files .) - -rm $@ - mkdir -p .tmp; touch .tmp/editorial-version - zip $@ $^ - zip $@ -j .tmp/editorial-version - -mj-msc.bbl: mj-msc.tex bib.bib - biber mj-msc - -mj-msc-gray.pdf: mj-msc.pdf - gs \ - -sOutputFile=$@ \ - -sDEVICE=pdfwrite \ - -sColorConversionStrategy=Gray \ - -dProcessColorModel=/DeviceGray \ - -dCompatibilityLevel=1.4 \ - -dNOPAUSE \ - -dBATCH \ - $< - -.PHONY: clean -clean: ## Clean the current working directory - -bash db stop - -rm -r .faux_test .faux_aggregate-rivers .faux_test-rivers .faux_visuals \ - .faux_db .faux_db_pre version.inc.tex vars.inc.tex version.aux \ - version.fdb_latexmk _minted-mj-msc .tmp \ - $(shell git ls-files -o mj-msc*) \ - $(addsuffix .pdf,$(FIGURES)) \ - $(addsuffix .pdf,$(RIVERS)) \ - $(SLIDES) - -.PHONY: clean-tables -clean-tables: ## Remove tables created during unit or rivers tests - bash db -c '\dt wm_*' | awk '/_/{print "drop table "$$3";"}' | bash db -f - - -rm .faux_db - -.PHONY: help -help: ## Print this help message - @awk -F':.*?## ' '/^[a-z0-9.-]*: *.*## */{printf "%-18s %s\n",$$1,$$2}' \ - $(MAKEFILE_LIST) - -.PHONY: wc -wc: mj-msc.pdf ## Character and page count - @pdftotext $< - | \ - awk '/\yReferences\y/{exit}; {print}' | \ - tr -d '[:space:]' | wc -c | \ - awk '{printf("Chars: %d, pages: %.1f\n", $$1, $$1/1500)}' - -define refresh_rivers_template -.PHONY: refresh-$(1) -refresh-$(1): aggregate-rivers.sql gdr2pgsql .faux_db_pre - @if [ ! -f "$$($(2))" ]; then \ - echo "ERROR: $(2)-static-*.zip not found. Run env $(2)=<...>"; \ - exit 1; \ - fi - ./gdr2pgsql "$$($(2))" "$(3)" "$(RIVERFILTER)" "$(1)" -endef - -$(eval $(call rivers_template,rivers-10.sql,GDB10LT,wm_rivers)) -$(eval $(call rivers_template,rivers-50.sql,grpk50LT,wm_rivers_50)) -$(eval $(call rivers_template,rivers-250.sql,grpk250LT,wm_rivers_250)) diff --git a/IV/README.md b/IV/README.md index fd055e5..4722379 100644 --- a/IV/README.md +++ b/IV/README.md @@ -1,80 +1,4 @@ Wang–Müller algorithm in PostGIS -------------------------------- -This is a work-in-progress implementation following "Line generalization based -on analysis of shape characteristics" by Wang and Müller, 1998. - -Structure ---------- - -There will be 2 deliverables from this folder: - -- `wm.sql`, the implementation. -- paper `mj-msc-full.pdf`, a MSc thesis, explaining it. - -It contains a few supporting files, notably: - -- `tests.sql` synthetic unit tests. -- `test-rivers.sql` tests with real rivers. -- `Makefile` glues everything together. -- `layer2img.py` converts a PostGIS layer to an embeddable image. -- `aggregate-rivers.sql` combines multiple river objects (linestrings or - multilinestrings) to a single one. -- `init.sql` initializes PostGIS database for running the tests. -- `rivers-*.sql` are national dataset snapshots of rivers (`Makefile` - contains code to update them). -- ... and a few more files necessary to build the paper. - -Running -------- - -`make help` lists the select commands for humans. As of writing: - -``` -# make help -mj-msc-full.pdf Thesis for publishing -test Unit tests (fast) -test-rivers Rivers tests (slow) -clean Clean the current working directory -clean-tables Remove tables created during unit or rivers tests -help Print this help message -wc Character and page count -refresh-rivers Refresh rivers-*.sql from Open Street Maps -``` - -To execute the algorithm, run: - -- `make test` for tests with synthetic data. -- `make test-rivers` for tests with real rivers. You may adjust the rivers and - data source (e.g. use a different country instead of Lithuania) by changing - the `Makefile` and the test files. Left as an exercise for the reader. - -Building the paper (pdf) ------------------------- - -``` -# make -j$(nproc) mj-msc-full.pdf -``` - -`mj-msc.tex` results in `mj-msc-full.pdf`, which will be at some point -published. It needs quite a few dependencies, including a functioning Docker -environment, postgresql client, geopandas, pygments, osm2pgsql, poppler, and a -"quite extensive" LaTeX installation. This was tested on Debian 11. - -Contributing ------------- - -Please reach out to me before contributing. As of writing, this is not ready to -accept broader contributions, TODO: - -- [x] Elimination operator. -- [x] Exaggeration operator. -- [ ] Combination operator. -- [ ] CI (unlikely to happen). -- [x] Known bug in `wm_self_crossing`: the program crashes with a river in - Lithuania. - -License -------- - -GPL 2.0 or later, same as PostGIS. +Moved to [github.com/motiejus/wm](https://github.com/motiejus/wm). diff --git a/IV/aggregate-rivers.sql b/IV/aggregate-rivers.sql deleted file mode 100644 index d305445..0000000 --- a/IV/aggregate-rivers.sql +++ /dev/null @@ -1,49 +0,0 @@ -/* Aggregates rivers by name and proximity. */ -drop function if exists aggregate_rivers; -create function aggregate_rivers() returns table( - id integer, - name text, - way geometry -) as $$ -declare - c record; - cc record; - changed boolean; -begin - while (select count(1) from wm_rivers_tmp) > 0 loop - select * from wm_rivers_tmp limit 1 into c; - delete from wm_rivers_tmp a where a.id = c.id; - changed = true; - while changed loop - changed = false; - for cc in ( - select * from wm_rivers_tmp a where - a.name = c.name and - st_dwithin(a.way, c.way, 500) - ) loop - c.way = st_linemerge(st_union(c.way, cc.way)); - delete from wm_rivers_tmp a where a.id = cc.id; - changed = true; - end loop; - end loop; -- while changed - return query select c.id, c.name, c.way; - end loop; -- count(1) from wm_rivers_tmp > 0 - return; -end -$$ language plpgsql; - -drop index if exists wm_rivers_tmp_id; -drop index if exists wm_rivers_tmp_gix; -drop table if exists wm_rivers_tmp; -create temporary table wm_rivers_tmp (id serial, name text, way geometry); -create index wm_rivers_tmp_id on wm_rivers_tmp(id); -create index wm_rivers_tmp_gix on wm_rivers_tmp using gist(way) include(name); - -insert into wm_rivers_tmp (name, way) - select p.vardas as name, p.shape as way from :srctable p; - -drop table if exists :dsttable; -create table :dsttable as ( - select * from aggregate_rivers() where st_length(way) >= 50000 -); -drop table wm_rivers_tmp; diff --git a/IV/amalgamate1.png b/IV/amalgamate1.png deleted file mode 100644 index 5bf3ed51c11ff31952867a506962dc8453d235f1..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 13240 zcmeHtcT|(xwr>Cd=~ARhuYw`;5_%IsI!FfzNr2D-B$Ut<6j20GR5}O(BE5=qL;242-FqMRz2}|x&Uo+scQQsYzO~kzzd6@zYqIzv4fHfANSR3i004#74Rs>` z052E!9CHyL_uJE1_6z`^we~kLM;k$WIXt|O4hUB`2O8r6=Yabm8~^~n(Sk$^FW7r8 z^|KOEAf7Qt=)9doA7yzUtNzoh!gYVXgr!(rKB0&tuM+p9 zEFT397;2^-_s$Lt9UtqJ1P6zVOV*!hH%zi09t9gN6n=0!ICMnbez&xEie)(dmi_tm z?hx4;mUs|L6?GVNa{7)esKK!Jp;$;Vmh3T>?D_GI@?m}B@u;b5=F#nU#p^?Bdn*m? 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Proc. conference, 1986. Vol. 2}, - pages={257--266}, - year={1986}, - organization={distributed Royal Institution of Chartered Surveyors} -} -@inproceedings{mcmaster1993spatial, - title={A spatial-object level organization of transformations for cartographic generalization}, - author={McMaster, RB and Barnett, Leone}, - booktitle={AUTOCARTO-CONFERENCE-}, - pages={386--386}, - year={1993}, - organization={Citeseer} -} -@inproceedings{jiang2003line, - title={Line simplification using self-organizing maps}, - author={Jiang, Bin and Nakos, Byron}, - booktitle={Proceedings of the ISPRS Workshop on Spatial Analysis and Decision Making, Hong Kong, China}, - pages={3--5}, - year={2003} -} -@article{dyken2009simultaneous, - title={Simultaneous curve simplification}, - author={Dyken, Christopher and D{\ae}hlen, Morten and Sevaldrud, Thomas}, - journal={Journal of geographical systems}, - volume={11}, - number={3}, - pages={273--289}, - year={2009}, - publisher={Springer} -} -@article{mustafa2006dynamic, - title={Dynamic simplification and visualization of large maps}, - author={Mustafa, Nabil and Krishnan, Shankar and Varadhan, Gokul and Venkatasubramanian, Suresh}, - journal={International Journal of Geographical Information Science}, - volume={20}, - number={3}, - pages={273--302}, - year={2006}, - publisher={Taylor \& Francis} -} -@article{nollenburg2008morphing, - title={Morphing polylines: A step towards continuous generalization}, - author={N{\"o}llenburg, Martin and Merrick, Damian and Wolff, Alexander and Benkert, Marc}, - journal={Computers, Environment and Urban Systems}, - volume={32}, - number={4}, - pages={248--260}, - year={2008}, - publisher={Elsevier} -} -@inproceedings{stanislawski2012automated, - title={Automated metric assessment of line simplification in humid landscapes}, - author={Stanislawski, Lawrence V and Raposo, Paulo and Howard, Michael and Buttenfield, Barbara P}, - booktitle={Proceedings of the AutoCarto}, - year={2012} -} - -% LIKELY UNNEEDED -@book{buttenfield1991map, - title={Map Generalization: Making rules for knowledge representation}, - author={Buttenfield, Barbara Pfeil and McMaster, Robert Brainerd}, - year={1991}, - publisher={Longman Scientific \& Technical London} -} - -@article{chaikin1974algorithm, - title={An algorithm for high-speed curve generation}, - author={Chaikin, George Merrill}, - journal={Computer graphics and image processing}, - volume={3}, - number={4}, - pages={346--349}, - year={1974}, - publisher={Elsevier} -} - -@article{knuth1976big, - title={Big omicron and big omega and big theta}, - author={Knuth, Donald E}, - journal={ACM Sigact News}, - volume={8}, - number={2}, - pages={18--24}, - year={1976}, - publisher={ACM New York, NY, USA} -} - -@book{bachmann1894analytische, - title={Die analytische zahlentheorie}, - author={Bachmann, Paul}, - volume={2}, - year={1894}, - publisher={Teubner} -} - -@article{landau1911, - title={Handbuch der Lehre von der Verteilung der Primzahlen}, - journal={Monatshefte f{\"u}r Mathematik und Physik}, - year={1911}, - month={12}, - day={01}, - volume={22}, - number={1}, - pages={A26-A26}, - issn={1436-5081}, - doi={10.1007/BF01742852}, -} - -@online{mappingunits, - author={Aileen Buckley}, - title={Guidelines for minimum size for text and symbols on maps}, - date={2008-01-16}, - url={https://www.esri.com/arcgis-blog/products/product/mapping/guidelines-for-minimum-size-for-text-and-symbols-on-maps/}, - organization={Esri}, - urldate={2021-05-03}, -} - -@online{cartoucheMinimalDimensions, - author={CartouCHe}, - title={Cartographic Design for Screen Maps}, - subtitle={Minimum Dimensions}, - date={2012-01-26}, - url={http://www.e-cartouche.ch/content_reg/cartouche/cartdesign/en/html/GenRules_learningObject3.html}, - urldate={2021-05-03}, -} - -@online{epsg3857, - author={MapTiler Team}, - title={WGS 84/Pseudo-Mercator}, - url={https://epsg.io/3857}, - urldate={2021-05-03}, -} - -@online{postgis311, - author={PostGIS Team}, - title={PostGIS 3.1.1}, - url={https://postgis.net/2021/01/28/postgis-3.1.1/}, - urldate={2021-05-12}, -} - -@online{postgisref, - author={PostGIS Team}, - title={PostGIS Reference}, - url={https://postgis.net/docs/reference.html}, - urldate={2021-05-12}, -} - -@online{wmsql, - author={Motiejus Jakštys}, - title={Wang--M{\"u}ller implementation in PostGIS}, - url={https://github.com/motiejus/wm}, - urldate={2021-05-19}, -} - -@online{openstreetmap, - author={OpenStreetMap contributors}, - title={Project that creates and distributes free world's geographic data}, - url={https://www.openstreetmap.org}, - urldate={2021-05-15}, - } - -@online{nzt, - author={Nacionalinė Žemės Tarnyba Prie Žemės Ūkio Ministerijos}, - title={Atviri Duomenys}, - url={http://nzt.lt/go.php/lit/Atviri-duomenys}, - urldate={2021-05-15}, - } - -@online{openmapwm, - author={Tomas Straupis}, - title={Test harness for Wang--M{\"u}ller algorithm}, - url={https://dev.openmap.lt/webgl/wm.html}, - urldate={2021-05-15}, -} - -@article{devangleserrorbends, - author={Gökgöz, Türkay and Sen, Alper and Memduhoğlu, Abdulkadir and Hacar, Müslüm}, - year={2015}, - month={10}, - pages={2185-2204}, - title={A New Algorithm for Cartographic Simplification of Streams and Lakes Using Deviation Angles and Error Bands}, - volume={4}, - journal={ISPRS International Journal of Geo-Information}, - doi={10.3390/ijgi4042185} -} diff --git a/IV/db b/IV/db deleted file mode 100755 index f01321a..0000000 --- a/IV/db +++ /dev/null @@ -1,49 +0,0 @@ -#!/bin/bash -set -euo pipefail - -name=wm-mj - -_psql() { - env \ - PGPASSWORD=osm \ - PGHOST=127.0.0.1 \ - PGUSER=osm \ - PGDATABASE=osm \ - psql "$@" -} - -_wait_for_postgres() { - >&2 echo -n "Waiting for postgres" - for _ in $(seq 240); do - if _psql -qc '\q' 2>/dev/null; then - >&2 echo " up" - exit 0 - fi - >&2 echo -n . - sleep 1 - done - >&2 echo " down" - exit 1 -} - -case ${1:-} in - start) - _psql -qc '\q' 2>/dev/null && exit 0 - docker run -d --rm \ - --net=host \ - -e POSTGRES_DBNAME=osm \ - -e POSTGRES_USER=osm \ - -e POSTGRES_PASSWORD=osm \ - --name "$name" \ - postgis/postgis:13-3.1-alpine \ - -c log_statement=all \ - -c listen_addresses=127.0.0.1 - _wait_for_postgres - ;; - stop) - docker stop "$name" - ;; - *) - _psql "$@" - ;; -esac diff --git a/IV/extract-and-generate b/IV/extract-and-generate deleted file mode 100755 index 5940e45..0000000 --- a/IV/extract-and-generate +++ /dev/null @@ -1,11 +0,0 @@ -#!/bin/bash -eu -s=${1:-mj-msc-full.pdf} -d=$(mktemp -d) -f=mj-msc.pdf -l="$d/make.log" -echo "Extracting $s to workdir $d/"; pdfdetach -saveall -o "$d" "$s" -echo "Logs in $l ..."; make -j "$(nproc)" -C "$d" "$f" &> "$l" || { - echo "Failed to generate. $l extract:"; tail -20 "$l"; exit 1 -} -echo "Opening $d/$f ..."; xdg-open "$d/$f" -echo "$d/$f was closed. Removing $d"; rm -r "$d" diff --git a/IV/gdr2pgsql b/IV/gdr2pgsql deleted file mode 100755 index 2a3a7df..0000000 --- a/IV/gdr2pgsql +++ /dev/null @@ -1,34 +0,0 @@ -#!/bin/bash -set -euo pipefail - -dbzip=$(realpath -s "$1") -tbl=$2 -filter=$3 -outfile=$4 - -if [[ "$dbzip" =~ " " ]]; then - echo "ERROR: $dbzip contains spaces" - exit 1 -fi - -set -x - -gdbname=$(unzip -Z1 "$dbzip" | awk -Fgdb '/.gdb/{print $1"gdb";exit}') - -now=$(TZ=UTC date +"%FT%TZ") -here=$(whoami)@$(hostname -f) - -mkdir -p ".tmp" -ogr2ogr -skipfailures -f PGDump /dev/stdout -t_srs epsg:3857 \ - "/vsizip/$dbzip/$gdbname" -nln "src_$tbl" hidro_l | \ - awk "!/^INSERT/{print}; /^INSERT/&&/${filter}/{print;next}" | \ - bash ./db | \ - grep -v '^INSERT 0 1' - -bash db -f aggregate-rivers.sql -v "srctable=src_$tbl" -v "dsttable=$tbl" -( - echo "-- Generated at $now on $here"; - echo "-- Rivers: $filter"; - docker exec wm-mj pg_dump --clean -Uosm osm -t "$tbl" | tr -d '\r' -) > ".tmp/$outfile" -mv ".tmp/$outfile" "$outfile" diff --git a/IV/in-container b/IV/in-container deleted file mode 100755 index fb8eabd..0000000 --- a/IV/in-container +++ /dev/null @@ -1,23 +0,0 @@ -#!/bin/bash -set -euo pipefail - -# Prefix the 'make <...>' with this script to build the artifact in an isolated -# container. This means host dependencies can only be Docker and a shell (to -# run this script). -# -# Usage: -# ./in-container make help -# ./in-container make -j mj-msc-full.pdf -# ... - -NAME=wm-mj-build -if [[ -z "$(docker images -q --filter "reference=$NAME")" ]]; then - docker build -t "$NAME" . -fi - -exec docker run -ti --rm \ - --net=host \ - -v /var/run/docker.sock:/var/run/docker.sock \ - -v $(git rev-parse --show-toplevel):/x \ - -w /x/$(basename ${PWD}) \ - "$NAME" "$@" diff --git a/IV/init.sql b/IV/init.sql deleted file mode 100644 index fad27d0..0000000 --- a/IV/init.sql +++ /dev/null @@ -1,33 +0,0 @@ --- This file initializes tables for unit and river tests. --- ST_SimplifyWM, when dbgname is non-empty, expects `wm_debug` table to be --- created. - --- to preview this somewhat conveniently in QGIS: --- stage || '_' || name || ' gen:' || coalesce(gen, 'Ø') || ' nbend:' || lpad(nbend, 4, '0') -drop table if exists wm_debug; -create table wm_debug( - id serial, - stage text not null, - name text not null, - gen bigint not null, - nbend bigint, - way geometry, - props jsonb -); - -drop table if exists wm_manual; -create table wm_manual ( - id serial, - name text, - way geometry, - props jsonb -); - --- Run ST_SimplifyWM in debug mode, so `wm_debug` is populated. That table --- is used for geometric assertions later in the file. -drop table if exists wm_demo; -create table wm_demo (name text, i bigint, way geometry); - --- wm_visuals holds visual aids for the paper. -drop table if exists wm_visuals; -create table wm_visuals (name text, way geometry); diff --git a/IV/layer2img.py b/IV/layer2img.py deleted file mode 100644 index 19d6c37..0000000 --- a/IV/layer2img.py +++ /dev/null @@ -1,133 +0,0 @@ -#!/usr/bin/python3 -""" -Convert PostGIS geometries to an image. To scale. - -Accepts a few geometry fine-tuning parameters. -""" - -import argparse -import geopandas -import psycopg2 -from matplotlib import rc -import matplotlib.pyplot as plt - -CMAP = 'tab20c' # 'Set3' # is nice too -PSQL_CREDS = "host=127.0.0.1 dbname=osm user=osm password=osm" -COLORS = { - 'black': '#000000', - 'green': '#1b9e77', - 'orange': '#d95f02', - 'purple': '#7570b3', -} -# see `NOTICE` in the LaTeX document; this is the width of the main text block. -TEXTWIDTH_CM = 12.12364 - -QUADRANTS = {'tr':1, 'tl':2, 'bl':3, 'br':4} - -def color(string): - return COLORS[string if string else 'black'] - - -def inch(cm): - return cm / 2.54 - - -def parse_args(): - kwcolor = {'type': color, 'default': 'black'} - parser = argparse.ArgumentParser(description=__doc__) - parser.add_argument('--g1-select') - parser.add_argument('--g1-linestyle') - parser.add_argument('--g1-label') - parser.add_argument('--g1-color', **kwcolor) - parser.add_argument('--g2-select') - parser.add_argument('--g2-linestyle') - parser.add_argument('--g2-label') - parser.add_argument('--g2-color', **kwcolor) - parser.add_argument('--g3-select') - parser.add_argument('--g3-linestyle') - parser.add_argument('--g3-label') - parser.add_argument('--g3-color', **kwcolor) - parser.add_argument('--legend', - help="Legend location, following matplotlib rules", default='best') - parser.add_argument('--widthdiv', default=1, type=float, - help="Divide the width by this number " - "(useful when two images are laid horizontally " - "in the resulting file") - parser.add_argument('--quadrant', choices=QUADRANTS.keys(), - help="Image is comprised of 4 quadrants. This variable, " - "when non-empty, will clip and return the requested quadrant") - parser.add_argument('--outfile', metavar='', - help="If unset, displayed on the screen") - return parser.parse_args() - - -def read_layer(select, width, maybe_quadrant): - if not select: - return - way = "way" - if maybe_quadrant: - way = "wm_quadrant(way, {})".format(QUADRANTS[maybe_quadrant]) - - conn = psycopg2.connect(PSQL_CREDS) - sql = "SELECT {way} as way1 FROM {select}".format(way=way, select=select) - - return geopandas.read_postgis(sql, con=conn, geom_col='way1') - - -def plot_args(geom, color, maybe_linestyle, maybe_label): - if geom is None: - return - - # polygons either have fillings or lines - if geom.geom_type[0] == 'Polygon': - if maybe_linestyle: - return { - 'edgecolor': 'black', - 'linestyle': maybe_linestyle, - 'color': (0, 0, 0, 0), - } - else: - return {'cmap': CMAP, 'alpha': .25} - - r = {'color': color} - if maybe_linestyle == 'invisible': - r['color'] = (0, 0, 0, 0) - elif maybe_linestyle: - r['linestyle'] = maybe_linestyle - - if maybe_label: - r['label'] = '\\normalfont %s' % maybe_label - - return r - - -def main(): - args = parse_args() - width = TEXTWIDTH_CM / args.widthdiv - g1 = read_layer(args.g1_select, width, args.quadrant) - g2 = read_layer(args.g2_select, width, args.quadrant) - g3 = read_layer(args.g3_select, width, args.quadrant) - c1 = plot_args(g1, args.g1_color, args.g1_linestyle, args.g1_label) - c2 = plot_args(g2, args.g2_color, args.g2_linestyle, args.g2_label) - c3 = plot_args(g3, args.g3_color, args.g3_linestyle, args.g3_label) - - rc('text', usetex=True) - rc('text.latex', preamble='\\usepackage{numprint}\n') - fig, ax = plt.subplots(constrained_layout=True) - fig.set_figwidth(inch(width)) - - g1 is not None and g1.plot(ax=ax, linewidth=.75, **c1) - g2 is not None and g2.plot(ax=ax, linewidth=.75, **c2) - g3 is not None and g3.plot(ax=ax, linewidth=.75, **c3) - - ax.legend(loc=args.legend, frameon=False) - ax.axis('off') - ax.margins(0, 0) - if args.outfile: - fig.savefig(args.outfile, bbox_inches='tight', dpi=600) - else: - plt.show() - - -if __name__ == '__main__': - main() diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex deleted file mode 100644 index 8331d6f..0000000 --- a/IV/mj-msc.tex +++ /dev/null @@ -1,1738 +0,0 @@ -\documentclass[a4paper]{article} - -\usepackage[T1]{fontenc} -\usepackage[american]{babel} -\usepackage[utf8]{inputenc} -\usepackage{fvextra} -\usepackage[autostyle,english=american]{csquotes} -\MakeOuterQuote{"} -\usepackage[ - maxbibnames=99, - style=numeric, - sorting=none, - alldates=iso, - seconds=true -]{biblatex} -\addbibresource{bib.bib} -\usepackage[ - pdfusetitle, - pdfkeywords={Line Generalization,Line Simplification,Wang--Mueller}, - pdfborderstyle={/S/U/W 0} % /S/U/W 1 to enable reasonable decorations -]{hyperref} -\usepackage{enumitem} -\usepackage[toc,page,title]{appendix} -\usepackage{caption} -\usepackage{subcaption} -\usepackage{dcolumn} -\usepackage{gensymb} -\usepackage{units} -\usepackage{varwidth} -\usepackage{tabularx} -\usepackage{float} -\usepackage{numprint} -\usepackage{tikz} -\usetikzlibrary{shapes.geometric,arrows,positioning} -\usepackage{fancyvrb} -\usepackage{layouts} -\usepackage{minted} -%\usepackage{charter} -%\usepackage{setspace} -%\doublespacing - -\input{version.inc} -\input{vars.inc} - -\newcommand{\onpage}[1]{\ref{#1} on page~\pageref{#1}} -\newcommand{\titlecite}[1]{\citetitle{#1}\cite{#1}} -\newcommand{\titleciteauthor}[1]{\citetitle{#1} by \citeauthor{#1}\cite{#1}} -\newcommand{\DP}{Douglas \& Peucker} -\newcommand{\VW}{Visvalingam--Whyatt} -\newcommand{\WM}{Wang--M{\"u}ller} -\newcommand{\WnM}{Wang and M{\"u}ller} -\newcommand{\WirM}{Wang ir M{\"u}ller} -% {\WM} algoritmo realizacija kartografinei upių generalizacijai -\newcommand{\MYTITLE}{{\WM} algorithm realization for cartographic line generalization} -\newcommand{\MYTITLENOCAPS}{wang--m{\"u}ller algorithm realization for cartographic line generalization} -\newcommand{\MYAUTHOR}{Motiejus Jakštys} -\newcommand{\inputcode}[2]{\inputminted[fontsize=\small]{#1}{#2}} -\newenvironment{longlisting}{\captionsetup{type=listing}}{} - -\title{\MYTITLE} -\author{\MYAUTHOR} -\date{\VCDescribe} - -\begin{document} - -\begin{titlepage} - \begin{center} - \includegraphics[width=0.2\textwidth]{vu.pdf} \\[4ex] - - \large - \textbf{\textsc{ - vilnius university \\ - faculty of chemistry and geosciences \\ - department of cartography and geoinformatics - }} \\[8ex] - - \textbf{\MYAUTHOR} \\[8ex] - - \normalsize - A Thesis Presented for the Degree of Master in Cartography \\[8ex] - - \LARGE - \textbf{\textsc{\MYTITLENOCAPS}} - - \vfill - - \normalsize - Supervisor Dr. Andrius Balčiūnas \\[16ex] - - \VCDescribe - \end{center} -\end{titlepage} - -\begin{abstract} -\label{sec:abstract} - - Currently available line simplification algorithms are rooted in - mathematics and geometry, and are unfit for bendy map features like rivers - and coastlines. {\WnM} observed how cartographers simplify these natural - features and created an algorithm. We implemented this algorithm and - documented it in great detail. Our implementation makes {\WM} algorithm - freely available in PostGIS, and this paper explains it. - - \vfill - - Šiuo metu esami linijų supaprastinimo algoritmai yra kilę iš matematikos ir - geometrijos, bet nėra tinkami lankstiems geografiniams objektams, tokiems - kaip upės ir pakrantės, atvaizduoti. {\WirM} ištyrė, kaip kartografai - atlieka upių generalizaciją, ir sukūrė algoritmą. Mes realizavome šį - algoritmą ir išsamiai jį dokumentavome. Mūsų {\WM} realizacija ir - dokumentacija yra nemokamos ir laisvai prieinamos, naudojant PostGIS - platformą. - -\end{abstract} - -\clearpage - -\tableofcontents - -\listoftables -\listoflistings - -\newpage - -\section{Introduction} -\label{sec:introduction} - -\iffalse -NOTICE: this value should be copied to layer2img.py:TEXTWIDTH, so dimensions -of inline images are reasonable. - -Textwidth in cm: {\printinunitsof{cm}\prntlen{\textwidth}} -\fi - -When creating small-scale maps, often the detail of the data source is greater -than desired for the map. While many features can be removed or simplified, it -is more tricky with natural features that have many bends, like coastlines, -rivers, or forest boundaries. - -To create a small-scale map from a large-scale data source, features need to be -simplified, i.e., detail should be reduced. While performing the -simplification, it is important to retain the "defining" shape of the original -feature. Otherwise, if the simplified feature looks too different from the -original, the result will look unrealistic. Simplification problem for some -objects can often be solved by non-geometric means: - -\begin{itemize} - \item Towns and cities can be filtered by the number of inhabitants. - \item Roads can be eliminated by the road length, number of lanes, or - classification of the road (local, regional, international). -\end{itemize} - -However, things are not as simple for natural features like rivers or -coastlines. If a river is nearly straight, it should remain such after -simplification. An overly straightened river will look like a canal, and the -other way around --- too curvy would not reflect the natural shape. Conversely, -if the river originally is highly wiggly, the number of bends should be -reduced, but not removed altogether. Natural line simplification problem can be -viewed as a task of finding a delicate balance between two competing goals: - -\begin{itemize} - \item Reduce detail by removing or simplifying "less important" features. - \item Retain enough detail, so the original is still recognizable. -\end{itemize} - -Given the discussed complexities with natural features, a fine line between -under-simplification (leaving an object as-is) and over-simplification (making a -straight line) needs to be found. Therein lies the complexity of simplification -algorithms: all have different trade-offs. - -The purpose of the thesis is to implement a cartographic line generalization -algorithm on the basis of {\WM} algorithm, using open-source software. Tasks: - -\begin{itemize} - \item Evaluate existing line simplification algorithms. - \item Identify main river generalization problems, using classical line - simplification algorithms. - \item Define the method of the {\WM} technical implementation. - \item Realize {\WM} algorithm technically, explaining the geometric - transformations in detail. - \item Apply the created algorithm for different datasets and compare - the results with national datasets. -\end{itemize} - -Scientific relevance of this work --- the simplification processes (steps) -described by the {\WM} algorithm --- are analyzed in detail, practically -implemented, and the implementation is described. That expands the knowledge of -cartographic theory about the generalization of natural objects' boundaries -after their natural defining properties. - -In the original {\WM} article introducing the algorithm, the steps are not -detailed in a way that can be put into practice for specific data; the steps are -specified in this work. Practically, this work makes it possible to use open-source software to perform cartographic line generalization. The developed -specialized cartographic line simplification algorithm can be applied by -cartographers to implement automatic data generalization solutions. Given the -open-source nature of this work, the algorithm implementation can be modified -freely. - -\section{Literature Review And Problematic} -\label{sec:literature-review-problematic} - -\subsection{Available Algorithms} - -This section reviews the classical line simplification algorithms, which, -besides being around for a long time, offer easily accessible implementations, -as well as more modern ones, which only theorize, but do not provide an -implementation. - -\subsubsection{{\DP}, {\VW} and Chaikin's} -\label{sec:dp-vwchaikin} - -{\DP}\cite{douglas1973algorithms} and {\VW}\cite{visvalingam1993line} are -"classical" line simplification computer graphics algorithms. They are -relatively simple to implement and require few runtime resources. Both of them -accept a single parameter based on desired scale of the map, which makes them -straightforward to adjust for different scales. - -Both algorithms are available in PostGIS, a free-software GIS suite: -\begin{itemize} - \item {\DP} via - \href{https://postgis.net/docs/ST_Simplify.html}{PostGIS \textsc{st\_simplify}}. - - \item {\VW} via - \href{https://postgis.net/docs/ST_SimplifyVW.html}{PostGIS - \textsc{st\_simplifyvw}}. -\end{itemize} - -It may be worthwhile to post-process those through Chaikin's line smoothing -algorithm\cite{chaikin1974algorithm} via -\href{https://postgis.net/docs/ST_ChaikinSmoothing.html}{PostGIS -\textsc{st\_chaikinsmoothing}}. - -In generalization examples, we will use two rivers: Šalčia and Visinčia. -These rivers were chosen because they have both large and small bends, and -thus are convenient to analyze for both small- and large-scale generalization. -Figure~\onpage{fig:salvis-25} illustrates the original two rivers without any -simplification. - -\begin{figure}[ht] - \centering - \includegraphics[width=\textwidth]{salvis-25k} - \caption{Example rivers for visual tests (1:{\numprint{25000}}).} - \label{fig:salvis-25} -\end{figure} - -\begin{figure}[ht] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-2x50k} - \caption{Example scaled 1:\numprint{50000}.} - \label{fig:salvis-2x50k} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \centering - \includegraphics[width=.2\textwidth]{salvis-250k-10x} - \caption{Example scaled 1:\numprint{250000}.} - \end{subfigure} - \caption{Down-scaled original river.} - \label{fig:salvis-50-250} -\end{figure} - -Same rivers, unprocessed but in higher scales (1:\numprint{50000} and -1:\numprint{250000}), are depicted in Figure~\ref{fig:salvis-50-250}. Some -river features are so compact that a reasonably thin line depicting the river -is touching itself, creating a thicker line. We can assume that some -simplification for scale 1:\numprint{50000} and especially for -1:\numprint{250000} is worthwhile. - -\begin{figure}[ht] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-dp64-2x50k} - \caption{Using {\DP}.} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-vw64-2x50k} - \caption{Using {\VW}.} - \end{subfigure} - \caption{Simplified using classical algorithms (1:\numprint{50000}).} - \label{fig:salvis-generalized-1x50k} -\end{figure} - -Figure~\ref{fig:salvis-generalized-1x50k} illustrates the same river bend, but -simplified using {\DP} and {\VW} algorithms. The resulting lines are jagged, -and thus the resulting line looks unlike a real river. To smoothen the jaggedness, -traditionally, Chaikin's\cite{chaikin1974algorithm} is applied after -generalization, illustrated in Figure~\ref{fig:salvis-generalized-chaikin-1x50k}. - -\begin{figure}[ht!] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-dpchaikin64-2x50k} - \caption{{\DP} and Chaikin's.} - \label{fig:salvis-dpchaikin64-2x50k} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-vwchaikin64-2x50k} - \caption{{\VW} and Chaikin's.} - \label{fig:salvis-vwchaikin64-2x50k} - \end{subfigure} - \caption{Simplified and smoothened river (1:\numprint{50000}).} - \label{fig:salvis-generalized-chaikin-1x50k} -\end{figure} - -\begin{figure}[ht!] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-overlaid-dpchaikin64-2x50k} - - \caption{Original (fig.~\ref{fig:salvis-2x50k}) and simplified - (fig.~\ref{fig:salvis-dpchaikin64-2x50k}).} - - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-overlaid-vwchaikin64-2x50k} - - \caption{Original (fig.~\ref{fig:salvis-2x50k}) and simplified - (fig.~\ref{fig:salvis-vwchaikin64-2x50k}.)} - - \end{subfigure} - \caption{Zoomed-in simplified and smoothened river and original.} - \label{fig:salvis-overlaid-generalized-chaikin-1x50k} -\end{figure} - -\begin{figure}[b] - \centering - \includegraphics[width=\textwidth]{amalgamate1} - \caption{Narrow bends amalgamating into thick unintelligible blobs.} - \label{fig:pixel-amalgamation} -\end{figure} - -The resulting simplified and smoothened example -(Figure~\onpage{fig:salvis-generalized-chaikin-1x50k}) yields a more -aesthetically pleasing result; however, it obscures natural river features. - -Given the absence of rocks, the only natural features that influence the river -direction are topographic: - -\begin{itemize} - \item Relatively straight river (completely straight or with small-angled - bends over a relatively long distance) implies greater slope, more - water, and/or faster flow. - - \item Bendy river, on the contrary, implies slower flow, slighter slope, - and/or less water. - -\end{itemize} -Both {\VW} and {\DP} have a tendency to remove the small bends altogether, -removing a valuable characterization of the river. - -Sometimes low-water rivers in slender slopes have many bends next to each -other. In low resolutions (either in small-DPI screens or paper, or when the -river is sufficiently zoomed out, or both), the small bends will amalgamate to -a unintelligible blob. Figure~\ref{fig:pixel-amalgamation} illustrates a -real-world example where a bendy river, normally 1 or 2 pixels wide, creates a -wide area, of which the shapes of the bend become unintelligible. In this -example, classical algorithms would remove these bends altogether. A -cartographer would retain a few of those distinctive bends, but would increase -the distance between the bends, remove some of the bends, or both. - -% TODO: figues shouldn't split the sentence. - -For the reasons discussed in this section, the "classical" {\DP} and {\VW} are -not well-suited for natural river generalization, and a more robust line -generalization algorithm is worthwhile to look for. - -\clearpage - -\subsubsection{Modern Approaches} - -Due to their simplicity and ubiquity, {\DP} and {\VW} have been established as -go-to algorithms for line generalization. During recent years, alternatives -have emerged. These modern replacements fall into roughly two categories: - -\begin{itemize} - - \item Cartographic knowledge was encoded to an algorithm (bottom-up - approach). One among these are \titlecite{wang1998line}, also known - as {\WM}'s algorithm. - - \item Mathematical shape transformation which yields a more cartographic - result. E.g., \titlecite{jiang2003line}, - \titlecite{dyken2009simultaneous}, \titlecite{mustafa2006dynamic}, - \titlecite{nollenburg2008morphing}, \titlecite{devangleserrorbends}. - -\end{itemize} - -Authors of most of the aforementioned articles have implemented the -generalization algorithm, at least to generate the illustrations in the -articles. However, code is not available for evaluation with a desired dataset, much less for use as a basis for creating new maps. To the author's knowledge, -{\WM}\cite{wang1998line} is available in a commercial product, but requires a -purchase of the commercial product suite, without a way to license the -standalone algorithm. - -{\WM} algorithm was created by encoding professional cartographers' knowledge -into a computer algorithm. It has a few main properties which make it -especially suitable for generalization of natural linear features: - -\begin{figure}[h!] - \centering - \includegraphics[width=.8\textwidth]{wang125} - \caption{Figure 12.5 in \cite{wang1998line}: example of cartographic line - generalization.} - \label{fig:wang125} -\end{figure} - -\begin{itemize} - \item Small bends are not always removed, but either combined (e.g., - 3 bends into 2), exaggerated, or removed, depending on the neighboring - bends. - \item Long and gentle bends are not straightened, but kept as-is. -\end{itemize} - -As a result of these properties, {\WM} algorithm retains the defining -properties of the natural features: high-current rivers keep their appearance -as such, instead of becoming canals; low-stream bendy rivers retain their -frequent small bends. - -Figure~\ref{fig:wang125}, sub-figure labeled "proposed method" (from the -original \titlecite{wang1998line}) illustrates the {\WM} algorithm. - -\subsection{Problematic with Generalization of Rivers} - -This section introduces the reader to simplification and generalization, and -discusses two main problems with current-day automatic cartographic line -generalization: - -\begin{itemize} - \item Currently available line simplification algorithms were created - to simplify geometries, but do not encode cartographic knowledge. - - \item Existing cartographic line generalization algorithms are not freely - accessible. -\end{itemize} - -\subsubsection{Simplification versus Generalization} - -It is important to note the distinction between simplification, line -generalization, and cartographic generalization. - -Simplification reduces an object's detail in isolation, not taking the object's -natural properties or surrounding objects into account. For example, if a -river is simplified, it may have an approximate shape of the original river, -but lose some shapes that define it. For example: - -\begin{itemize} - - \item Low-water rivers in slender slopes have many small bends next to each - other. A non-cartographic line simplification may remove all of them, - thus losing an important river's characteristic feature: after such - simplification, it will be hard to tell that the original river was - low-water in a slender slope. - - \item Low-angle river bend river over a long distance differs significantly - from a completely straight canal. Non-cartographic line simplification - may replace that bend with a straight line, making the river more - similar to a canal than a river. - -\end{itemize} - -In other words, simplification processes the line, ignoring its geographic -features. It works well when the features are human-made (e.g., roads, -administrative boundaries, buildings). There is a number of freely available -non-cartographic line simplification algorithms, which this paper will review. - -Contrary to line simplification, cartographic generalization does not focus -into a single feature class (e.g., rivers), but the whole map. For example, -line simplification may change river bends in a way that bridges (and roads to -the bridges) become misplaced. While line simplification is limited to a single -feature class, cartographic generalization is not. Fully automatic cartographic -generalization is not yet a solved problem. % . - -Cartographic line generalization falls in between the two: it does more than -line simplification, and less than cartographic generalization. Cartographic -line generalization deals with a single feature class, takes into account its -geographic properties, but ignores other features. This paper examines {\WM}'s -\titlecite{wang1998line}, a cartographic line generalization algorithm. - -\subsubsection{Availability of Generalization Algorithms} - -Lack of robust openly available generalization algorithm implementations poses -a problem for map creation with free software: there is no high-quality -simplification algorithm to create down-scaled maps, so any cartographic work, -which uses line generalization as part of its processing, will be of sub-par -quality. We believe that the availability of high-quality open-source tools is an -important foundation for future cartographic experimentation and development, -thus it benefits the cartographic society as a whole. - -{\WM}'s commercial availability signals something about the value of the -algorithm: at least the authors of the commercial software suite deemed it -worthwhile to include it. However, not everyone has access to the commercial -software suite, access to funds to buy the commercial suite, or access to the -operating system required to run the commercial suite. PostGIS, in contrast, is -free itself, and runs on free platforms. Therefore, algorithm -implementations that run on PostGIS or other free platforms are useful to a -wider cartographic society than proprietary ones. - -\subsubsection{Unfitness of Line Simplification Algorithms} - -Section~\ref{sec:dp-vwchaikin} illustrates the current gaps with line -simplification algorithms for real rivers. To sum up, we highlight the -following cartographic problems from our examples: - -\begin{description} - - \item[Long bends] should remain as long bends, instead of becoming fully - straight lines. - - \item[Many small bends] should not be removed. To retain a river's character, - the algorithm should retain some small bends, and, when they are too - small to be visible, they should be combined or exaggerated. - -\end{description} - -We are limiting the problem to cartographic line generalization. That is, full -cartographic generalization, which takes topology and other feature classes -into account, is out of scope. - -Figure~\onpage{fig:wang125} illustrates {\WM} algorithm from their original -paper. Note how the long bends retain curvy, and how some small bends get -exaggerated. - -\section{Methodology} -\label{sec:methodology} - -The original {\WM}'s algorithm \cite{wang1998line} leaves something to be -desired for a practical implementation: it is not straightforward to implement -the algorithm from the paper alone. - -Explanations in this document are meant to expand, rather than substitute, the -original description in {\WM}. Therefore, familiarity with the original paper is -assumed, and, for some sections, having the original close-by is necessary to -meaningfully follow this document. - -This paper describes {\WM} in detail that is more useful for anyone who wishes -to follow the algorithm implementation more closely: each section is expanded -with additional commentary, and illustrations added for non-obvious steps. Corner -cases are discussed, too. - -\subsection{Main Geometry Elements Used by Algorithm} -\label{sec:vocab} - -This section defines and explains the geometry elements that are used -throughout this paper and the implementation. Assume Euclidean geometry -throughout this document, unless noted otherwise. - - -\begin{description} - - \item[\normalfont\textsc{vertex}] is a point on a plane, can be expressed - by a pair of $(x,y)$ coordinates. - - \item[\normalfont\textsc{line segment}] or \textsc{segment} joins two - vertices by a straight line. A segment can be expressed by two - coordinate pairs: $(x_1, y_1)$ and $(x_2, y_2)$. Line segment and - segment are used interchangeably. - - \item[\normalfont\textsc{line}] or \textsc{linestring} represents a single - linear feature. For example, a river or a coastline. - - Geometrically, a line is a series of connected line segments, or, - equivalently, a series of connected vertices. Each vertex connects to - two other vertices, with the exception of the vertices at either ends of the line: - these two connect to a single other vertex. - - \item[\normalfont\textsc{multiline}] or \textsc{multilinestring} is a - collection of linear features. Throughout this implementation, this is - used rarely (normally, a river is a single line) but can be valid - when, for example, a river has an island. - - \item[\normalfont\textsc{bend}] is a subset of a line that humans perceive - as a curve. The geometric definition is complex and is discussed in - section~\ref{sec:definition-of-a-bend}. - - \item[\normalfont\textsc{baseline}] is a line between the bend's first and last - vertices. - - \item[\normalfont\textsc{sum of inner angles}] is a measure of how "curved" - the bend is. Assume that first and last bend vertices are vectors. Then sum - of inner angles will be the angular difference of those two vectors. - - \item[\normalfont\textsc{algorithmic complexity}] measured in \textsc{big o - notation}, is a relative measure that helps explain how - long\footnote{the upper bound, i.e., the worst case.} the - algorithm will run depending on its input. It is widely used in computing - science when discussing the efficiency of a given algorithm. - - For example, given $n$ objects and time complexity of $O(log(n))$, the - time it takes to execute the algorithm is logarithmic to $n$. - Conversely, if complexity is $O(n^2)$, then the time it takes to - execute the algorithm grows quadratically with input. Importantly, if - the input size doubles, the time it takes to run the algorithm - quadruples. - - \textsc{big o notation} was first suggested by - Bachmann\cite{bachmann1894analytische} and Landau\cite{landau1911} in - late \textsc{xix} century, and clarified and popularized for computing - science by Donald Knuth\cite{knuth1976big} in the 1970s. - -\end{description} - -\clearpage - -\subsection{Algorithm Implementation Process} -\label{sec:algorithm-implementation-process} - -\tikzset{ - startstop/.style={trapezium,text centered,minimum height=2em, - trapezium left angle=70,trapezium right angle=110,draw=black,fill=red!20}, - proc/.style={rectangle,minimum height=2em,text centered,draw=black, - fill=orange!20}, - decision/.style={diamond,minimum height=2em,text centered,aspect=3, - draw=black,fill=green!20}, - arrow/.style={thick,->,>=stealth}, -} - -\begin{figure}[!ht] - \centering - \begin{tikzpicture}[node distance=1.5cm,auto] - \node (start) [startstop] {Read \textsc{linestring}}; - \node (detect) [proc,below of=start] {Detect bends}; - \node (inflections) [proc,below of=detect] {Fix gentle inflections}; - \node (selfcrossing) [proc,below of=inflections] {Eliminate self-crossing}; - \node (mutated1) [decision,below of=selfcrossing] {Mutated?}; - \node (bendattrs) [proc,below of=mutated1] {Compute bend attributes}; - \node (exaggeration) [proc,below of=bendattrs] {Exaggeration}; - \node (mutated2) [decision,below of=exaggeration] {Mutated?}; - \node (elimination) [proc,below of=mutated2] {Elimination}; - \node (mutated3) [decision,below of=elimination] {Mutated?}; - \node (stop) [startstop,below of=mutated3] {Stop}; - - \coordinate [right of=mutated1,node distance=5cm] (mutated1y) {}; - \coordinate [right of=mutated2,node distance=5cm] (mutated2y) {}; - \coordinate [right of=mutated3,node distance=5cm] (mutated3y) {}; - - \draw [arrow] (start) -- (detect); - \draw [arrow] (detect) -- (inflections); - \draw [arrow] (inflections) -- (selfcrossing); - \draw [arrow] (selfcrossing) -- (mutated1); - \draw [arrow] (mutated1) -| node [near start] {Yes} (mutated1y) |- (detect); - \draw [arrow] (mutated1) -- node[anchor=west] {No} (bendattrs); - \draw [arrow] (bendattrs) -- (exaggeration); - \draw [arrow] (exaggeration) -- (mutated2); - \draw [arrow] (mutated2) -| node [near start] {Yes} (mutated2y) |- (detect); - \draw [arrow] (mutated2) -- node[anchor=west] {No} (elimination); - \draw [arrow] (mutated3) -| node [near start] {Yes} (mutated3y) |- (detect); - \draw [arrow] (mutated3) -- node[anchor=west] {No} (stop); - \draw [arrow] (elimination) -- (mutated3); - \end{tikzpicture} - \caption{Flow chart of the implementation workflow.} - \label{fig:flow-chart} -\end{figure} - -Figure~\ref{fig:flow-chart} visualizes the algorithm steps for each line. -\textsc{multilinestring} features are split to \textsc{linestring} features and -executed in order. - -Judging from {\WM} prototype flow chart (depicted in figure 11 of the original -paper), their approach is iterative for the line: it will process the line in -sequence, doing all steps, before moving on to the next step. We will call this -approach "streaming", because it does not require to have the full line to -process it. - -We have taken a different approach: process each step fully for the line, -before moving to the next step. This way provides the following advantages: - -\begin{itemize} - - \item For \textsc{eliminate self-crossing} stage, when it finds a bend with - the right sum of inflection angles, it checks the whole line for - self-crossings. This is impossible with streaming because it requires - having the full line in memory. It could be optimized by, for example, - looking for a fixed number of neighboring bends (say, 10), but that - would complicate the implementation. - - \item \textsc{fix gentle inflections} is iterating the same line twice from - opposite directions. That could be re-written to streaming fashion, but - it complicates the implementation, too. - -\end{itemize} -On the other hand, comparing to the {\WM} prototype flow chart, our -implementation uses more memory (because it needs to have the full line before -processing), and some steps are unnecessarily repeated, like re-computing the -bend's attributes during repeated iterations. - -\subsection{Technical Implementation} -\label{sec:technical-implementation} - -Technical algorithm realization was created in \titlecite{postgis311}. PostGIS -is a PostgreSQL extension for working with spatial data. - -PostgreSQL is an open-source relational database, widely used in industry and -academia. PostgreSQL can be interfaced from nearly any programming language; -therefore, solutions written in PostgreSQL (and their extensions) are usable in -many environments. On top of that, PostGIS implements a rich set of -functions\cite{postgisref} for working with geometric and geographic objects. - -Due to its wide applicability and rich library of spatial functions, PostGIS is -the implementation language of the {\WM} algorithm. The implementation exposes -the entrypoint function \textsc{st\_simplifywm}, in -listing~\ref{lst:st-simplifywm}. - -\begin{listing} -\begin{minted}[fontsize=\small]{sql} -create function ST_SimplifyWM( - geom geometry, - dhalfcircle float, - intersect_patience integer default 10, - dbgname text default null -) returns geometry - \end{minted} - \caption{Function \textsc{st\_simplifywm}.} - \label{lst:st-simplifywm} -\end{listing} - -This function accepts the following parameters: -\begin{description} - - \item[\normalfont\textsc{geom}] is the input geometry. Either - \textsc{linestring} or \textsc{multilinestring}. - - \item[\normalfont\textsc{dhalfcircle}] is the diameter of the half-circle. - Explained in section~\ref{sec:bend-scaling-and-dimensions}. - - \item[\normalfont\textsc{intersect\_patience}] is an optional parameter to - exaggeration operator, explained in - section~\ref{sec:exaggeration-operator}. - - \item[\normalfont\textsc{dbgname}] is an optional human-readable name of - the figure. Explained in section~\ref{sec:debugging}. - -\end{description} - -The function \textsc{st\_simplifywm} calls into helper functions, which detect, -transform, or remove bends. These helper functions are also defined in the -implementation and are part of the algorithm technical realization. All -supporting functions use spatial manipulation functions provided by PostGIS. - -\subsection{Automated Tests} -\label{sec:automated-tests} - -As part of the algorithm realization, an automated test suite has been -developed. Shapes to test each function have been hand-crafted, and expected -results have been manually calculated. The test suite executes parts of the -algorithm against a predefined set of geometries, and asserts that the output -matches the resulting hand-calculated geometries. - -The full set of test geometries is visualized in Figure~\ref{fig:test-figures}. - -\begin{figure}[ht] - \centering - \includegraphics[width=\textwidth]{test-figures} - \caption{Geometries for automated test cases.} - \label{fig:test-figures} -\end{figure} - -Test suite can be executed with a single command and completes in about a -second. Having an easily accessible test suite boosts confidence that no -unexpected bugs have snug in while modifying the algorithm. - -We will explain two instances when automated tests were very useful during -the implementation: -\begin{itemize} - - \item Created a function \textsc{wm\_exaggeration}, which exaggerates bends - following the rules. It worked well over simple geometries but, due to - a subtle bug, created a self-crossing bend in Visinčia. The offending - bend was copied to the automated test suite, which helped fix the bug. - Now the test suite contains the same bend (a hook-like bend on the - right-hand side of Figure~\ref{fig:test-figures}) and code to verify - that it was correctly exaggerated. - - \item During algorithm development, automated tests run about once a - minute. They quickly find logical and syntax errors. In contrast, - running the algorithm with real rivers takes a few minutes, which - increases the feedback loop, and takes longer to fix the "simple" - errors. - -\end{itemize} - -Whenever we find and fix a bug, we aim to create an automated test case for it, -so the same bug is not re-introduced by whoever works next on the same piece of -code. - -Besides testing for specific cases, an automated test suite ensures future -stability and longevity of the implementation itself: when new contributors -start changing code, they have higher assurance they have not broken -an already-working code. - -\subsection{Reproducibility} -\label{sec:reproducing-the-paper} - -It is widely believed that the ability to reproduce the results of a published -study is important to the scientific community. In practice, however, it is -often hard or impossible: research methodologies, as well as algorithms -themselves, are explained in prose, which, due to the nature of the non-machine -language, lends itself to inexact interpretations. - -This article, besides explaining the algorithm in prose, includes the program -of the algorithm in a way that can be executed on reader's workstation. On top -of it, all the illustrations in this paper are generated using that algorithm -from a predefined list of test geometries (see -section~\ref{sec:automated-tests}). - -This article and accompanying code are accessible on GitHub as of 2021-05-21 -\cite{wmsql}. - -Instructions how to re-generate all the visualizations are in -appendix~\ref{sec:code-regenerate}. The visualization code serves as a good -example reference for anyone willing to start using the algorithm. - -\section{Algorithm Implementation} - -As alluded in section~\ref{sec:introduction}, {\WM} paper skims over -certain details which are important to implement the algorithm. This section -goes through each algorithm stage, illustrating the intermediate steps and -explaining the author's desiderata for a more detailed description. - -Illustrations of the following sections are extracted from the automated test -cases which were written during the algorithm implementation (as discussed in -section~\ref{sec:automated-tests}). - -\subsection{Debugging} -\label{sec:debugging} - -This implementation includes debugging facilities in a form of a table -\textsc{wm\_debug}. The table's schema is written in -listing~\ref{lst:wm-debug-sql}. - -When debug mode is active, implementation steps will store their results, which -can be useful to manually inspect the results of intermediate actions. Besides -manual inspection, most of the figure illustrations in this article are -visualized from the \textsc{wm\_debug} table. Debugging mode can be activated -by passing a non-empty \textsc{dbgname} string to the function -\textsc{st\_simplifywm} (this function was described in -section~\ref{sec:technical-implementation}). By convention, \textsc{dbgname} is -the name of the geometry that is being simplified, e.g., \textsc{šalčia}. The -purpose of each column in \textsc{wm\_debug} is described below: - -\begin{description} - - \item[\normalfont\textsc{id}] is a unique identifier for each feature. - Generated automatically by PostgreSQL. Useful when it is necessary to - copy one or more features to a separate table for unit tests, as - described in section~\ref{sec:automated-tests}. - - \item[\normalfont\textsc{stage}] is the stage of the algorithm. As of - writing, there are a few: - \begin{description} - \item[\normalfont\textsc{afigures}] at the beginning of the loop. - \item[\normalfont\textsc{bbends}] after bends are detected. - - \item[\normalfont\textsc{cinflections}] after gentle inflections - are fixed. - - \item[\normalfont\textsc{dcrossings}] after self-crossings are - eliminated. - - \item[\normalfont\textsc{ebendattrs}] after bend attributes are - calculated. - - \item[\normalfont\textsc{gexaggeration}] after bends have been - exaggerated. - - \item[\normalfont\textsc{helimination}] after bends have been - eliminated. - - \end{description} - - Some of these have sub-stages which are encoded by a dash and a - sub-stage name, e.g., \textsc{bbends-polygon} creates polygon - geometries after polygons have been detected; this particular example - is used to generate colored polygons in - Figure~\ref{fig:fig8-definition-of-a-bend}. - - \item[\normalfont\textsc{name}] is the name of the geometry, which comes from - parameter~\textsc{dbgname}. - - \item[\normalfont\textsc{gen}] is the top-level iteration number. In other - words, the number of times the execution flow passes through - \textsc{detect bends} phase as depicted in - Figure~\onpage{fig:flow-chart}. - - \item[\normalfont\textsc{nbend}] is the bend's index in its \textsc{line}. - - \item[\normalfont\textsc{way}] is the geometry column. - - \item[\normalfont\textsc{props}] is a free-form JSON object to store - miscellaneous values. For example, \textsc{ebendattrs} phase stores a - boolean property \textsc{isolated}, which signifies whether the bend is - isolated or not (explained in section~\ref{sec:isolated-bend}). - -\end{description} - -When debug mode is turned off (that is, \textsc{dbgname} is left unspecified), -\textsc{wm\_debug} is empty and the algorithm runs slightly faster. - -\begin{listing}[h!] - \begin{minted}[fontsize=\small]{sql} -drop table if exists wm_debug; -create table wm_debug( - id serial, - stage text not null, - name text not null, - gen bigint not null, - nbend bigint, - way geometry, - props jsonb -); - \end{minted} - \caption{\textsc{wm\_debug} table definition} - \label{lst:wm-debug-sql} -\end{listing} - - -\subsection{Merging Pieces of a River into One} - -Example river geometries were sourced from OpenStreetMap\cite{openstreetmap} -and NŽT\cite{nzt}. Rivers in both data sources are stored in shorter line -segments, and multiple segments (usually hundreds or thousands for significant -rivers) define one full river. While it is convenient to store and edit, these -segments are not explicitly related to each other. This poses a problem for -simplification algorithms which manipulate on full linear features at a time: -full river geometries, but not their parts. - -Since these rivers do not have an explicit relationship to connect them -together, they were connected using heuristics: if two line segments share a -name and are within 500 meters from each other, then they form a single river. -For all line simplification algorithms, all rivers need to be combined and -this way proved to be reasonably effective. Source code for this operation can -be found in listing~\onpage{lst:aggregate-rivers.sql}. - -\subsection{Bend Scaling And Dimensions} -\label{sec:bend-scaling-and-dimensions} - -{\WM} accepts a single input parameter: the diameter of a half-circle. If the -bend's adjusted size (explained in detail in section~\ref{sec:shape-of-a-bend}) -is greater than the area of the half-circle, then the bend will be left -untouched. If the bend's adjusted size is smaller than the area of the provided -half-circle, the bend will be simplified: either exaggerated, combined, or -eliminated. - -The extent of line simplification, as well as the half-circle's diameter, -depends on the desired target scale. Simplification should be more aggressive -for smaller target scales and less aggressive for larger scales. This section -goes through the process of finding the correct variable to {\WM} algorithm. -What is the minimal, but still eligible, figure that should be displayed on -the map? - -According to \titlecite{cartoucheMinimalDimensions}, the map is typically held -at a distance of 30 cm. Recommended minimum symbol size, given viewing distance -of 45 cm (1.5 feet), is 1.5 mm, as analyzed in \titlecite{mappingunits}. - -In our case, our target is line bend, rather than a symbol. Assume 1.5 mm is a -diameter of the bend. A semi-circle of 1.5 mm diameter is depicted in -Figure~\ref{fig:half-circle}. A bend of this size or larger, when adjusted to -scale, will not be simplified. - -\begin{figure}[ht] - \centering - \begin{tikzpicture}[x=1mm,y=1mm] - \draw[] (-10, 0) -- (-.75,0) arc (225:-45:.75) -- (10, 0); - \end{tikzpicture} - \caption{Smallest feature that will be not simplified (to scale).} - \label{fig:half-circle} -\end{figure} - -\begin{table}[h!] - \centering - \begin{tabular}{ c D{.}{.}{1} } - Scale & \multicolumn{1}{c}{$D(m)$} \\ \hline - 1:\numprint{10000} & 15 \\ - 1:\numprint{15000} & 22.5 \\ - 1:\numprint{25000} & 37.5 \\ - 1:\numprint{50000} & 75 \\ - 1:\numprint{250000} & 220 \\ - \end{tabular} - \caption{{\WM} half-circle diameter $D$ for popular scales.} - \label{table:scale-halfcirlce-diameter} -\end{table} - -{\WM} algorithm does not have a notion of scale, but it does have a notion of -distance: it accepts a single parameter $D$, the half-circle's diameter. -Assuming measurement units in projected coordinate system are meters (for -example, \titlecite{epsg3857}), some popular scales are highlighted in -table~\ref{table:scale-halfcirlce-diameter}. - -\subsection{Definition of a Bend} -\label{sec:definition-of-a-bend} - -The original article describes a bend as follows: - -\begin{displaycquote}{wang1998line} - A bend can be defined as that part of a line which contains a number of - subsequent vertices, with the inflection angles on all vertices included in - the bend being either positive or negative and the inflection of the bend's - two end vertices being in opposite signs. -\end{displaycquote} - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{fig8-definition-of-a-bend} - - \caption{Similar to figure 8 in \cite{wang1998line}: detected bends are - highlighted.} - - \label{fig:fig8-definition-of-a-bend} -\end{figure} - -Here are some non-obvious characteristics that are necessary when writing code -to detect the bends: - -\begin{itemize} - \item End segments of each line should also belong to bends. That way, all - segments belong to 1 or 2 bends. - - \item First and last segments of each bend (except for the two end-line - segments) are also the first vertex of the next bend. -\end{itemize} - -\subsection{Gentle Inflection at the End of a Bend} - -\begin{displaycquote}{wang1998line} - But if the inflection that marks the end of a bend is quite small, people - would not recognize this as the bend point of a bend -\end{displaycquote} - -Figure~\ref{fig:fig5-gentle-inflection} visualizes the original paper's figure 5, -when a single vertex is moved outwards the end of the bend. - -\begin{figure}[ht] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{fig5-gentle-inflection-before} - \caption{Before applying the inflection rule.} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{fig5-gentle-inflection-after} - \caption{After applying the inflection rule.} - \end{subfigure} - \caption{Figure 5 in \cite{wang1998line}: gentle inflections at the ends of - the bend.} - \label{fig:fig5-gentle-inflection} -\end{figure} - -\begin{figure}[h!] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{inflection-1-gentle-inflection-before} - \caption{Before applying the inflection rule.} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{inflection-1-gentle-inflection-after} - \caption{After applying the inflection rule.} - \end{subfigure} - \caption{Gentle inflection at the end of the bend with multiple vertices.} - \label{fig:inflection-1-gentle-inflection} -\end{figure} - -The illustration for this section was clear but insufficient: it does not -specify how many vertices should be included when calculating the end-of-bend -inflection. The iterative approach was chosen: as long as the angle is -"right" and the baseline is becoming shorter, the algorithm should keep -re-assigning vertices to different bends. There is no upper bound -on the number of iterations. - -To prove that the algorithm implementation is correct for multiple vertices, -additional example was created and illustrated in -Figure~\ref{fig:inflection-1-gentle-inflection}: the rule re-assigns two -vertices to the next bend. - -Note that to find and fix the gentle bends' inflections, the algorithm should -run twice, both ways. Otherwise, if it is executed only one way, the steps will -fail to match some bends that should be adjusted. Current implementation works -as follows: - -\begin{enumerate} - \item Run the algorithm from the beginning to the end. - \item \label{rev1} Reverse the line and each bend. - \item Run the algorithm again. - \item \label{rev2} Reverse the line and each bend. - \item Return result. -\end{enumerate} - -Reversing the line and its bends is straightforward to implement but costly: -the two reversal steps cost additional time and memory. The algorithm could be -made more optimal with a similar version of the algorithm, but the one which -goes backwards. In this case, steps \ref{rev1} and \ref{rev2} could be spared, -that way saving memory and computation time. - -The "quite small angle" was arbitrarily chosen to \smallAngle. - -\subsection{Self-Line Crossing When Cutting a Bend} - -When a bend's baseline crosses another bend, it is called self-crossing. -Self-crossing is undesirable for the upcoming bend manipulation operators; therefore, -should be removed. There are a few rules on when and how they should be removed ---- this section explains them in higher detail, discusses their time -complexity and applied optimizations. Figure~\ref{fig:fig6-selfcrossing} is -copied from the original article. - -\begin{figure}[ht] - \centering - \includegraphics[width=.5\textwidth]{fig6-selfcrossing} - \caption{Originally figure 6: the bend's baseline (orange) is crossing a neighboring bend.} - \label{fig:fig6-selfcrossing} -\end{figure} - -\begin{figure}[ht] - \centering - \includegraphics[width=.5\textwidth]{selfcrossing-1} - \caption{The bend's baseline (orange) is crossing a non-neighboring bend.} - \label{fig:selfcrossing-1-non-neighbor} -\end{figure} - -% TODO: figure should not split the text. - -Looking at the {\WM} paper alone, it may seem like self-crossing may happen -only with the neighboring bend. This would mean an efficient $O(n)$ -implementation\footnote{where $n$ is the number of bends in a line. See -explanation of \textsc{algorithmic complexity} in section~\ref{sec:vocab}.}. -However, as one can see in Figure~\ref{fig:selfcrossing-1-non-neighbor}, it may -not be the case: any other bend in the line may be crossing it. - -If one translates the requirements to code in a straightforward way, it would -be quite computationally expensive: naively implemented, complexity of checking -every bend with every bend is $O(n^2)$. In other words, the time it takes to -run the algorithm grows quadratically with the number of vertices. - -It is possible to optimize this step and skip checking a large number of bends. -Only bends, the inner angles' sum of which is larger than $180^\circ$, can ever -self-cross. That way, only a fraction of bends need to be checked. The -worst-case complexity is still $O(n^2)$, when all bends' inner angles are -larger than $180^\circ$. Having this optimization, the algorithmic complexity -(as a result, the time it takes to execute the algorithm) drops by the -fraction of bends, the inner angles' sum of which is smaller than $180^\circ$. - -\subsection{Attributes of a Single Bend} - -\textsc{compactness index} is "the ratio of the area of the polygon over the -circle whose circumference length is the same as the length of the -circumference of the polygon" \cite{wang1998line}. Given a bend, its -compactness index is calculated as follows: - -\begin{enumerate} - - \item Construct a polygon by joining first and last vertices of the bend. - - \item Calculate the area of the polygon $A_{p}$. - - \item Calculate perimeter $P$ of the polygon. The same value is the - circumference of the circle: $C = P$. - - \item Given the circle's circumference $C$, the circle's area $A_{c}$ is: - - \[ - A_c = \frac{C^2}{4\pi} - \] - - \item Compactness index $c$ is the area of the polygon $A_p$ divided by the - area of the circle $A_c$: - - \[ - c = \frac{A_p}{A_c} = - \frac{A_p}{ \frac{C^2}{4\pi} } = - \frac{4\pi A_p}{C^2} - \] - -\end{enumerate} - -Once this operation is complete, each bend will have a list of properties -which will be used by other modifying operators. - -\subsection{Shape of a Bend} -\label{sec:shape-of-a-bend} - -This section introduces \textsc{adjusted size} $A_{adj}$ which trivially -derives from \textsc{compactness index} $c$ and "polygonized" bend's area $A_{p}$: - -\[ - A_{adj} = \frac{0.75 A_{p}}{c} -\] - -Adjusted size is necessary later to compare bends with each other, or to decide if -the bend is within the simplification threshold. - -Sometimes, when working with {\WM}, it is useful to convert between -half-circle's diameter $D$ and adjusted size $A_{adj}$. These easily derive -from circle's area formula $A = 2\pi \frac{D}{2}^2$: - -\[ - D = 2\sqrt{\frac{2 A_{adj}}{\pi}} -\] - -In reverse, adjusted size $A_{adj}$ from half-circle's diameter: - -\[ - A_{adj} = \frac{\pi D^2}{8} -\] - -\subsection{Isolated Bend} -\label{sec:isolated-bend} - -Bend itself and its "isolation" can be described by \textsc{average curvature}, -which is \textcquote{wang1998line}{geometrically defined as the ratio of -inflection over the length of a curve.} - -Two conditions must be followed to claim that a bend is isolated: - -\begin{enumerate} - \item \textsc{average curvature} of neighboring bends should be larger - than the "candidate" bend's curvature. The article did not offer a - value; this implementation arbitrarily chose $\isolationThreshold$. - - \item Bends on both sides of the "candidate" bend should be longer than a - certain value. This implementation does not (yet) define such a - constraint and will only follow the average curvature constraint above. - -\end{enumerate} - -We believe unclear criteria for \textsc{isolated bend} is one of the main -causes for jagged lines in section~\ref{sec:results}, and is a suggested -further area of research in section~\ref{sec:future-suggestions}. - -\subsection{The Context of a Bend: Isolated And Similar Bends} - -To find out whether two bends are similar, they are compared by 3 components: - -\begin{enumerate} - \item \textsc{adjusted size} $A_{adj}$. - \item \textsc{compactness index} $c$. - \item \textsc{baseline length} $l$. -\end{enumerate} - -Components 1, 2 and 3 represent a point in a 3-dimensional space, and Euclidean -distance $d(p,q)$ between those is calculated to differentiate bends $p$ and -$q$: - -\[ - d(p,q) = \sqrt{(A_{adj(p)}-A_{adj(q)})^2 + - (c_p-c_q)^2 + - (l_p-l_q)^2} -\] - -The smaller the distance $d$, the more similar the bends are. - -\clearpage -\subsection{Elimination Operator} - -Figure~\ref{fig:elimination-through-iterations} illustrates steps of figure 8 -from the original paper. There is not much to add to the original description -beyond repeating the elimination steps in an illustrated example. - -\begin{figure}[ht] - \centering - \begin{subfigure}[b]{\textwidth} - \includegraphics[width=\textwidth]{fig8-elimination-gen1} - \caption{Original} - \end{subfigure} - \begin{subfigure}[b]{\textwidth} - \includegraphics[width=\textwidth]{fig8-elimination-gen2} - \caption{Iteration 1} - \end{subfigure} - \begin{subfigure}[b]{\textwidth} - \includegraphics[width=\textwidth]{fig8-elimination-gen3} - \caption{Iteration 2 (result)} - \end{subfigure} - \caption{Originally figure 8: the bend elimination through iterations.} - \label{fig:elimination-through-iterations} -\end{figure} - -\subsection{Combination Operator} -\label{sec:combination-operator} - -Combination operator was not implemented in this version. - -\subsection{Exaggeration Operator} -\label{sec:exaggeration-operator} - -Exaggeration operator finds bends, of which \textsc{adjusted size} is smaller -than the \textsc{diameter of the half-circle}. Once a target bend is found, it -will be exaggerated in increments until either becomes true: - -\begin{itemize} - \item \textsc{adjusted size} of the exaggerated bend is larger than the area of - the half-circle. - - \item The exaggerated bend starts intersecting with a neighboring bend. - Then exaggeration aborts, and the bend remains as if it were one step - before the intersection. - -\end{itemize} - -Exaggeration operator uses a hardcoded parameter \textsc{exaggeration step} $s -\in (1,2]$. It was arbitrarily picked to {\exaggerationEnthusiasm} for this -implementation. A single exaggeration increment is done as follows: - -\begin{enumerate} - \item Find a candidate bend. - \item Find the bend's baseline. - \item Find \textsc{midpoint}, the center of the bend's baseline. - - \item Find \textsc{midbend}, the center of the bend. Distance from one - baseline vertex to \textsc{midbend} should be the same as from - \textsc{midbend} to the other baseline vertex. - - \item Mark each bend's vertex with a number between $[1,s]$. The number is - derived with elements linearly between the start vertex and - \textsc{midbend}, with values somewhat proportional to the azimuth - between these lines: - - \begin{itemize} - \item \textsc{midbend} and the point. - \item \textsc{midpoint} and the point. - \end{itemize} - - The other half of the bend, from \textsc{midbend} to the final vertex, - is linearly interpolated between $[s,1]$, using the same rules as for - the first half. - - The first version of the algorithm used simple linear interpolation - based on the point's position in the line. The current version applies - a few coefficients, which were derived empirically, by observing the - resulting bend. - - \item Each point (except the beginning and end vertices of the bend) will - be placed farther away from the baseline. The length of misplacement is - the marked value in the previous step. - -\end{enumerate} - -\begin{figure}[ht] - \centering - \includegraphics[width=.5\textwidth]{isolated-1-exaggerated} - \caption{Example isolated exaggerated bend.} - \label{fig:isolated-1-exaggerated} -\end{figure} - -The technical implementation of the algorithm contains two implementations of -exaggeration operator: \textsc{wm\_exaggerate\_bend} is the original one. It -uses simple linear interpolation. It is fast, but simple. It tends to leave -jagged bends. \textsc{wm\_exaggerate\_bend2} is a more computationally -expensive function, which leaves better-looking exaggerated bends. - -Both functions are interchangeable and can be found in listing~\ref{lst:wm.sql}. -Figure~\ref{fig:isolated-1-exaggerated} illustrates an exaggerated bend using -\textsc{wm\_exaggerate\_bend2}. - -\section{Results} -\label{sec:results} - -This section visualizes the results, discusses robustness and issues of the -generalization, and suggests specific improvements. - -One of our goals is to compare the generalized lines with the official -generalized dataset\cite{nzt}. Therefore, we have selected the target scales -that the official sources offer, too: 1:\numprint{50000} and -1:\numprint{250000}. The \textsc{dhalfcircle} values for the subset are as -follow: - -\begin{table}[ht] - \centering - \begin{tabular}{ c D{.}{.}{1} } - Scale & \multicolumn{1}{c}{$D(m)$} \\ \hline - 1:\numprint{50000} & 75 \\ - 1:\numprint{250000} & 220 \\ - \end{tabular} -\end{table} - -Our generalized results are viewed from the following angles: -\begin{itemize} - \item Compare to the non-simplified originals. - \item Compare to the official datasets. - \item Compare to {\DP} and {\VW}. -\end{itemize} - -\subsection{Generalization Results of Analyzed Rivers} -\label{sec:generalization-results-of-analyzed-rivers} - -\subsubsection{Medium-Scale (1:\numprint{50000})} -\label{sec:analyzed-medium-scale} - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{salvis-wm75--grpk10-1x50k} - \caption{2x zoomed-in {\WM} for 1:\numprint{50000}.} - \label{fig:salvis-wm75--grpk10-1x50k} -\end{figure} - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{salvis-wm75--grpk10-1x50ktr} - \caption{Top--right part of Figure~\ref{fig:salvis-wm75--grpk10-1x50k}.} - \label{fig:salvis-wm75--grpk10-1x50ktr} -\end{figure} - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{salvis-wm75--grpk10-1x50ktl} - \caption{Left part of Figure~\ref{fig:salvis-wm75--grpk10-1x50k}.} - \label{fig:salvis-wm75--grpk10-1x50ktl} -\end{figure} - -As one can see in Figure~\ref{fig:salvis-wm75--grpk10-1x50k}, the illustrations deliver -what was promised by the algorithm, but with a few caveats. Left side of the -figure looks reasonably well simplified: long bends remain slightly curved, -small bends are removed or slightly exaggerated. - -Figure's~\ref{fig:salvis-wm75--grpk10-1x50k} left part is clipped to -Figure~\ref{fig:salvis-wm75--grpk10-1x50ktl}. As one can see, some bends were well -exaggerated, and some bends were eliminated. - -Top--right side (clipped in Figure~\ref{fig:salvis-wm75--grpk10-1x50ktl}), some jagged -and sharp bends appear. These will become more pronounced in even larger-scale -simplification in the next section. - -To sum up, mid-scale simplification works well for some geometries, but creates -sharp edges for others. - -\clearpage - -\subsubsection{Large-Scale (1:\numprint{250000})} -\label{sec:analyzed-large-scale} - -As visible in Figure~\ref{fig:salvis-wm220-10x}, for large-scale map, some of the -resulting bends look significantly exaggerated. Why is that? -Figure~\ref{fig:salvis-wm220-overlaid-zoom} zooms in the large-scale -simplification and overlays the original. - -\begin{figure}[ht] - \centering - \begin{subfigure}[b]{.49\textwidth} - \centering - \includegraphics[width=.2\textwidth]{salvis-250k-10x} - \caption{Original.} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \centering - \includegraphics[width=.2\textwidth]{salvis-wm220-10x} - \caption{Simplified.} - \end{subfigure} - \caption{GRPK10 simplified with {\WM} for 1:\numprint{250000}.} - \label{fig:salvis-wm220-10x} -\end{figure} - -\begin{figure}[ht] - \centering - \includegraphics[width=.8\textwidth]{salvis-wm-overlaid-250k-zoom} - \caption{10x zoomed-in {\WM} for 1:\numprint{250000}.} - \label{fig:salvis-wm220-overlaid-zoom} -\end{figure} - -A conglomeration of bends is visible, especially in top--right side of the -illustration. We assume this was caused by two bends significantly exaggerated, -leaving no space to exaggerate those between the two. - -\subsubsection{Discussion} - -For mid-size scales of 1:\numprint{50000}, the implemented algorithm works well -for certain geometries, and poorly for others. This test surfaced two areas for -future research and improvement: - -\begin{itemize} - - \item Exaggeration is sometimes creating sharp edges, especially when the - exaggerated bend is quite small. When sharp edges are created, - exaggeration could interpolate more points in the bend, and exaggerate - using the interpolated points. - - \item In larger scales, when bends do not have space to exaggerate, they - should be combined or eliminated instead. - -\end{itemize} - -\subsection{Comparison with National Spatial Datasets} - -There are a few datasets used in this comparison: GRPK10, GRPK50 and -GRPK250. They are vector datasets which include rivers. They can be -downloaded for free from \cite{nzt}. Here are the meanings of the codenames: - -\begin{description} - - \item[GRPK10] is a dataset of highest detail. Suited for maps of scale - 1:\numprint{10000}. - - \item[GRPK50] is suited for maps of scale 1:\numprint{50000}. - - \item[GRPK250] offers the least detail, and is suited for maps of - scale 1:\numprint{250000}. - -\end{description} - -During the analysis, we ran {\WM} on GRPK10 for 2 destination scales: -1:\numprint{50000} and 1:\numprint{250000}.\footnote{parameter calculation is -detailed in section~\ref{sec:bend-scaling-and-dimensions}.} This section -compares the resulting {\WM}--generalized rivers to GRPK50 and GRPK250. - -\subsubsection{Medium-Scale (1:\numprint{50000})} - -For our research location, the national dataset GRPK10 is almost equivalent to -GRPK50, with a few nuances. Figure~\ref{fig:salvis-wm75-grpk50-grpk10-1x50k} -illustrates all three shapes: GRPK50, {\WM}--simplified GRPK10, and the -original GRPK10. - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{salvis-wm75-grpk50-grpk10-1x50k} - - \caption{GRPK10, GRPK50 and {\WM} for 1:\numprint{50000}.} - - \label{fig:salvis-wm75-grpk50-grpk10-1x50k} -\end{figure} - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{salvis-wm75-grpk50-grpk10-1x50ktl} - \caption{Left side of Figure~\ref{fig:salvis-wm75-grpk50-grpk10-1x50k}.} - \label{fig:salvis-wm75-grpk50-grpk10-1x50ktl} -\end{figure} - -\begin{figure}[h!] - \centering - \includegraphics[width=\textwidth]{salvis-wm75-grpk50-grpk10-1x50ktr} - \caption{Top--right side of Figure~\ref{fig:salvis-wm75-grpk50-grpk10-1x50k}.} - \label{fig:salvis-wm75-grpk50-grpk10-1x50ktr} -\end{figure} - -Although figures are almost identical, -Figure~\ref{fig:salvis-wm75-grpk50-grpk10-1x50ktr} illustrates two small bends -that have been removed in GRPK50, but have been exaggerated by our -implementation. - -\clearpage - -\subsubsection{Large-Scale (1:\numprint{250000})} -\label{sec:national-large-scale} - -Figure~\ref{fig:salvis-wm220} illustrates the original GRPK250 and the -{\WM}--simplified version. As section~\ref{sec:analyzed-large-scale} explains, -the algorithm tries to exaggerate many bends to a great size. However, GRPK250 -takes the opposite approach --- only the very basic shapes of the largest bends -are retained. Time and customers will tell, which approach is more appropriate, -after the current {\WM} implementation receives some time and attention, as -desired in section~\ref{sec:future-suggestions}. - -\begin{figure}[h!] - \centering - \begin{subfigure}[b]{.49\textwidth} - \includegraphics[width=\textwidth]{salvis-grpk250-2x} - \caption{GRPK250.} - \end{subfigure} - \hfill - \begin{subfigure}[b]{.49\textwidth} - \centering - \includegraphics[width=\textwidth]{salvis-wm220} - \caption{{\WM}-simplified GRPK10.} - \end{subfigure} - \caption{GRPK250 and {\WM}--simplified GRPK10.} - \label{fig:salvis-wm220} -\end{figure} - -\subsection{Comparison with {\DP} and {\VW}} - -It is time to visually compare our implementation with the classical -algorithms: {\DP}, {\VW} and Chaikin. Since we have established that more work is -needed for small-scale maps (1:\numprint{250000}), we will limit the comparison -in this section to 1:\numprint{50000}. - -\begin{figure}[h!] - \includegraphics[width=\textwidth]{salvis-wm75-dp64-grpk10-1x50k} - \caption{} - \label{fig:salvis-wm75-dp64-grpk10-1x50k} -\end{figure} - -\begin{figure}[h!] - \includegraphics[width=\textwidth]{salvis-wm75-dpchaikin64-grpk10-1x50k} - \caption{} - \label{fig:salvis-wm75-dpchaikin64-grpk10-1x50k} -\end{figure} - -\clearpage - -\begin{figure}[h!] - \includegraphics[width=\textwidth]{salvis-wm75-vw64-grpk10-1x50k} - \caption{} - \label{fig:salvis-wm75-vw64-grpk10-1x50k} -\end{figure} - -\begin{figure}[h!] - \includegraphics[width=\textwidth]{salvis-wm75-vwchaikin64-grpk10-1x50k} - \caption{} - \label{fig:salvis-wm75-vwchaikin64-grpk10-1x50k} -\end{figure} - -\clearpage - -\subsection{Testing Results Online} -\label{sec:testing-results-online} - -An on-line tool\cite{openmapwm} has been developed to test incoming parameters -to {\WM} algorithm. A user should select a river of interest, enter the -\textsc{dhalfcircle} parameter and click "Submit". The simplified line feature -will be overlaid on top of the map. - -Figure~\ref{fig:openmap-wm-good} illustrates the end result that looks -reasonably well. Figure~\ref{fig:openmap-wm-bad} illustrates that the algorithm -produces poorly simplified results for some geometries. - -\begin{figure}[ht] - \centering - \includegraphics[width=\textwidth]{openmap-wm-good.png} - \caption{Example on-line test tool for {\WM} algorithm.} - \label{fig:openmap-wm-good} -\end{figure} - -\begin{figure}[ht] - \centering - \includegraphics[width=.5\textwidth]{openmap-wm-bad.png} - \caption{Another example from the on-line test tool.} - \label{fig:openmap-wm-bad} -\end{figure} - -\section{Conclusions} -\label{sec:conclusions} - -Classical and modern line simplification algorithms were evaluated, -main problems with them identified. A method for {\WM} technical -implementation was defined, and the algorithm implemented. Each geometric -transformation was described and visualized. The implemented algorithm was -applied for different shapes and compared to national (Lithuanian) datasets. - -About 1,000 lines of Procedural SQL were written for the algorithm and tests, -and a few hundred lines of supporting scripts in Make, Python, Awk, Bash. With -the help of its permissive license and early interest, the algorithm code has -already been used to create a prototype on-line service to evaluate the -algorithm robustness. - -\section{Future Suggestions} -\label{sec:future-suggestions} - -These are the areas for possible future work with this, published, -implementation: - -\begin{itemize} - - \item Implement bend combination operator - (section~\ref{sec:combination-operator}). - - \item Fine-tune parameters for bend exaggeration. - Section~\ref{sec:generalization-results-of-analyzed-rivers} contains - a exaggerated bends that became sharp and includes some future ideas. - - \item What are the exaggeration limits when working with large scales? - Section~\ref{sec:national-large-scale} discusses examples that some - limits are necessary. - - \item Research when bends should be marked as \textsc{isolated}. As is - seen from examples, the current criteria are not robust enough. - - \item Once the points above yield a satisfactory result, the efficiency of the - algorithm could be improved to work on the lines in "streaming" fashion - (more details in section~\ref{sec:algorithm-implementation-process}). - -\end{itemize} - -That sums up what could be improved without changing the algorithm in a -significant way. Other than that, further area of research is working towards -graduating the algorithm from "isolated cartographic generalization" to "full -cartographic generalization". The current operators of {\WM} algorithm have a -few venues to preserve the surrounding topology. This could be further -researched and extended. - -\section{Acknowledgments} -\label{sec:acknowledgments} - -I would like to thank my thesis supervisor, Dr. Andrius Balčiūnas, for his help -in formulating the requirements and providing early editorial feedback for the -thesis. - -I am grateful to Tomas Straupis, who handed me the {\WM}\cite{wang1998line} -paper on a warm pre-COVID summer evening. I got intrigued. He was also an early -beta-tester of my implementation, and helped me understand where the initial -algorithm descriptions were ambiguous. - -Many thanks to NŽT\cite{nzt} for providing the datasets with a very permissive -license. - -\printbibliography - -\begin{appendices} - -\section{Code Listings} - -This section contains code listings of the {\WM} algorithm. - -\subsection{Re-Generating This Paper} -\label{sec:code-regenerate} - -As explained in section~\ref{sec:reproducing-the-paper}, illustrations in - this paper are generated from a small list of sample geometries. To observe - the source geometries or regenerate this paper, run this script (assuming - the name of this document is \textsc{mj-msc-full.pdf}). - - Listing~\ref{lst:extract-and-generate} will extract the source files from - the \textsc{mj-msc-full.pdf} to a temporary directory, run the top-level - \textsc{make} command, and display the generated document. Source code for - the algorithm, as well as other supporting files, can be found in the - temporary directory. - -\begin{longlisting} - \inputcode{bash}{extract-and-generate} - \caption{\textsc{extract-and-generate}} - \label{lst:extract-and-generate} -\end{longlisting} - -\subsection{Function \textsc{st\_simplifywm}} -\begin{longlisting} - \inputcode{postgresql}{wm.sql} - \caption{\textsc{wm.sql}} - \label{lst:wm.sql} -\end{longlisting} - -\subsection{Function \textsc{aggregate\_rivers}} -\begin{longlisting} - \inputcode{postgresql}{aggregate-rivers.sql} - \caption{\textsc{aggregate-rivers.sql}} - \label{lst:aggregate-rivers.sql} -\end{longlisting} - -\end{appendices} -\end{document} diff --git a/IV/notes.txt b/IV/notes.txt deleted file mode 100644 index d7aa55b..0000000 --- a/IV/notes.txt +++ /dev/null @@ -1,117 +0,0 @@ -Self-line crossing when cutting a bend --------------------------------------- - -The self-line-crossing may happen after a few bends have been skipped. E.g. -ends of A<->B cross the line, but "swallow" a few more in between: - - ,______ - / \ - |___A | \ \ - \ | B\ | __ - \ | | | / \ - / | | |___,---,___/A | - / | \_________________| - \ | - \ | \ \ - / / B\ | _ __ - ----/ / | | / \ / \ - / ,____/ | |___/ \___/A | - / B| \_________________| - | - - - -If a bend with 180+ deg sum of inflection angles is found, its line between -inflection angles (AB in our examples) must be crossed with all the other bends -to detect a possible line-crossing. This is O(N*M), where N is the total number -of line segments, and M is the number of qualifying bends. It is expensive. - -Also, there is another way to remove self-crossing, without removing most of -the bend. E.g. from: - - \ / - B\ | __ - | | / \ - | |____/A | - \__________| - -Instead of: - - \ / - \/ A' - B - -To: - - \ \_ - B\ `-,_.__ - | A' \ - | | - \__________| - -But perhaps it doesn't look quite as natural. I will trust the original -article to do the right thing here and remove the bend altogether. - -ALSO: the bends should be iterated from different directions: - -for i := 0; i < len(bends); i++ { - for j := 0; j < i; j++ { - ... - } - for j := len(bends); j > i; j-- { - ... - } -} - -So if there are multiple bends between the baseline, they will be cut -correctly. - -The Context of a Bend ---------------------- - -Similar bends: - -> For example, if bend 1 has four unit areas and bend 2 has six unit areas, the -> average size is five units, and the normalized areas of bends 1 and 2 are -> 4/5=0.8 and 6/5=1.2, respectively. - -My comment: everything until this sentence is clear. However, "unit areas" is -misleading: there is little reason to normalize areas, but leave the distances -intact (if we'd like to normalize areas, it would make sense to square-root -them). - -Removing that removes changes the meaning of the sentence that **euclidean -distance** is normalized (the composite of the bend properties), rather than -a single component. - -Offered structure ------------------ - -- Introduction -- Previous research overview -- Methodology and methodics -- Results -- Conclusions -- Literature review -- Appendix - -for 2021-04-19 --------------- - -- literatūros šaltinių analizė -- literatūros šaltinių priskyrimas atskiroms magistro darbo struktūrinėms dalims - -analizės uždaviniai: -- galutinis problemos formulavimas -- darbo tikslo formulavimas -- uždavinių formulavimas -- aktualumo -- naujumo -- pritaikomumo formulavimas - -Angl.: - -- trūksta literatūros apžvalgos: pervadinti šiuolaikinius sprendimus į tai -- mažiausiai 2 poskyriai skyriuje. -- techninė dalis -- į rezultatus. -- "eksperimento rezultatai" eina į "darbo rezultatus". diff --git a/IV/openmap-wm-bad.png b/IV/openmap-wm-bad.png deleted file mode 100644 index 9f73bf903806e6acc0c5f13aa6c770a46c4abcba..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 66326 zcmXt9bySn@-yRL4VT3dzM@dTeknV;dFhmd#>5%Tx-Q6M$(x}8nNC`>_A}t-#NWA;L z=lpigb9T=Dx$k}Yx<1zvtEZz%45R}B003fjHK+jqfZ>jQyznv6zgTb=DWJay+|jXOFgZd~PrN z}Y5z4Rp0Ygd8JA?o<8+WGD5 zEJCq1D~HK~i7k%@3frk(zdWDU2gS`=BOsXOE_j^?ifxU*E&_X^uiN9c{@2zT%nx?R zHo4A_NXe&(CkbaE6N+Y!8fc&(j<^Nh`e&WHRRtdWM+P%u)UANf&y$mr!_3m{stL3;^!w}` zssk@>2i6U=KUX=sowz*9HwKY~g<{tmM{^GeMV-W|Q1g*<(d!bEVjCjb!FAY4;VMvL zM06|%Tz!2?ClADRo4W+^{gpH(O8g^#ZN5_OgWX8I1)BG|1x*UC%*hFZ|QqJ{L zTz-KrgODJ~5*;=+whq(ieERvRLg^Wgin-Z04%HqPw|4{Z&sE>Nw-W#YGPqD|jP^MJ zEmoP#t<{!5!6hWUL5{XcMT=liuP*~I`v+{OLPc(<=CNIu1_#FI z?lTwJeYcGp(^eb+t>X>hgHIS)lE}b1oJ{{xc%8di7?}6VQd3iBm)NuuoqY?O-?*C! zR2ukg?Hvpl$YslGU%~|Q5SZK~Z*4a2;K7B9JGp)4&l|O`P=J929L}g<;ufY6Qn9rp zt~!Yg=>F7c(2beZ1SK|9``q?L^h^hW_P`ufvxU^ZqTZodx#Z>DK<)p9?74@TO#pj^Xe6DG3OTzKLaN%ecZk96YgF? zm;ep*mMqgn%|>|`Gj1d|!Mp$K5)pSaY|clrL6;imRpgHmOaS`i+74AZ`nh9?04PrO z*IDN?&$C6AfR-jXyDhLtw~P-%-_TgYSxNDt>zTYX&F0_gfB-xvC#NRI^_W2KYiz3Z z9C+@Tk91@L)f7*tt0bi;h-=+|-g(RvYVD=l_Y(y&#eQc1)M`G;0mpU$qBf$;LQ|;K zq}@|XC4%(ReF?f;8U~xg*~2-#yD3 zj}vfc7*5s??&hPkilHg^ym7_*q2d2*6xTi6wxyH>ti~z*q-1CeiaT-)63eRxL7Kbl z6ol)aNO{#%6ZeEvpxkAz4Gi!=_m=^z?I+MXz1o z&i8HYwcRY<5MdAB-r`Q!r;g21)+53p&ECMyW~yYW{yYZ_@(*|Xd}Z=@e04>#J_NFY zTKWt+L_7*jX-W*xPllW6AVV4Du_CI7;n~IFGijC1uL$j&21AW@t&ekZvV(#jS3O)$ z5SRkC`2R)Kq<#1S0hT}m0jE-60%TPn@h0JX5rV_Q(nuZgJBvzSvKe?Cnt{pfw(1Ss zIuf|{FHJRKXlHzCz`|OEaN;h)o6e-p+|(J`QsNh1rjh$VxL)Q!kykxIVUK&8Bhqvo1Y8Hu=C2=!L%l!{xO|Y_F zv)VlYyphR3ALKQ-s&6H^RY1t8>RTH#ZM6Q_&^6Uqri*aq=q;paGV@ zR1dqwb#`{{f7_U`Q`HyexU`UhF&d3*gcS(kg{u}3PN<~oH}K%D;A*i3eIR9u=WO_k zG?3C_J$d{1@nP*XH>2T6F>8-tuqt;=2g+w-S0`iVLnW0KIY!i`!I%#^C+z)^E;~Lx zPOJab=5ZH5fAhnGCob&T3tkVhJibmxKsEtm91YHD{+&n;BP1cYf`1`JUcd^}KX&}I z-8L>H6*J(p(TKQ#2kXNis4}8f&7WRS#Z($%z@X#Y3LR_f%I#tqDcISSG&HTYQt0BuVIl`Dh5eCqXDJes(zO4EXFsRgH^sxtPyVp#ad>-oPNcBy_x6~j26q00ywvvm z9d>Vd0#?IF)*!H%ORZ!hZG>>#>^DLN1s9B})vO|~jd5Up3`8WKvUh2A8C_stlKXb0 z73F|$Qx+bc*#S+I$30ff=*pVP*mKEUlMCrc6U?+&U93npz8*$bRaIqC|Cg?~Q=O1qdXq6Zj#;V}9to-x z3aZn*6Zr)WxW}m*!zOt$1R6nRVekD(=?w!ZG6bwn=sU>OKAiW15VxO5tK24mcc_NX z7}?Rcv;86y!%1il-(TF+>!j%cXziEwKf!e(H}NsH%yoD(Dc_mQ4SqnpeUi6k z3?!02jA!LZuRFFOSZfWeWLfR@28q#|FK+7V+>(hb*KGy>E9i| z2}}?>e`*Y~sN^L72PLc+0!

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zJxuxbVT^}^T2{7K$b97U_N2YLouWbz05DYHTO{u=6xrM-scT0WePwYeF_F02v_^{L z;vJ@S5X>KkgOVwiAvalS+ltfP17+J_yS4d$Va38?Mj5F500000NkvXXu0mjfOVZSe diff --git a/IV/rivers-10.sql b/IV/rivers-10.sql deleted file mode 100644 index 0f7c36c..0000000 --- a/IV/rivers-10.sql +++ /dev/null @@ -1,54 +0,0 @@ --- Generated at 2021-05-16T11:57:10Z on motiejus@mtpad.i.jakstys.lt --- Rivers: Visinčia|Šalčia|Nemunas --- --- PostgreSQL database dump --- - --- Dumped from database version 13.2 --- Dumped by pg_dump version 13.2 - -SET statement_timeout = 0; -SET lock_timeout = 0; -SET idle_in_transaction_session_timeout = 0; -SET client_encoding = 'UTF8'; -SET standard_conforming_strings = on; -SELECT pg_catalog.set_config('search_path', '', false); -SET check_function_bodies = false; -SET xmloption = content; -SET client_min_messages = warning; -SET row_security = off; - -DROP TABLE public.wm_rivers; -SET default_tablespace = ''; - -SET default_table_access_method = heap; - --- --- Name: wm_rivers; Type: TABLE; Schema: public; Owner: osm --- - -CREATE TABLE public.wm_rivers ( - id integer, - name text, - way public.geometry -); - - -ALTER TABLE public.wm_rivers OWNER TO osm; - --- --- Data for Name: wm_rivers; Type: TABLE DATA; Schema: public; Owner: osm --- - -COPY public.wm_rivers (id, name, way) FROM stdin; -3 Nemunas 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-107 Šalčia 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-547 Nemunas (Rusnė) 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-\. - - --- --- PostgreSQL database dump complete --- - diff --git a/IV/rivers-250.sql b/IV/rivers-250.sql deleted file mode 100644 index 7673b4b..0000000 --- a/IV/rivers-250.sql +++ /dev/null @@ -1,52 +0,0 @@ --- Generated at 2021-05-16T11:55:12Z on motiejus@mtpad.i.jakstys.lt --- Rivers: Visinčia|Šalčia|Nemunas --- --- PostgreSQL database dump --- - --- Dumped from database version 13.2 --- Dumped by pg_dump version 13.2 - -SET statement_timeout = 0; -SET lock_timeout = 0; -SET idle_in_transaction_session_timeout = 0; -SET client_encoding = 'UTF8'; -SET standard_conforming_strings = on; -SELECT pg_catalog.set_config('search_path', '', false); -SET check_function_bodies = false; -SET xmloption = content; -SET client_min_messages = warning; -SET row_security = off; - -DROP TABLE public.wm_rivers_250; -SET default_tablespace = ''; - -SET default_table_access_method = heap; - --- --- Name: wm_rivers_250; Type: TABLE; Schema: public; Owner: osm --- - -CREATE TABLE public.wm_rivers_250 ( - id integer, - name text, - way public.geometry -); - - -ALTER TABLE public.wm_rivers_250 OWNER TO osm; - --- --- Data for Name: wm_rivers_250; Type: TABLE DATA; Schema: public; Owner: osm --- - -COPY public.wm_rivers_250 (id, name, way) FROM stdin; -1 Visinčia 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-2 Šalčia 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-\. - - --- --- PostgreSQL database dump complete --- - diff --git a/IV/rivers-50.sql b/IV/rivers-50.sql deleted file mode 100644 index 5011b81..0000000 --- a/IV/rivers-50.sql +++ /dev/null @@ -1,54 +0,0 @@ --- Generated at 2021-05-16T11:54:48Z on motiejus@mtpad.i.jakstys.lt --- Rivers: Visinčia|Šalčia|Nemunas --- --- PostgreSQL database dump --- - --- Dumped from database version 13.2 --- Dumped by pg_dump version 13.2 - -SET statement_timeout = 0; -SET lock_timeout = 0; -SET idle_in_transaction_session_timeout = 0; -SET client_encoding = 'UTF8'; -SET standard_conforming_strings = on; -SELECT pg_catalog.set_config('search_path', '', false); -SET check_function_bodies = false; -SET xmloption = content; -SET client_min_messages = warning; -SET row_security = off; - -DROP TABLE public.wm_rivers_50; -SET default_tablespace = ''; - -SET default_table_access_method = heap; - --- --- Name: wm_rivers_50; Type: TABLE; Schema: public; Owner: osm --- - -CREATE TABLE public.wm_rivers_50 ( - id integer, - name text, - way public.geometry -); - - -ALTER TABLE public.wm_rivers_50 OWNER TO osm; - --- --- Data for Name: wm_rivers_50; Type: TABLE DATA; Schema: public; Owner: osm --- - -COPY public.wm_rivers_50 (id, name, way) FROM stdin; -1 Nemunas 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-29 Visinčia 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-415 Nemunas (Rusnė) 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-\. - - --- --- PostgreSQL database dump complete --- - diff --git a/IV/slides-2021-03-29.txt b/IV/slides-2021-03-29.txt deleted file mode 100644 index f52e0af..0000000 --- a/IV/slides-2021-03-29.txt +++ /dev/null @@ -1,90 +0,0 @@ ---- -title: Wang & Müller linijų generalizacijos algoritmo įgyvendinimas upių pavyzdžiu -author: Motiejus Jakštys -description: | - Prezentacija apie magistrinio darbo progresą vertinimo grupei -date: | - 2021-03-29 \ - ![](../misc/Logo_vilniaus_universitetas.png){width=2in} -lang: lt-LT -header-includes: | - \definecolor{vulightgrey}{RGB}{220,220,220} - \definecolor{vudarkgrey}{RGB}{65,65,65} - \definecolor{vupurple}{RGB}{123,0,63} - \definecolor{darkgreen}{RGB}{32,96,32} - - \setbeamercolor{title}{fg=vupurple} - \setbeamercolor{frametitle}{fg=vupurple} - \setbeamercolor{item}{fg=vupurple} - \setbeamercolor{normal text}{fg=vudarkgrey} -... - -# Problema - -- Dabartiniai atvirai prieinami algoritmai - - Visvalingam-Whyatt - - Douglas-Peucker - -- Problematika - - nepritaikyti gamtiniams objektams: upėms, krantų linijoms - - prarandami raiškūs gamtinių objektų elementai: vingiai, kilpos - -- Alternatyvos - - egzistuoja tik teorinės - - nėra implementacijos - - net teorinėms -- neapibrėžti parametrai - -# Aktualumas - -- Smulkesnių mastelių žemėlapių georeferenciniai duomenys kuriami taikant - automatizuoto generalizavimo metodus (pvz., GDR10LT generaluzuojant į - GDR50LT, GDR250LT). -- Nėra atvirai prieinamo sprendimo gamtinių linijinių objektų generalizacijai - -# Etapai: Wang & Müller techninio įgyvendinimo - -::: nonincremental -- Įlinkių atpažinimas -- Silpnas pasislinkimas įlinkio gale -- Įlinkio kirtimas kitu įlinkiu -- Patikrinimas su Nemunu, Šalčia ir Visinčia -- Įlinkių matavimai: - - dydis ir forma - - izoliuoti, panašūs -- Operatoriai: - - Specifinio įlinkio pašalinimo - - Dviejų įlinkių kombinavimo į vieną - - Izoliuotų įlinkių padidinimo -- Pritaikymas visoms Lietuvos upėms -::: - -# Etapai: analizės ir darbo rašymo - -::: nonincremental -- Esamų algoritmų apžvalga -- Problemos aprašymas -- Pasirinkto generalizacijos sprendimo apibūdinimas -- Sukurtos implementacijos aptarimas - - privalumai - - trūkumai -- Nauda praktikoje -- Tolimesnių tyrimų kryptys -::: - -# Naujumas - -Šis darbas pasiūlys iki šiol neegzistuojantį atvirą sprendimą gamtinių -linijinių objektų generalizacijai (Lietuvoje -- GDR50 ir GDR250 analogus) - -# Tolimesnis pritaikymas - -- Sukurta algoritmo techninė realizacija atviro kodo GIS bus pradžia tolesniam jo -pritaikymui kitiems gamtiniams objektams: ežerų kranto linija, jūrų, -kontinentų, miškų ribos. - -- Kadangi rezultatas bus techninė realizacija, o ne rašinėlis, tai suteikia -toliau galimybę vystyti sprendimą. - -# Klausimai - -Ačiū už dėmesį. diff --git a/IV/test-rivers.sql b/IV/test-rivers.sql deleted file mode 100644 index 966c996..0000000 --- a/IV/test-rivers.sql +++ /dev/null @@ -1,20 +0,0 @@ -\set ON_ERROR_STOP on -SET plpgsql.extra_errors TO 'all'; - --- This fails with real rivers since dcf4c02307baeece51470a961a113a8fad68fad5 --- (adding GDB10LT data). The same rivers from OpenStreetMaps work. --- There seems to be a bug in wm_exaggeration. - -do $$ -declare - npoints bigint; - secs bigint; -begin - select * from ST_SimplifyWM_Estimate((select st_union(way) from wm_rivers)) into npoints, secs; - raise notice 'Total points: %', npoints; - raise notice 'Expected duration: %s (+-%s)', ceil(secs), floor(secs*.5); -end $$ language plpgsql; - -delete from wm_debug where name in (select distinct name from wm_rivers); -delete from wm_demo where name in (select distinct name from wm_rivers); -insert into wm_demo (name, way) select name, ST_SimplifyWM(way, 75, null, name) from wm_rivers; diff --git a/IV/test.sql b/IV/test.sql deleted file mode 100644 index d51b8e1..0000000 --- a/IV/test.sql +++ /dev/null @@ -1,198 +0,0 @@ -\i wm.sql - --- https://stackoverflow.com/questions/19982373/which-tools-libraries-do-you-use-to-unit-test-your-pl-pgsql -create or replace function assert_equals(expected anyelement, actual anyelement) returns void as $$ -begin - if expected = actual or (expected is null and actual is null) then - --do nothing - else - raise exception 'Assertion Error. Expected <%> but was <%>', expected, actual; - end if; -end $$ language plpgsql; - -drop function if exists dbg_geomsummary; -create function dbg_geomsummary(geoms geometry[]) returns void as $$ - declare i int4; -begin - raise notice 'len: %', array_length(geoms, 1); - for i in 1..array_length(geoms, 1) loop - raise notice '% %: %', st_geometrytype(geoms[i]), lpad(i::text, 2, '0'), st_astext(geoms[i]); - end loop; -end -$$ language plpgsql; - -drop table if exists wm_figures; -create table wm_figures (name text, way geometry); --- add fig8.gpkg to postgis: --- ogr2ogr -update -f PostgreSQL PG:"host=127.0.0.1 user=osm password=osm dbname=osm" fig8.gpkg --- to "normalize" a new line when it's in `f`: --- select st_astext(st_snaptogrid(st_transscale(geometry, -19.5, .016, 4000, 4000), 1)) from f; -insert into wm_figures (name, way) values - ('fig3', 'LINESTRING(0 0,12 0,13 4,20 2,20 0,32 0,33 10,38 16,43 15,44 10,44 0,60 0)'::geometry), - ('fig3-1', 'LINESTRING(0 0,12 0,13 4,20 2,20 0,32 0,33 10,38 16,43 15,44 10,44 0)'::geometry), - ('fig5', 'LINESTRING(0 39,19 52,27 77,26 104,41 115,49 115,65 103,65 75,53 45,63 15,91 0)'::geometry), - ('fig6', 'LINESTRING(84 47,91 59,114 64,122 80,116 92,110 93,106 106,117 118,136 107,135 76,120 45,125 39,141 39,147 32)'::geometry), - ('fig8', 'LINESTRING(173 12,174 10,180 8,186 8,186 13,191 11,189 6,201 5,203 11,216 16,216 6,222 6,229 3,236 2,239 6,243 8,248 6)'::geometry), - ('inflection-1', 'LINESTRING(110 24,114 20,133 20,145 15,145 0,136 8,123 10,114 10,111 2)'::geometry), - ('multi-island', 'MULTILINESTRING((-15 10,-10 10,-5 11,0 11,5 11,10 10,11 9,13 10,15 9),(-5 11,-2 15,0 16,2 15,5 11))'::geometry), - ('selfcrossing-1','LINESTRING(-27 180,-20 166,-21 142,-18 136,55 136,55 136,71 145,44 165,37 146,22 145,14 164,11 164,3 146,-12 146,-13 176,-18 184)'::geometry), - ('isolated-1', 'LINESTRING(-50 103,-48 102,-30 103,-31 105,-31 107,-27 107,-26 103,-6 103,-4 104)'::geometry), - ('isolated-2', 'LINESTRING(250 100,246 104,234 105,230 106,225 101,224 93,217 78,206 69)'::geometry); - -insert into wm_figures (name, way) values ('fig6-rev',ST_Reverse( - ST_Translate((select way from wm_figures where name='fig6'), 60, 0))); -insert into wm_figures (name, way) values ('fig6-combi', ST_Union( - ST_Translate((select way from wm_figures where name='fig6'), 0, 90), - ST_Translate((select way from wm_figures where name='fig6'), 80, 90) - )); - -insert into wm_figures (name, way) values ('selfcrossing-1-rev',ST_Reverse( - ST_Translate((select way from wm_figures where name='selfcrossing-1'), 0, 60))); - --- 3395 is now "reserved" for figures. -update wm_figures set way=st_setsrid(way, 3395); - -delete from wm_debug where name in (select distinct name from wm_figures); -delete from wm_demo where name in (select distinct name from wm_figures); -insert into wm_demo (name, way) select name, ST_SimplifyWM(way, .1, null, name) from wm_figures where name not in ('fig8', 'isolated-1'); -insert into wm_demo (name, way) select name, ST_SimplifyWM(way, 14, null, name) from wm_figures where name in ('fig8', 'isolated-1', 'isolated-2'); - -drop function if exists wm_debug_get; -create function wm_debug_get( _stage text, _name text, OUT ways geometry[]) as $$ -declare -begin - ways = array((select way from wm_debug where stage=_stage and name=_name order by id)); -end $$ language plpgsql; - -do $$ -declare - vbends geometry[]; -begin - vbends = wm_debug_get('bbends', 'fig3'); - perform assert_equals(5, array_length(vbends, 1)); - perform assert_equals('LINESTRING(0 0,12 0,13 4)', st_astext(vbends[1])); - perform assert_equals('LINESTRING(12 0,13 4,20 2,20 0)', st_astext(vbends[2])); - perform assert_equals('LINESTRING(20 2,20 0,32 0,33 10)', st_astext(vbends[3])); - perform assert_equals('LINESTRING(32 0,33 10,38 16,43 15,44 10,44 0)', st_astext(vbends[4])); - perform assert_equals(4, array_length(wm_detect_bends((select way from wm_figures where name='fig3-1')), 1)); - select wm_detect_bends((select way from wm_figures where name='fig5')) into vbends; - perform assert_equals(3, array_length(vbends, 1)); -end $$ language plpgsql; - -do $$ -declare - vbends geometry[]; - vinflections geometry[]; -begin - vinflections = wm_debug_get('cinflections', 'fig5'); - perform assert_equals('LINESTRING(0 39,19 52,27 77)', st_astext(vinflections[1])); - perform assert_equals('LINESTRING(19 52,27 77,26 104,41 115,49 115,65 103,65 75,53 45)', st_astext(vinflections[2])); - perform assert_equals('LINESTRING(65 75,53 45,63 15,91 0)', st_astext(vinflections[3])); - - -- inflections-1, the example in fix_gentle_inflections docstring - select array((select way from wm_debug where name='inflection-1' and stage='bbends')) into vbends; - select array((select way from wm_debug where name='inflection-1' and stage='cinflections')) into vinflections; - perform assert_equals(vbends[1], vinflections[1]); -- unchanged - perform assert_equals('LINESTRING(114 20,133 20,145 15,145 0,136 8,123 10,114 10)', st_astext(vinflections[2])); - perform assert_equals('LINESTRING(123 10,114 10,111 2)', st_astext(vinflections[3])); -end $$ language plpgsql; - -do $$ -declare - fig6 constant text default 'LINESTRING(84 47,91 59,114 64,120 45,125 39,141 39,147 32)'; - selfcrossing1 constant text default 'LINESTRING(-27 180,-20 166,-13 176,-18 184)'; - vcrossings geometry[]; - mutated boolean; -begin - select * from wm_self_crossing(wm_debug_get('cinflections', 'fig6')) into vcrossings, mutated; - perform assert_equals(true, mutated); - perform assert_equals( - fig6, - (select st_astext( - st_linemerge(st_union(way)) - ) from (select unnest(vcrossings) way) a) - ); - - select * from wm_self_crossing(wm_debug_get('cinflections', 'fig6-rev')) into vcrossings, mutated; - perform assert_equals(true, mutated); - perform assert_equals( - fig6, - (select st_astext( - st_translate(st_reverse(st_linemerge(st_union(way))), -60, 0) - ) from (select unnest(vcrossings) way) a) - ); - - select * from wm_self_crossing(wm_debug_get('cinflections', 'fig6-combi')) into vcrossings, mutated; - perform assert_equals(true, mutated); - perform assert_equals( - 'MULTILINESTRING((84 137,91 149,114 154,120 135,125 129,141 129,147 122),(164 137,171 149,194 154,200 135,205 129,221 129,227 122))', - (select st_astext( - st_linemerge(st_union(way)) - ) from (select unnest(vcrossings) way) a) - ); - - - select * from wm_self_crossing(wm_debug_get('cinflections', 'selfcrossing-1')) into vcrossings, mutated; - perform assert_equals(true, mutated); - perform assert_equals( - selfcrossing1, - (select st_astext( - st_linemerge(st_union(way)) - ) from (select unnest(vcrossings) way) a) - ); - - select * from wm_self_crossing(wm_debug_get('cinflections', 'selfcrossing-1-rev')) into vcrossings, mutated; - perform assert_equals(true, mutated); - perform assert_equals( - selfcrossing1, - (select st_astext( - st_translate(st_reverse(st_linemerge(st_union(way))), 0, -60) - ) from (select unnest(vcrossings) way) a) - ); - -end $$ language plpgsql; - --- verifying bends in fig8 are eliminated like explained in the WM paper -do $$ -declare - fig8gen2 constant text default 'LINESTRING(173 12,174 10,180 8,186 8,189 6,201 5,203 11,216 16,216 6,229 3,236 2,239 6,243 8,248 6)'; - fig8gen3 constant text default 'LINESTRING(173 12,174 10,180 8,189 6,201 5,203 11,216 16,216 6,229 3,236 2,239 6,243 8,248 6)'; - eliminations geometry[]; -begin - eliminations = wm_debug_get('afigures', 'fig8'); - perform assert_equals(fig8gen2, st_astext(eliminations[2])); - perform assert_equals(fig8gen3, st_astext(eliminations[3])); -end $$ language plpgsql; - --- testing wm_exaggerate_bend2 in isolation -do $$ -declare - fig3b2 geometry; - bend geometry; - size float; -begin - select way from wm_debug where name='fig3' and stage='bbends' and gen=1 and nbend=2 into fig3b2; - size = wm_adjsize(fig3b2); - bend = wm_exaggerate_bend2(fig3b2, size, 50.); - perform assert_equals('ST_LineString', st_geometrytype(bend)); - insert into wm_debug(stage, name, gen, nbend, way) values('manual', 'fig3', 1, 1, bend); -end $$ language plpgsql; - --- misc visuals -do $$ - declare fig6b1 geometry; - declare fig6b2 geometry; - declare sclong geometry; - declare scshort geometry; -begin - select way from wm_debug where name='fig6' and stage='bbends' and gen=1 into fig6b1 limit 1 offset 0; - select way from wm_debug where name='fig6' and stage='bbends' and gen=1 into fig6b2 limit 1 offset 2; - insert into wm_visuals (name, way) values('fig6-baseline', st_makeline(st_startpoint(fig6b2), st_endpoint(fig6b2))); - insert into wm_visuals (name, way) values('fig6-newline', st_makeline(st_endpoint(fig6b1), st_endpoint(fig6b2))); - - select way from wm_debug where name='selfcrossing-1' and stage='bbends' and gen=1 into sclong limit 1 offset 1; - select way from wm_debug where name='selfcrossing-1' and stage='bbends' and gen=1 into scshort limit 1 offset 4; - insert into wm_visuals (name, way) values('selfcrossing-1-baseline', st_makeline(st_startpoint(sclong), st_endpoint(sclong))); - insert into wm_visuals (name, way) values('selfcrossing-1-newline', st_makeline(st_startpoint(sclong), st_endpoint(scshort))); -end $$ language plpgsql; - diff --git a/IV/vars.awk b/IV/vars.awk deleted file mode 100644 index f979a82..0000000 --- a/IV/vars.awk +++ /dev/null @@ -1,26 +0,0 @@ -#!/usr/bin/awk -f - -BEGIN { FS="[(); ]" } - -/small_angle constant real default radians/ { - x1 += 1; - d1 = sprintf("\\newcommand{\\smallAngle}{$%d^\\circ$}",$8); -} -/isolation_threshold constant real default / { - x2 += 1; - d2 = sprintf("\\newcommand{\\isolationThreshold}{%.1f}",$7); -} -/scale2 constant float default / { - x3 += 1; - d3 = sprintf("\\newcommand{\\exaggerationEnthusiasm}{%.1f}",$7); -} - -END{ - if(x1 == 1 && x2 == 1 && x3 == 1) { - print d1 > "vars.inc.tex" - print d2 >> "vars.inc.tex" - print d3 >> "vars.inc.tex" - } else { - exit 1 - } -} diff --git a/IV/visuals.sql b/IV/visuals.sql deleted file mode 100644 index 89c6206..0000000 --- a/IV/visuals.sql +++ /dev/null @@ -1,146 +0,0 @@ -\set ON_ERROR_STOP on -SET plpgsql.extra_errors TO 'all'; - --- wm_bbox clips a geometry by a bounding box around a given object, --- matching dimensions of A-class paper (1 by sqrt(2)). -drop function if exists wm_bbox; -create function wm_bbox( - center geometry, - scaledwidth float -) returns geometry as $$ -declare - halfX float; - halfY float; -begin - halfX = scaledwidth / 2; - halfY = halfX * sqrt(2); - return st_envelope( - st_union( - st_translate(center, halfX, halfY), - st_translate(center, -halfX, -halfY) - ) - ); -end $$ language plpgsql; - --- wm_quadrant divides the given geometry to 4 rectangles --- and returns the requested quadrant following cartesian --- convention: --- +----------+ --- | II | I | ---- +----------+ --- | III | IV | --- +-----+----+ --- matching dimensions of A-class paper (1 by sqrt(2). -drop function if exists wm_quadrant; -create function wm_quadrant( - geom geometry, - quadrant integer -) returns geometry as $$ -declare - xmin float; - xmax float; - ymin float; - ymax float; -begin - xmin = st_xmin(geom); - xmax = st_xmax(geom); - ymin = st_ymin(geom); - ymax = st_ymax(geom); - - if quadrant = 1 or quadrant = 2 then - ymin = (ymin + ymax)/2; - else - ymax = (ymin + ymax)/2; - end if; - - if quadrant = 2 or quadrant = 3 then - xmax = (xmin + xmax)/2; - else - xmin = (xmin + xmax)/2; - end if; - - return st_intersection( - geom, - st_makeenvelope(xmin, ymin, xmax, ymax, st_srid(geom)) - ); -end $$ language plpgsql; - - -drop function if exists wm_salvisbbox; -create function wm_salvisbbox( - geom geometry, - scaledwidth float -) returns geometry as $$ -declare - ret geometry; -begin - with multismall as ( - select st_intersection( - st_union(geom), - wm_bbox( - st_closestpoint( - (select way from wm_rivers where name='Šalčia'), - (select way from wm_rivers where name='Visinčia') - ), - scaledwidth - ) - ) ways - ) - -- protecting against very small bends that were cut - -- in the corner of the picture - select st_union(a.geom) - from st_dump((select ways from multismall)) a - where st_length(a.geom) >= 100 - into ret; - - return ret; -end $$ language plpgsql; - -delete from wm_debug where name like 'salvis%'; -delete from wm_visuals where name like 'salvis%'; -insert into wm_visuals(name, way) values - ('salvis-grpk10', ( - wm_salvisbbox( - (select st_union(way) from wm_rivers where name in ('Šalčia', 'Visinčia')), - :scaledwidth - ) - )), - ('salvis-grpk50', ( - wm_salvisbbox( - (select st_union(way) from wm_rivers_50 where name in ('Šalčia', 'Visinčia')), - :scaledwidth - ) - )), - ('salvis-grpk250', ( - wm_salvisbbox( - (select st_union(way) from wm_rivers_250 where name in ('Šalčia', 'Visinčia')), - :scaledwidth - ) - )); - -do $$ -declare - i integer; - geom1 geometry; - geom2 geometry; - geom3 geometry; -begin - foreach i in array array[16, 32, 64, 256] loop - geom1 = st_simplify((select way from wm_visuals where name='salvis-grpk10'), i); - geom2 = st_simplifyvw((select way from wm_visuals where name='salvis-grpk10'), i*i); - insert into wm_visuals(name, way) values - ('salvis-dp' || i, geom1), - ('salvis-dpchaikin' || i, st_chaikinsmoothing(geom1, 5)), - ('salvis-vw' || i, geom2), - ('salvis-vwchaikin' || i, st_chaikinsmoothing(geom2, 5)); - end loop; - - -- more than 220 doesn't work, because there is an exaggerated bend near - -- Šalčia-Visinčia crossing, and it "exaggerates" to the - -- other river. - foreach i in array array[75, 220] loop - geom3 = st_simplifywm((select way from wm_visuals where name='salvis-grpk10'), i, 50, 'salvis-wm' || i); - insert into wm_visuals(name, way) values - ('salvis-wm' || i, geom3); - end loop; -end $$ language plpgsql; diff --git a/IV/vu.pdf b/IV/vu.pdf deleted file mode 100644 index 4d8c569fcc5ebb10d174d693e495ae66ced400ed..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 11905 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zd<&aOf06pAyR*`g?aKG24UIL#H*wQ)0ob1lP%u1F4v}a6+TQ5V`4>;!keUZGmY~qk z&@ZI#Ds-y}*M9@Pe3VvmkbPs|CF~ll!x+d@vYiLL(rDiy{10L2wJgK7(>%{8yYfY2 zf~CMJXM)%g@XB@7jA6o3!G2T(_s*I>G|fbJ{J;uB(-L~^mVyJf4fJ$hXxHsVQy0qJ^`l% z(Y&P&K;T*;Qz5}-+q4Tt_oF0;l-Mw4Z`&xMIsK6_zKt%i*7UpTi$2uB|g> zmSSw+WZ$ht<43s4fQXGOsbdjVLuO+^By3>;g?M zZN3}1F(ZH{SY1dix?f2t%d#7xAk(JzrR3eKa1YJvs;xZ|S~BO_N(!_MtL zU|emgCK}l7h4J>5uyI42f`Na@4;$zrYN7uMJR-<{g@yY+72x25+sOYTA)^0_!vD8E zCZnH3((!-Wq)ZHwO7hE;{v!%bU*`KI5&a~@{}ssa|Ea*n2mOx(Q$lJ+y#W82LOw5R z8|pmNf7KTf`Y}jwDE^}%;%?^jrwr-8ld2#Kp%eX|o|Oo2@Dr6t|I??M= 2 from st_dumppoints(bend)) then - bends = bends || bend; - end if; - - if dbgname is not null then - for i in 1..array_length(bends, 1) loop - insert into wm_debug(stage, name, gen, nbend, way) values( - 'bbends', dbgname, dbggen, i, bends[i]); - - dbgpolygon = null; - if st_npoints(bends[i]) >= 3 then - dbgpolygon = st_makepolygon( - st_addpoint(bends[i], st_startpoint(bends[i])) - ); - end if; - insert into wm_debug(stage, name, gen, nbend, way) values( - 'bbends-polygon', dbgname, dbggen, i, dbgpolygon); - end loop; - end if; -end $$ language plpgsql; - --- wm_fix_gentle_inflections moves bend endpoints following "Gentle Inflection --- at End of a Bend" section. --- --- The text does not specify how many vertices can be "adjusted"; it can --- equally be one or many. This function is adjusting many, as long as the --- cumulative inflection angle is small (see variable below). --- --- The implementation could be significantly optimized to avoid `st_reverse` --- and array reversals, trading for complexity in wm_fix_gentle_inflections1. -drop function if exists wm_fix_gentle_inflections; -create function wm_fix_gentle_inflections( - INOUT bends geometry[], - dbgname text default null, - dbggen integer default null -) as $$ -declare - len int4; - bends1 geometry[]; - dbgpolygon geometry; -begin - len = array_length(bends, 1); - - bends = wm_fix_gentle_inflections1(bends); - for i in 1..len loop - bends1[i] = st_reverse(bends[len-i+1]); - end loop; - bends1 = wm_fix_gentle_inflections1(bends1); - - for i in 1..len loop - bends[i] = st_reverse(bends1[len-i+1]); - end loop; - - if dbgname is not null then - for i in 1..array_length(bends, 1) loop - insert into wm_debug(stage, name, gen, nbend, way) values( - 'cinflections', dbgname, dbggen, i, bends[i]); - - dbgpolygon = null; - if st_npoints(bends[i]) >= 3 then - dbgpolygon = st_makepolygon( - st_addpoint(bends[i], - st_startpoint(bends[i])) - ); - end if; - - insert into wm_debug(stage, name, gen, nbend, way) values( - 'cinflections-polygon', dbgname, dbggen, i, dbgpolygon); - end loop; - end if; -end $$ language plpgsql; - --- wm_fix_gentle_inflections1 fixes gentle inflections of an array of lines in --- one direction. An implementation detail of wm_fix_gentle_inflections. -drop function if exists wm_fix_gentle_inflections1; -create function wm_fix_gentle_inflections1(INOUT bends geometry[]) as $$ -declare - -- the threshold when the angle is still "small", so gentle inflections can - -- be joined - small_angle constant real default radians(45); - ptail geometry; -- tail point of tail bend - phead geometry[]; -- 3 tail points of head bend - i int4; -- bends[i] is the current head -begin - for i in 2..array_length(bends, 1) loop - -- Predicate: two bends will always share an edge. Assuming (A,B,C,D,E,F) - -- is a bend: - -- C________D - -- / \ - -- \________/ \_______/ - -- A B E F - -- - -- Then edges (A,B) and (E,F) are shared with the neighboring bends. - -- - -- - -- Assume this curve (figure `inflection-1`), going clockwise from A: - -- - -- \______B - -- A `-------. C - -- | - -- G___ F | - -- / `-----.____+ D - -- E - -- - -- After processing the curve following the definition of a bend, the bend - -- [A-E] would be detected. Assuming inflection point E and F are "small", - -- the bend needs to be extended by two edges to [A,G]. - select geom from st_dumppoints(bends[i-1]) - order by path[1] asc limit 1 into ptail; - - while true loop - -- copy last 3 points of bends[i-1] (tail) to ptail - select array( - select geom from st_dumppoints(bends[i]) order by path[1] asc limit 3 - ) into phead; - - -- if the bend got too short, stop processing it - exit when array_length(phead, 1) < 3; - - -- inflection angle between ptail[1:3] is "large", stop processing - exit when abs(st_angle(phead[1], phead[2], phead[3]) - pi()) > small_angle; - - -- distance from head's 1st vertex should be larger than from 2nd vertex - exit when st_distance(ptail, phead[2]) < st_distance(ptail, phead[3]); - - -- Between two bends, bend with smaller baseline wins when two - -- neighboring bends can have gentle inflections. This is a heuristic - -- that can be safely removed, but in practice has shown to avoid - -- creating some very bendy lines. - exit when st_distance(st_pointn(bends[i], 1), st_pointn(bends[i], -1)) < - st_distance(st_pointn(bends[i-1], 1), st_pointn(bends[i-1], -1)); - - -- Detected a gentle inflection. - -- Move head of the tail to the tail of head - bends[i] = st_removepoint(bends[i], 0); - bends[i-1] = st_addpoint(bends[i-1], phead[3]); - end loop; - - end loop; -end $$ language plpgsql; - --- wm_if_selfcross returns whether baseline of bendi crosses bendj. --- If it doesn't, returns a null geometry. --- Otherwise, it will return the baseline split into a few parts where it --- crosses bendj. -drop function if exists wm_if_selfcross; -create function wm_if_selfcross( - bendi geometry, - bendj geometry -) returns geometry as $$ -declare - a geometry; - b geometry; - multi geometry; -begin - a = st_pointn(bendi, 1); - b = st_pointn(bendi, -1); - multi = st_split(bendj, st_makeline(a, b)); - - if st_numgeometries(multi) = 1 then - return null; - end if; - - if st_numgeometries(multi) = 2 and - (st_contains(bendj, a) or st_contains(bendj, b)) then - return null; - end if; - - return multi; -end $$ language plpgsql; - --- wm_self_crossing eliminates self-crossing from the bends, following the --- article's section "Self-line Crossing When Cutting a Bend". -drop function if exists wm_self_crossing; -create function wm_self_crossing( - INOUT bends geometry[], - dbgname text default null, - dbggen integer default null, - OUT mutated boolean -) as $$ -declare - i int4; - j int4; - multi geometry; -begin - mutated = false; - <> - for i in 1..array_length(bends, 1) loop - continue when abs(wm_inflection_angle(bends[i])) <= pi(); - -- sum of inflection angles for this bend is >180, so it may be - -- self-crossing. Now try to find another bend in this line that - -- crosses an imaginary line of end-vertices - - -- Go through each bend in the given line, and see if has a potential to - -- cross bends[i]. The line-cut process is different when ij; - -- therefore there are two loops, one for each case. - for j in 1..i-1 loop - multi = wm_if_selfcross(bends[i], bends[j]); - continue when multi is null; - mutated = true; - - -- remove first vertex of the following bend, because the last - -- segment is always duplicated with the i'th bend. - bends[i+1] = st_removepoint(bends[i+1], 0); - bends[j] = st_geometryn(multi, 1); - bends[j] = st_setpoint( - bends[j], - st_npoints(bends[j])-1, - st_pointn(bends[i], st_npoints(bends[i])) - ); - bends = bends[1:j] || bends[i+1:]; - continue bendloop; - end loop; - - for j in reverse array_length(bends, 1)..i+1 loop - multi = wm_if_selfcross(bends[i], bends[j]); - continue when multi is null; - mutated = true; - - -- remove last vertex of the previous bend, because the last - -- segment is duplicated with the i'th bend. - bends[i-1] = st_removepoint(bends[i-1], st_npoints(bends[i-1])-1); - bends[i] = st_makeline( - st_pointn(bends[i], 1), - st_removepoint(st_geometryn(multi, st_numgeometries(multi)), 0) - ); - bends = bends[1:i] || bends[j+1:]; - continue bendloop; - end loop; - end loop; - - if dbgname is not null then - insert into wm_debug(stage, name, gen, nbend, way) values( - 'dcrossings', dbgname, dbggen, generate_subscripts(bends, 1), - unnest(bends) - ); - end if; -end $$ language plpgsql; - -drop function if exists wm_inflection_angle; -create function wm_inflection_angle (IN bend geometry, OUT angle real) as $$ -declare - p0 geometry; - p1 geometry; - p2 geometry; - p3 geometry; -begin - angle = 0; - for p0 in select geom from st_dumppoints(bend) order by path[1] asc loop - p3 = p2; - p2 = p1; - p1 = p0; - continue when p3 is null; - angle = angle + abs(pi() - st_angle(p1, p2, p3)); - end loop; -end $$ language plpgsql; - -drop function if exists wm_bend_attrs; -drop function if exists wm_elimination; -drop function if exists wm_exaggeration; -drop type if exists wm_t_attrs; -create type wm_t_attrs as ( - adjsize real, - baselinelength real, - curvature real, - isolated boolean -); -create function wm_bend_attrs( - bends geometry[], - dbgname text default null, - dbggen integer default null -) returns wm_t_attrs[] as $$ -declare - isolation_threshold constant real default 0.5; - attrs wm_t_attrs[]; - attr wm_t_attrs; - bend geometry; - i int4; - needs_curvature real; - skip_next boolean; - dbglastid integer; -begin - for i in 1..array_length(bends, 1) loop - bend = bends[i]; - attr.adjsize = 0; - attr.baselinelength = st_distance(st_startpoint(bend), st_endpoint(bend)); - attr.curvature = wm_inflection_angle(bend) / st_length(bend); - attr.isolated = false; - if st_numpoints(bend) >= 3 then - attr.adjsize = wm_adjsize(bend); - end if; - attrs[i] = attr; - end loop; - - for i in 1..array_length(attrs, 1) loop - if dbgname is not null then - insert into wm_debug (stage, name, gen, nbend, way, props) values( - 'ebendattrs', dbgname, dbggen, i, bends[i], - jsonb_build_object( - 'adjsize', attrs[i].adjsize, - 'baselinelength', attrs[i].baselinelength, - 'curvature', attrs[i].curvature, - 'isolated', false - ) - ) returning id into dbglastid; - end if; - - -- first and last bends can never be isolated by definition - if skip_next or i = 1 or i = array_length(attrs, 1) then - -- invariant: two bends that touch cannot be isolated. - if st_npoints(bends[i]) > 3 then - skip_next = false; - end if; - continue; - end if; - - needs_curvature = attrs[i].curvature * isolation_threshold; - if attrs[i-1].curvature < needs_curvature and - attrs[i+1].curvature < needs_curvature then - attr = attrs[i]; - attr.isolated = true; - attrs[i] = attr; - skip_next = true; - - if dbgname is not null then - update wm_debug - set props=props || jsonb_build_object('isolated', true) - where id=dbglastid; - end if; - end if; - end loop; - - return attrs; -end $$ language plpgsql; - --- sm_st_split a line by a point in a more robust way than st_split. --- See https://trac.osgeo.org/postgis/ticket/2192 -drop function if exists wm_st_split; -create function wm_st_split( - input geometry, - blade geometry -) returns geometry as $$ -declare - type1 text; - type2 text; -begin - type1 = st_geometrytype(input); - type2 = st_geometrytype(blade); - if not (type1 = 'ST_LineString' and - type2 = 'ST_Point') then - raise 'Arguments must be LineString and Point, got: % and %', type1, type2; - end if; - return st_split(st_snap(input, blade, 0.00000001), blade); -end $$ language plpgsql; - --- wm_exaggerate_bend2 is the second version of bend exaggeration. Uses --- non-linear interpolation by point azimuth. Slower, but produces nicer --- exaggerated geometries. -drop function if exists wm_exaggerate_bend2; -create function wm_exaggerate_bend2( - INOUT bend geometry, - size float, - desired_size float -) as $$ -declare - scale2 constant float default 1.2; -- exaggeration enthusiasm - midpoint geometry; -- midpoint of the baseline - points geometry[]; - startazimuth float; - azimuth float; - diffazimuth float; - point geometry; - sss float; - protect int = 10; -begin - if size = 0 then - raise 'invalid input: zero-area bend'; - end if; - midpoint = st_lineinterpolatepoint(st_makeline( - st_pointn(bend, 1), - st_pointn(bend, -1) - ), .5); - startazimuth = st_azimuth(midpoint, st_pointn(bend, 1)); - - while (size < desired_size) and (protect > 0) loop - protect = protect - 1; - for i in 2..st_npoints(bend)-1 loop - point = st_pointn(bend, i); - azimuth = st_azimuth(midpoint, point); - diffazimuth = degrees(azimuth - startazimuth); - if diffazimuth > 180 then - diffazimuth = diffazimuth - 360; - elseif diffazimuth < -180 then - diffazimuth = diffazimuth + 360; - end if; - diffazimuth = abs(diffazimuth); - if diffazimuth > 90 then - diffazimuth = 180 - diffazimuth; - end if; - sss = ((scale2-1) * (diffazimuth / 90)^0.5); - point = st_transform( - st_project( - st_transform(point, 4326)::geography, - st_distance(midpoint, point) * sss, azimuth)::geometry, - st_srid(midpoint) - ); - bend = st_setpoint(bend, i-1, point); - end loop; - size = wm_adjsize(bend); - end loop; -end $$ language plpgsql; - --- wm_exaggerate_bend exaggerates a given bend. Uses naive linear --- interpolation. Faster than wm_exaggerate_bend2, but result visually looks --- worse. -drop function if exists wm_exaggerate_bend; -create function wm_exaggerate_bend( - INOUT bend geometry, - size float, - desired_size float -) as $$ -declare - scale constant float default 1.2; -- exaggeration enthusiasm - midpoint geometry; -- midpoint of the baseline - splitbend geometry; -- bend split across its half - bendm geometry; -- bend with coefficients to prolong the lines - points geometry[]; -begin - if size = 0 then - raise 'invalid input: zero-area bend'; - end if; - midpoint = st_lineinterpolatepoint(st_makeline( - st_pointn(bend, 1), - st_pointn(bend, -1) - ), .5); - - while size < desired_size loop - splitbend = wm_st_split(bend, st_lineinterpolatepoint(bend, .5)); - -- Convert bend to LINESTRINGM, where M is the fraction by how - -- much the point will be prolonged: - -- 1. draw a line between midpoint and the point on the bend. - -- 2. multiply the line length by M. Midpoint stays intact. - -- 3. the new set of lines form a new bend. - -- Uses linear interpolation; can be updated to gaussian or similar; - -- then interpolate manually instead of relying on st_addmeasure. - bendm = st_collect( - st_addmeasure(st_geometryn(splitbend, 1), 1, scale), - st_addmeasure(st_geometryn(splitbend, 2), scale, 1) - ); - - points = array(( - select st_scale( - st_makepoint(st_x(geom), st_y(geom)), - st_makepoint(st_m(geom), st_m(geom)), - midpoint - ) - from st_dumppoints(bendm) - order by path[1], path[2] - )); - - bend = st_setsrid(st_makeline(points), st_srid(bend)); - size = wm_adjsize(bend); - end loop; -end $$ language plpgsql; - - --- wm_adjsize calculates adjusted size for a polygon. Can return 0. -drop function if exists wm_adjsize; -create function wm_adjsize(bend geometry, OUT adjsize float) as $$ -declare - polygon geometry; - area float; - cmp float; -begin - adjsize = 0; - polygon = st_makepolygon(st_addpoint(bend, st_startpoint(bend))); - -- Compactness Index (cmp) is defined as "the ratio of the area of the - -- polygon over the circle whose circumference length is the same as the - -- length of the circumference of the polygon". I assume they meant the - -- area of the circle. So here goes: - -- 1. get polygon area P. - -- 2. get polygon perimeter = u. Pretend it's our circle's circumference. - -- 3. get A (area) of the circle from u: A = u^2/(4pi) - -- 4. divide P by A: cmp = P/A = P/(u^2/(4pi)) = 4pi*P/u^2 - area = st_area(polygon); - cmp = 4*pi()*area/(st_perimeter(polygon)^2); - if cmp > 0 then - adjsize = (area*(0.75/cmp)); - end if; -end $$ language plpgsql; - --- wm_exaggeration is the Exaggeration Operator described in the WM paper. -create function wm_exaggeration( - INOUT bends geometry[], - attrs wm_t_attrs[], - dhalfcircle float, - intersect_patience integer, - dbgname text default null, - dbggen integer default null, - OUT mutated boolean -) as $$ -declare - desired_size constant float default pi()*(dhalfcircle^2)/8; - bend geometry; - tmpint geometry; - i integer; - n integer; - last_id integer; -begin - mutated = false; - <> - for i in 1..array_length(attrs, 1) loop - if attrs[i].isolated and attrs[i].adjsize < desired_size then - bend = wm_exaggerate_bend2(bends[i], attrs[i].adjsize, desired_size); - -- Does bend intersect with the previous or next - -- intersect_patience bends? If they do, abort exaggeration for this one. - - -- Do close-by bends intersect with this one? Special - -- handling first, because 2 vertices need to be removed before checking. - n = st_npoints(bends[i-1]); - if n > 3 then - continue when st_intersects(bend, - st_removepoint(st_removepoint(bends[i-1], n-1), n-2)); - end if; - if n > 2 then - tmpint = st_intersection(bend, st_removepoint(bends[i-1], n-1)); - continue when st_npoints(tmpint) > 1; - end if; - - n = st_npoints(bends[i+1]); - if n > 3 then - continue when st_intersects(bend, - st_removepoint(st_removepoint(bends[i+1], 0), 0)); - end if; - if n > 2 then - tmpint = st_intersection(bend, st_removepoint(bends[i+1], 0)); - continue when st_npoints(tmpint) > 1; - end if; - - for n in -intersect_patience+1..intersect_patience-1 loop - continue when n in (-1, 0, 1); - continue when i+n < 1; - continue when i+n > array_length(attrs, 1); - - -- More special handling: if the neigbhoring bend has 3 vertices, the - -- neighbor's neighbor may just touch the tmpbendattr.bend; in this - -- case, the nearest vertex should be removed before comparing. - tmpint = bends[i+n]; - if st_npoints(tmpint) > 2 then - if n = -2 and st_npoints(bends[i+n+1]) = 3 then - tmpint = st_removepoint(tmpint, st_npoints(tmpint)-1); - elsif n = 2 and st_npoints(bends[i+n-1]) = 3 then - tmpint = st_removepoint(tmpint, 0); - end if; - end if; - - continue bendloop when st_intersects(bend, tmpint); - end loop; - - -- No intersections within intersect_patience, mutate bend! - mutated = true; - bends[i] = bend; - - -- remove last vertex of the previous bend and first vertex of the next - -- bend, because bends always share a line segment together this is - -- duplicated in a few places, because PostGIS does not allow (?) - -- mutating an array when passed to a function. - bends[i-1] = st_addpoint( - st_removepoint(bends[i-1], st_npoints(bends[i-1])-1), - st_pointn(bends[i], 1), - -1 - ); - - bends[i+1] = st_addpoint( - st_removepoint(bends[i+1], 0), - st_pointn(bends[i], st_npoints(bends[i])-1), - 0 - ); - if dbgname is not null then - insert into wm_debug (stage, name, gen, nbend, way) values( - 'gexaggeration', dbgname, dbggen, i, bends[i]); - end if; - end if; - end loop; -end $$ language plpgsql; - -create function wm_elimination( - INOUT bends geometry[], - attrs wm_t_attrs[], - dhalfcircle float, - dbgname text default null, - dbggen integer default null, - OUT mutated boolean -) as $$ -declare - desired_size constant float default pi()*(dhalfcircle^2)/8; - leftsize float; - rightsize float; - i int4; -begin - mutated = false; - - i = 1; - while i < array_length(attrs, 1)-1 loop - i = i + 1; - continue when attrs[i].adjsize = 0; - continue when attrs[i].adjsize > desired_size; - - if i = 2 then - leftsize = attrs[i].adjsize + 1; - else - leftsize = attrs[i-1].adjsize; - end if; - - if i = array_length(attrs, 1)-1 then - rightsize = attrs[i].adjsize + 1; - else - rightsize = attrs[i+1].adjsize; - end if; - - continue when attrs[i].adjsize >= leftsize; - continue when attrs[i].adjsize >= rightsize; - - -- Local minimum. Elminate bend! - mutated = true; - bends[i] = st_makeline(st_pointn(bends[i], 1), st_pointn(bends[i], -1)); - - -- remove last vertex of the previous bend and - -- first vertex of the next bend, because bends always - -- share a line segment together - bends[i-1] = st_addpoint( - st_removepoint(bends[i-1], st_npoints(bends[i-1])-1), - st_pointn(bends[i], 1), - -1 - ); - - bends[i+1] = st_addpoint( - st_removepoint(bends[i+1], 0), - st_pointn(bends[i], st_npoints(bends[i])-1), - 0 - ); - -- the next bend's adjsize is now messed up; it should not be taken - -- into consideration for other local minimas. Skip over 2. - i = i + 2; - end loop; - - if dbgname is not null then - insert into wm_debug(stage, name, gen, nbend, way) values( - 'helimination', - dbgname, - dbggen, - generate_subscripts(bends, 1), - unnest(bends) - ); - end if; -end $$ language plpgsql; - - -drop function if exists ST_SimplifyWM_Estimate; -create function ST_SimplifyWM_Estimate( - geom geometry, - OUT npoints bigint, - OUT secs bigint -) as $$ -declare - lines geometry[]; - l_type text; -begin - l_type = st_geometrytype(geom); - if l_type = 'ST_LineString' then - lines = array[geom]; - elseif l_type = 'ST_MultiLineString' then - lines = array((select a.geom from st_dump(geom) a order by path[1] asc)); - else - raise 'Unknown geometry type %', l_type; - end if; - - npoints = 0; - for i in 1..array_length(lines, 1) loop - npoints = npoints + st_numpoints(lines[i]); - end loop; - secs = npoints / 33; -end $$ language plpgsql; - --- ST_SimplifyWM simplifies a given geometry using Wang & Müller's --- "Line Generalization Based on Analysis of Shape Characteristics" algorithm, --- 1998. --- Input parameters: --- - geom: ST_LineString or ST_MultiLineString: the geometry to be simplified --- - dhalfcircle: the diameter of a half-circle, whose area is an approximate --- threshold for small bend elimination. If bend's area is larger than that, --- the bend will be left alone. -drop function if exists ST_SimplifyWM; -create function ST_SimplifyWM( - geom geometry, - dhalfcircle float, - intersect_patience integer default 10, - dbgname text default null -) returns geometry as $$ -declare - gen integer; - i integer; - j integer; - line geometry; - lines geometry[]; - bends geometry[]; - attrs wm_t_attrs[]; - mutated boolean; - l_type text; -begin - if intersect_patience is null then - intersect_patience = 10; - end if; - l_type = st_geometrytype(geom); - if l_type = 'ST_LineString' then - lines = array[geom]; - elseif l_type = 'ST_MultiLineString' then - lines = array((select a.geom from st_dump(geom) a order by path[1] asc)); - else - raise 'Unknown geometry type %', l_type; - end if; - - <> - for i in 1..array_length(lines, 1) loop - mutated = true; - gen = 1; - - while mutated loop - - if dbgname is not null then - insert into wm_debug (stage, name, gen, nbend, way) values( - 'afigures', dbgname, gen, i, lines[i]); - end if; - - bends = wm_detect_bends(lines[i], dbgname, gen); - bends = wm_fix_gentle_inflections(bends, dbgname, gen); - - select * from wm_self_crossing(bends, dbgname, gen) into bends, mutated; - if not mutated then - attrs = wm_bend_attrs(bends, dbgname, gen); - - select * from wm_exaggeration(bends, attrs, - dhalfcircle, intersect_patience, dbgname, gen) into bends, mutated; - end if; - - -- TODO: wm_combination - - if not mutated then - select * from wm_elimination(bends, attrs, - dhalfcircle, dbgname, gen) into bends, mutated; - end if; - - if mutated then - lines[i] = st_linemerge(st_union(bends)); - - if st_geometrytype(lines[i]) != 'ST_LineString' then - -- For manual debugging: - --insert into wm_manual(name, way) - --select 'non-linestring-' || a.path[1], a.geom - --from st_dump(lines[i]) a - --order by a.path[1]; - raise '[%] Got % (in %) instead of ST_LineString. ' - 'Does the exaggerated bend intersect with the line? ' - 'If so, try increasing intersect_patience.', - gen, st_geometrytype(lines[i]), dbgname; - --exit lineloop; - end if; - gen = gen + 1; - continue; - end if; - end loop; - end loop; - - if l_type = 'ST_LineString' then - return st_linemerge(st_union(lines)); - elseif l_type = 'ST_MultiLineString' then - return st_union(lines); - end if; -end $$ language plpgsql;