commit c8f40e18025443ddd8a704790890b896c127b8c5 (tree)
parent 0e5289a44ffedb637dc021559650a4f3491b116c
Author: Motiejus Jakštys <motiejus@uber.com>
Date: Mon, 3 May 2021 15:42:33 +0300
use degrees where possible
Diffstat:
2 files changed, 14 insertions(+), 36 deletions(-)
diff --git a/IV/bib.bib b/IV/bib.bib
@@ -202,7 +202,6 @@
month={1},
day={26},
url={http://www.e-cartouche.ch/content_reg/cartouche/cartdesign/en/html/GenRules_learningObject3.html},
- organization={CartouCHe},
urldate={2021-05-03},
}
diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex
@@ -1,15 +1,15 @@
\documentclass[a4paper]{article}
-\usepackage[T1,T2A]{fontenc} % T2A is for Cyrillic characters
+\usepackage[T1]{fontenc}
\usepackage[american]{babel}
\usepackage[utf8]{inputenc}
-\usepackage [autostyle, english=american]{csquotes}
+\usepackage [autostyle,english=american]{csquotes}
\MakeOuterQuote{"}
\usepackage[maxbibnames=99,style=numeric,sorting=none,alldates=edtf]{biblatex}
\addbibresource{bib.bib}
\usepackage[
pdfusetitle,
- pdfkeywords={Line Generalization,Cartographic Line Generalization,Wang--Mueller},
+ pdfkeywords={Line Generalization,Line Simplification,Wang--Mueller},
pdfborderstyle={/S/U/W 0} % /S/U/W 1 to enable reasonable decorations
]{hyperref}
\usepackage{enumitem}
@@ -29,6 +29,8 @@
%\usepackage{setspace}
%\doublespacing
+\input{version.inc}
+\input{vars.inc}
\IfFileExists{./editorial-version}{\def \mjEditorial {}}{}
\ifx \mjEditorial \undefined
\usepackage{minted}
@@ -38,10 +40,6 @@
\newcommand{\inputcode}[2]{\verbatiminput{#2}}
\fi
-\input{version.inc}
-\input{vars.inc}
-
-
\newcommand{\onpage}[1]{\ref{#1} on page~\pageref{#1}}
\newcommand{\titlecite}[1]{\citetitle{#1}\cite{#1}}
\newcommand{\DP}{Douglas \& Peucker}
@@ -50,7 +48,7 @@
\newcommand{\WnM}{Wang and M{\"u}ller}
% {\WM} algoritmo realizacija kartografinei upių generalizacijai
\newcommand{\MYTITLE}{{\WM} algorithm realization for cartographic line generalization}
-\newcommand{\MYTITLESC}{wang--m{\"u}ller algorithm realization for cartographic line generalization}
+\newcommand{\MYTITLENOCAPS}{wang--m{\"u}ller algorithm realization for cartographic line generalization}
\newcommand{\MYAUTHOR}{Motiejus Jakštys}
\title{\MYTITLE}
@@ -76,7 +74,7 @@
A thesis presented for the degree of Master in Cartography \\[8ex]
\LARGE
- \textbf{\textsc{\MYTITLESC}}
+ \textbf{\textsc{\MYTITLENOCAPS}}
\vfill
@@ -444,25 +442,6 @@ This section defines vocabulary and terms as defined in the rest of the paper.
\end{description}
-\subsection{Radians and Degrees}
-
-This document contains a few constant angles expressed in radians.
-Table~\ref{table:radians} summarizes some of the values used in this document
-and the implementation.
-
-\begin{table}[h]
- \centering
- \begin{tabular}{|c|c|c|c|c|c|c|}
- \hline
- Degrees & $30^\circ$ & $45^\circ$ & $90^\circ$ & $180^\circ$ & $360^\circ$ \\
- \hline
- Radians & $\nicefrac{\pi}{6}$ & $\nicefrac{\pi}{4}$ & $\nicefrac{\pi}{2}$ & $\pi$ & $2\pi$ \\
- \hline
- \end{tabular}
- \caption{Some angular degree and radian values mentioned in this article.}
- \label{table:radians}
-\end{table}
-
\subsection{Automated tests}
\label{sec:automated-tests}
@@ -771,13 +750,13 @@ 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 with the number of vertices.
-It is possible to optimize this step and skip checking most of the bends. Only
-bends whose sum of inner angles is larger than $\pi$ can ever self-cross. If
-the value is less than $\pi$, it cannot cross other bends. 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 $\pi$, but, assuming no
-more than $20\%$ of the bends' inner angles are larger than $\pi$, the time it
-takes to run this piece of the algorithm drops by $80\%$.
+It is possible to optimize this step and skip checking a large number of bends.
+Only bends whose sum of inner angles 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) is drops by the
+fraction of bends whose sum of inner angles is smaller than $180^\circ$.
\subsection{Attributes of a Single Bend}
