From 0ee48680591b8d011dfcac40618df0bdbcff0f85 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Motiejus=20Jak=C5=A1tys?= Date: Mon, 12 Apr 2021 13:33:51 +0300 Subject: [PATCH] additional gentle-inflection illustration --- IV/Makefile | 23 +++++++++++++- IV/mj-msc.tex | 88 +++++++++++++++++++++++++++++++++------------------ 2 files changed, 80 insertions(+), 31 deletions(-) diff --git a/IV/Makefile b/IV/Makefile index f4d2d87..19ccf44 100644 --- a/IV/Makefile +++ b/IV/Makefile @@ -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 $@ diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex index 57e2e15..bf78a4c 100644 --- a/IV/mj-msc.tex +++ b/IV/mj-msc.tex @@ -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}