From 8cf79b422428593ef6ca8a1ef3115c48a0a9fa83 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Motiejus=20Jak=C5=A1tys?= <desired.mta@gmail.com>
Date: Mon, 25 May 2020 17:37:58 +0300
Subject: [PATCH] explain tolerances

---
 II/Referatas/mj-referatas.tex |  31 +++++++++++++++++++------------
 II/Referatas/zeimena.gpkg     | Bin 167936 -> 167936 bytes
 2 files changed, 19 insertions(+), 12 deletions(-)

diff --git a/II/Referatas/mj-referatas.tex b/II/Referatas/mj-referatas.tex
index 45e8a37..aeba9f7 100644
--- a/II/Referatas/mj-referatas.tex
+++ b/II/Referatas/mj-referatas.tex
@@ -6,6 +6,7 @@
 \usepackage[english]{babel}
 \usepackage[maxbibnames=99,style=authoryear]{biblatex}
 \usepackage[pdfusetitle]{hyperref}
+\usepackage{enumitem}
 \addbibresource{bib.bib}
 \usepackage{caption}
 \usepackage{subcaption}
@@ -16,6 +17,9 @@
 \usetikzlibrary{er,positioning}
 \input{version}
 
+\newcommand{\DP}{Douglas \& Peucker}
+\newcommand{\VW}{Visvalingam-Whyatt}
+
 \title{
     Cartografic Generalization of Lines \\
     (example of rivers) \\ \vspace{4mm}
@@ -28,8 +32,6 @@ http://bl.ocks.org/msbarry/9152218
 small scale: 1:XXXXXX
 large scale: 1:XXX
 
-take douglas-pecker and check for different scales.
-
 a4: 210x297mm
 a6: 105x148xmm
 a7: 74x105mm
@@ -41,15 +43,6 @@ connect rivers first to a single polylines:
 ideal hypothesis: mueller algorithm + topology may fully realize cartographic generalization tasks.
 
 what scales and what distances?
-
-https://postgis.net/docs/ST_SimplifyVW.html
-https://postgis.net/docs/ST_Simplify.html
-https://postgis.net/docs/ST_SimplifyPreserveTopology.html
-
-how is tolerance bound to scale?
-- just use same parameter.
-
-
 \fi
 
 \author{Motiejus Jakštys}
@@ -120,7 +113,7 @@ general public:
 
 For comparison reasons, this article will be using Lakaja and large part of Žeimena
 (see figure~\ref{fig:zeimena} on page~\pageref{fig:zeimena}). This location was
-chosen because it is a combination of straight and curved river shape,
+chosen because the river exhibits both both straight and curved shape, is a
 combination of two curly rivers, and author's familiarity with the location.
 
 \begin{figure}
@@ -132,6 +125,20 @@ combination of two curly rivers, and author's familiarity with the location.
 
 \section{Mathematical and geometrical algorithms}
 
+To visually evaluate the sample above, we created a few examples for {\DP}
+and {\VW} using the following parameters:
+
+\begin{enumerate}[label=(\Roman*)]
+    \item {\DP} tolerance: $tolerance := 125 * 2^n, n = 0,1,...,5$.
+    \item {\VW} tolerance: $vwtolerance = tolerance ^ 2$\label{itm:2}.
+\end{enumerate}
+
+Item~\ref{itm:2} requires explanation. Tolerance for {\DP} is specified in
+linear units, in this case, meters. Tolerance for {\VW} is specified in areal
+units, in this case, square meters $m^2$. As author was not able to locate
+formal comparisons between the two (i.e. how to calculate one tolerance value
+from another, so the results are comparable?), {\DP} tolerance was arbitrarily
+squared. To the author's understanding, this provides reasonalbe results.
 
 \renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
 \begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
diff --git a/II/Referatas/zeimena.gpkg b/II/Referatas/zeimena.gpkg
index 8e3e2d113b8807389d8cb6c8491c4e0b2ade9601..354483ea8a81a3de682d00f8cf26f9dda6bf3090 100644
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