From d66013892b430be22506294c07da2c34b55476e2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Motiejus=20Jak=C5=A1tys?= <motiejus@jakstys.lt>
Date: Wed, 19 May 2021 22:57:47 +0300
Subject: [PATCH] gentle inflection is now documented

---
 mj-msc.tex | 18 +++++++++++++++++-
 notes.txt  |  8 --------
 2 files changed, 17 insertions(+), 9 deletions(-)

diff --git a/mj-msc.tex b/mj-msc.tex
index a58a088..2d54afa 100644
--- a/mj-msc.tex
+++ b/mj-msc.tex
@@ -359,10 +359,26 @@ vertices to the next bend instead of one.
         \includegraphics[width=\textwidth]{inflection-1-gentle-inflection-after}
         \caption{After applying the inflection rule}
     \end{subfigure}
-    \caption{Gentle inflection at the end of the bend when multiple vertices is moved.}
+    \caption{Gentle inflection at the end of the bend when multiple vertices is moved}
     \label{fig:inflection-1-gentle-inflection}
 \end{figure}
 
+To find and fix the gentle bends' inflections requires to run the algorithm in
+both directions; if implemented as documented, the steps will fail to match
+some bends that should be mutated. This implementation does it in the following way:
+
+\begin{enumerate}
+    \item Run the algorithm from beginning to the end.
+    \item \label{rev1} Reverse the line and each bend.
+    \item Run the algorithm again.
+    \item \label{rev2} Reverse the line and each bend.
+    \item Return result.
+\end{enumerate}
+
+The current implementation is the most straight-forward, but not optimal:
+reversing of lines and bends could be avoided by walking backwards the lines.
+In this case, steps \ref{rev1} and \ref{rev2} could be remove. That would save
+both memory and computation time.
 
 \section{Self-line Crossing When Cutting a Bend}
 
diff --git a/notes.txt b/notes.txt
index bf2c494..051a86a 100644
--- a/notes.txt
+++ b/notes.txt
@@ -1,11 +1,3 @@
-Gentle inflection at the end of the bend
-----------------------------------------
-
-The article does not specify how many vertices should be included when
-calculating the end-of-bend inflection. We chose the iterative approach -- as
-long as the angle is "right" and the distance is (greedily) decreasing, keep
-going.
-
 Self-line crossing when cutting a bend
 --------------------------------------