From 5e81833134e30566c389a1257ebb4fb777c51470 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Motiejus=20Jak=C5=A1tys?= <motiejus@uber.com>
Date: Sun, 9 May 2021 13:48:28 +0300
Subject: [PATCH] Start explaining exaggeration

---
 IV/mj-msc.tex | 35 ++++++++++++++++++++++-------------
 1 file changed, 22 insertions(+), 13 deletions(-)

diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex
index f98f7e1..aa645c8 100644
--- a/IV/mj-msc.tex
+++ b/IV/mj-msc.tex
@@ -1096,32 +1096,41 @@ Combination operator was not implemented in this version.
 
 \subsection{Exaggeration Operator}
 
-Exaggeration operator finds bends whose \textsc{adjusted size} is smaller than
-the incoming parameter --- \textsc{half-circle diameter}. Once it finds the
-bend, it will exaggerate it in increments until either becomes true:
+Exaggeration operator finds bends of which \textsc{adjusted size} is smaller
+than the \textsc{diameter of the half-circle}. Once a target bend is found, it
+will be exaggerated it in increments until either becomes true:
 
 \begin{itemize}
     \item \textsc{adjusted size} of the exaggerated bend is larger than area of
         the half-circle.
-    \item The exaggerated bend starts intersecting with a neighboring bend. Then,
+
+    \item The exaggerated bend starts intersecting with a neighboring bend.
+        Then exaggeration aborts, and the bend remains as if it were one step
+        before the intersection.
+
 \end{itemize}
 
-Exaggeration operator requires a constant \textsc{exaggeration step} $s$, which
-should be between 1 and 2. It was arbitrarily picked to \exaggerationEnthusiasm
-for this implementation. A single exaggeration increment is done as follows:
+Exaggeration operator uses a hardcoded parameter \textsc{exaggeration step} $s
+\in (1,2]$. It was arbitrarily picked to {\exaggerationEnthusiasm} for this
+implementation. A single exaggeration increment is done as follows:
 
 \begin{enumerate}
     \item Find a candidate bend.
     \item Find the bend's baseline.
     \item Find \textsc{midpoint}, the center of the bend's baseline.
 
-    \item Mark each bend's vertex with a number between $[1,s]$. The number is
-        derived with elements linearly interpolated between the start and
-        mid-points of the bend. The other half of the bend, from mid-point to
-        the final vertex, is linearly interpolated between $[s,1]$.
+    \item Find \textsc{midbend}, the center of the bend. Distance from one
+        baseline vertex to \textsc{midbend} should be the same as from
+        \textsc{midbend} to the other baseline vertex.
 
-    \item Each point will be placed farther away from the baseline. The length
-        of misplacement is the marked value in the previous step. I.e.
+    \item Mark each bend's vertex with a number between $[1,s]$. The number is
+        derived with elements linearly interpolated between the start vertex
+        and \textsc{midbend}. The other half of the bend, from \textsc{midbend}
+        to the final vertex, is linearly interpolated between $[s,1]$.
+
+    \item Each point (except the beginning and end vertices of the bend) will
+        be placed farther away from the baseline. The length of misplacement is
+        the marked value in the previous step.
 
 \end{enumerate}