commit f5da753322cf28700f7cbc144d5c8fdc48259ab1 (tree)
parent 4c5d6e6e59bcc4e12950fd1e66749ce9bd5f4871
Author: Motiejus Jakštys <motiejus@uber.com>
Date: Wed, 14 Apr 2021 16:48:11 +0300
adjusted size and compactness index
Diffstat:
2 files changed, 34 insertions(+), 5 deletions(-)
diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex
@@ -458,7 +458,7 @@ bends need to be checked.
\subsection{Attributes of a Single Bend}
-Compactness Index $cmp$ is "the ratio of the area of the polygon over the
+\textsc{Compactness Index} is "the ratio of the area of the polygon over the
circle whose circumference length is the same as the length of the
circumference of the polygon" \cite{wang1998line}. We assume the area of the
circle is meant. Given a bend, its compactness index is calculated as follows:
@@ -486,10 +486,39 @@ circle is meant. Given a bend, its compactness index is calculated as follows:
\end{enumerate}
+Other than that, once this section is implemented, each bend will have a list
+of properties, upon which actions later will be performed.
+
\subsection{Shape of a Bend}
+This section introduces \textsc{adjusted size}, which trivially derives from
+\textsc{compactness index} $cmp$ and shape's area $A$:
+
+\[
+ adjsize = \frac{0.75 A}{cmp}
+\]
+
+Adjusted size becomes necessary later to compare bends with each other, and
+find out similar ones.
+
\subsection{The Context of a Bend: Isolated and Similar Bends}
+To find out whether two bends are similar, they are compared by 3 components:
+
+\begin{enumerate}
+ \item \textsc{Adjusted Size}
+ \item \textsc{Compactness index}
+ \item Baseline length
+\end{enumerate}
+
+These 3 components represent a point in the 3-dimensional space, and Euclidean
+distance $d$ between those is calculated to differentiate between bends $p$ and
+$q$:
+
+\[
+ d(p,q) = \sqrt{(adjsize_p - adjsize_q)^2 + (cmp_p - cmp_q)^2 + (baseline_p - baseline_q)^2}
+\]
+
\subsection{Elimination Operator}
\subsection{Combination Operator}
@@ -524,8 +553,8 @@ We strongly believe in the ability to reproduce the results is critical for any
This was tested on Linux Debian 11 with upstream packages only.
-\subsection{Algorithm code listings}
-\inputminted[fontsize=\small]{postgresql}{wm.sql}
+%\subsection{Algorithm code listings}
+%\inputminted[fontsize=\small]{postgresql}{wm.sql}
\end{appendices}
\end{document}
diff --git a/IV/wm.sql b/IV/wm.sql
@@ -353,8 +353,8 @@ begin
-- area of the circle. So here goes:
-- 1. get polygon area P.
-- 2. get polygon perimeter = u. Pretend it's our circle's circumference.
- -- 3. get A (area) of the circle from u: A = (u^2)/(4*pi)
- -- 4. divide P by A: cmp = P/A = P/((u^2)*4*pi) = 4*pi*P/u^2
+ -- 3. get A (area) of the circle from u: A = u^2/(4pi)
+ -- 4. divide P by A: cmp = P/A = P/(u^2/(4pi)) = 4pi*P/u^2
res.area = st_area(polygon);
res.cmp = fourpi*res.area/(st_perimeter(polygon)^2);
if res.cmp > 0 then
