test harness

bib.bib

@@ -228,3 +228,24 @@
   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},
+}

mj-msc.tex

@@ -909,11 +909,20 @@ When debug mode is turned off (that is, \textsc{dbgname} is left unspecified),
 
 \subsection{Merging pieces of the river into one}
 
-% TODO
+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.
 
-NOTE: explain how different river segments are merged into a single line. This
+Since these rivers do not have an explicit relationship to connect them
-is not explained in the {\WM} paper, but is a necessary prerequisite. This is
+together, they were connected using heuristics: if two line segments share a
-implemented in \textsc{aggregate-rivers.sql}.
+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 listings~\onpage{lst:aggregate-rivers.sql}.
 
 \subsection{Bend scaling and dimensions}
 \label{sec:bend-scaling-and-dimensions}
@@ -1002,7 +1011,7 @@ but with bends colored as polygons: each color is a distinctive bend.
     \centering
     \includegraphics[width=\textwidth]{fig8-definition-of-a-bend}
 
-    \caption{similar to figure 8 in \cite{wang1998line}: detected bends are
+    \caption{Similar to figure 8 in \cite{wang1998line}: detected bends are
     highlighted.}
 
     \label{fig:fig8-definition-of-a-bend}
@@ -1031,7 +1040,7 @@ when a single vertex is moved outwards the end of the bend.
         \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
+    \caption{Figure 5 in \cite{wang1998line}: gentle inflections at the ends of
     the bend.}
     \label{fig:fig5-gentle-inflection}
 \end{figure}
@@ -1347,7 +1356,8 @@ isolated bends are exaggerated, and some small bends are removed.
     \label{fig:salvis-wm-220-250k}
 \end{figure}
 
-% TODO: expand
+% TODO: expand section and remove clear-page.
+\clearpage
 
 \subsection{Generalization result comparison with national spatial data sets}
 
@@ -1355,9 +1365,28 @@ isolated bends are exaggerated, and some small bends are removed.
 
 \subsection{Testing results online}
 
-% TODO: [Siūlau įdėti nuorodą į web app, kur būtų galima interaktyviai
+An on-line tool\cite{openmapwm} has been developed to test incoming parameters
-% pastestuoti rezultatus. Jeigu planuotum dėti, tuomet galima nedidelį poskyrį
+to {\WM} algorithm. A user should select a river of interest, enter the
-% pridėti Testing Results]
+\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}

vars.awk

@@ -10,7 +10,7 @@ BEGIN { FS="[(); ]" }
   x2 += 1;
   d2 = sprintf("\\newcommand{\\isolationThreshold}{%.1f}",$7);
 }
-/scale constant float default / {
+/scale2 constant float default / {
   x3 += 1;
   d3 = sprintf("\\newcommand{\\exaggerationEnthusiasm}{%.1f}",$7);
 }

wm.sql

@@ -417,7 +417,9 @@ begin
   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,
@@ -425,7 +427,7 @@ create function wm_exaggerate_bend2(
   desired_size float
 ) as $$
 declare
-  scale constant float default 1.2; -- exaggeration enthusiasm
+  scale2 constant float default 1.2; -- exaggeration enthusiasm
   midpoint geometry; -- midpoint of the baseline
   points geometry[];
   startazimuth float;
@@ -459,7 +461,7 @@ begin
       if diffazimuth > 90 then
         diffazimuth = 180 - diffazimuth;
       end if;
-      sss = ((scale-1) * (diffazimuth / 90)^0.5);
+      sss = ((scale2-1) * (diffazimuth / 90)^0.5);
       point = st_transform(
         st_project(
           st_transform(point, 4326)::geography,
@@ -472,6 +474,60 @@ begin
   end loop;
 end $$ 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 $$