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additional gentle-inflection illustration

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Motiejus Jakštys 2021-05-19 22:57:47 +03:00 committed by Motiejus Jakštys
parent b2f2299c44
commit ff1860da87
2 changed files with 80 additions and 31 deletions
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23
Makefile
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@ -7,7 +7,9 @@ NON_ARCHIVABLES = notes.txt referatui.txt slides-2021-03-29.txt
ARCHIVABLES = $(filter-out $(NON_ARCHIVABLES),$(shell git ls-files .))
FIGURES = fig8-definition-of-a-bend.pdf \
fig5-gentle-inflection-before.pdf \
fig5-gentle-inflection-after.pdf
fig5-gentle-inflection-after.pdf \
inflection-1-gentle-inflection-before.pdf \
inflection-1-gentle-inflection-after.pdf
.PHONY: test
test: .faux_test
@ -89,6 +91,25 @@ fig5-gentle-inflection-after.pdf: layer2img.py Makefile .faux_test
--group2-where="name='fig5' AND stage='cinflections-polygon' AND gen=1" \
--outfile=$@
inflection-1-gentle-inflection-before.pdf: layer2img.py Makefile .faux_test
python ./layer2img.py \
--group1-table=wm_debug \
--group1-where="name='inflection-1' AND stage='bbends' AND gen=1" \
--group2-cmap=1 \
--group2-table=wm_debug \
--group2-where="name='inflection-1' AND stage='bbends-polygon' AND gen=1" \
--outfile=$@
inflection-1-gentle-inflection-after.pdf: layer2img.py Makefile .faux_test
python ./layer2img.py \
--group1-table=wm_debug \
--group1-where="name='inflection-1' AND stage='cinflections' AND gen=1" \
--group2-cmap=1 \
--group2-table=wm_debug \
--group2-where="name='inflection-1' AND stage='cinflections-polygon' AND gen=1" \
--outfile=$@
.faux_test: tests.sql wm.sql .faux_db
./db -f tests.sql
touch $@

88
mj-msc.tex
View File

@ -185,12 +185,43 @@ The original \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 \cite{wang1998line}. Therefore familiarity with the
original paper is assumed, and, for some sections, having it close-by is
necessary to meaningfully follow this document.
In this paper we describe {\WM} in a detail that is more useful for algorithm:
each section will be expanded, with more elaborate and exact illustrations for
every step of the algorithm.
Algorithms discussed in this paper assume Euclidean geometry.
\section{Vocabulary and terminology}
This section defines vocabulary and terms as defined in the rest of the paper.
\begin{description}
\item[Vertex] is a point on a plane, can be expressed by a pair of $(x,y)$
coordinates.
\item[Line Segment (or 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[Line] represents a single linear feature in the real world. For
example, a river or a coastline. {\tt LINESTRING} in GIS terms.
Geometrically, A line is a series of connected line segments, or,
equivalently, a series of connected vertices. Each vertex connects to
two other vertices, except those vertices at either ends of the line:
these two connect to a single other vertex.
\item[Bend] is a subset of a line that humans perceive as a curve. For the
purpose of this paper, the geometric definition is complex and is
discussed in section~\onpage{sec:definition-of-a-bend}.
\end{description}
\section{Automated tests}
\label{sec:automated-tests}
@ -215,31 +246,6 @@ The full test suite can be executed with a single command, and completes in a
few seconds. Having an easily accessible test suite boosts confidence that no
unexpected bugs have snug in while modifying the algorithm.
\section{Vocabulary and terminology}
This section defines vocabulary and terms as defined in the rest of the paper.
\begin{description}
\item[Vertex] is a point on a plane, can be expressed unambiguously by a
pair of $(x,y)$ coordinates.
\item[Line Segment (or 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[Line] represents a single linear feature in the real world. For
example, a river or a coastline. {\tt LINESTRING} in GIS terms.
Geometrically, A line is a series of connected line segments, or,
equivalently, a series of connected vertices. Each vertex connects to
two other vertices, except those vertices at either ends of the line:
these two connect to a single other vertex.
\item[Bend] is a subset of a line that humans perceive as a curve. For the
purpose of this paper, the geometric definition is complex and is
discussed in section~\onpage{sec:definition-of-a-bend}.
\end{description}
\chapter{Description of the implementation}
Like alluded in section~\onpage{sec:introduction}, \cite{wang1998line} paper
@ -281,11 +287,8 @@ illustration of the detected bends.
\section{Gentle Inflection at End of a Bend}
The example in this section was clear, but insufficient: it does not specify
how many vertices should be included when calculating the end-of-bend
inflection. We chose the iterative approach -- as long as the angle is "right"
and the distance is decreasing, the algorithm should keep going; practically
not having an upper bound on the number of iterations.
Figure~\ref{fig:fig5-gentle-inflection} visualizes original paper's Figure 5,
when a single vertex is moved outwards the end of the bend.
\begin{figure}[h]
\centering
@ -302,6 +305,31 @@ not having an upper bound on the number of iterations.
\label{fig:fig5-gentle-inflection}
\end{figure}
The example in this section was clear, but insufficient: it does not specify
how many vertices should be included when calculating the end-of-bend
inflection. We chose the iterative approach -- as long as the angle is "right"
and the distance is decreasing, the algorithm should keep going; practically
not having an upper bound on the number of iterations.
Additional example, not found in the original paper, is illustrated in
figure~\onpage{fig:inflection-1-gentle-inflection}: it moves a few vertices.
\begin{figure}[h]
\centering
\begin{subfigure}[b]{.45\textwidth}
\includegraphics[width=\textwidth]{inflection-1-gentle-inflection-before}
\caption{Before applying the inflection rule}
\end{subfigure}
\hfill
\begin{subfigure}[b]{.45\textwidth}
\includegraphics[width=\textwidth]{inflection-1-gentle-inflection-after}
\caption{After applying the inflection rule}
\end{subfigure}
\caption{Originally Figure 5: gentle inflections at the ends of the bend}
\label{fig:inflection-1-gentle-inflection}
\end{figure}
\section{Self-line Crossing When Cutting a Bend}
\section{Attributes of a Single Bend}