motiejus/wm
1
Fork 0
Code Releases Activity

definitions

Browse Source
This commit is contained in:
Motiejus Jakštys 2021-05-19 22:57:47 +03:00 committed by Motiejus Jakštys
parent 1d3e7c749c
commit 92f848e7a4
1 changed files with 43 additions and 14 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

57
mj-msc.tex
View File

@ -23,6 +23,8 @@
\definecolor{mypurple}{RGB}{117,112,179}
\input{version}
\newcommand{\onpage}[1]{\ref{#1} on page~\pageref{#1}}
\newcommand{\DP}{Douglas \& Peucker}
\newcommand{\VW}{Visvalingam--Whyatt}
\newcommand{\WM}{Wang--M{\"u}ller}
@ -187,6 +189,8 @@ 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{Automated tests}
As part of the algorithm realization, an automated test suite has been
@ -195,9 +199,9 @@ 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 geometry.
The full set of test geometries is visualized in figure~\ref{fig:test-figures}
on page~\pageref{fig:test-figures}. The figure includes arrows depicting
line direction.
The full set of test geometries is visualized in
figure~\onpage{fig:test-figures}. The figure includes arrows depicting line
direction.
\begin{figure}[H]
\centering
@ -210,12 +214,37 @@ 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 "bend". 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~\ref{sec:introduction}, \cite{wang1998line} 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 detailed description.
Like alluded in section~\onpage{sec:introduction}, \cite{wang1998line} 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 detailed description.
Step illustrations of the following sections are extracted from the automated
test cases.
@ -224,10 +253,11 @@ Bends are illustrated using the following algorithm:
\begin{itemize}
\item Join the first and last vertices of the line, creating a polygon.
\item Color the polygons using a diverging color scheme.
\item Color the polygons.
\end{itemize}
\section{Definition of a Bend}
\label{sec:definition-of-a-bend}
\begin{figure}[H]
\centering
@ -236,15 +266,14 @@ Bends are illustrated using the following algorithm:
\label{fig:fig8-definition-of-a-bend}
\end{figure}
End vertices of all lines should also be part of the bend. That way, all
vertices belong to 1 or 2 bends. This characteristic is not obvious when
End line segments of all lines should also be part of the bend. That way, all
line segments belong to 1 or 2 bends. This characteristic is not obvious when
reading the introductory sections, but becomes unavoidable (there could be no
other way) when reading the following sections in detail.
Last vertex of each bend (except for the two end-line vertices) is also the
first vertex of the next bend. This is apparent when looking at the
illustration of the detected bends. However, the original {\WM} paper did not
have such an explanation or illustration.
First and last segments of each bend (except for the two end-line segments) is
also the first vertex of the next bend. This is apparent when looking at the
illustration of the detected bends.
\section{Gentle Inflection at End of a Bend}