From 8db2ab61439643e50e4ddefef255ee5f5c23b84d Mon Sep 17 00:00:00 2001
From: Lukas H <3811822+chordowl@users.noreply.github.com>
Date: Thu, 13 Feb 2020 00:17:33 +0100
Subject: [PATCH] paper1: Fix erroneous arm length formula

Replaces instances of `sin` in the formula for the arm length with `cos`.

This must've been a mix-up while this was written up, as the code (<https://github.com/raphlinus/spline-research/blob/master/curves.js#L219>) uses `cos`.
Now, paper and code match.
(If one uses `sin`, the arm length seems to have the wrong sign, and even if one fixes that, the resulting curve behaves rather weirdly).
---
 paper1/paper1.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/paper1/paper1.tex b/paper1/paper1.tex
index e514278..4464040 100644
--- a/paper1/paper1.tex
+++ b/paper1/paper1.tex
@@ -111,7 +111,7 @@ \section{A new spline}
 
 \[
 \begin{aligned}
-\mbox{arm length} & = \tfrac{5}{12}(\sin \theta_a - 0.2\sin 3\theta_a), \quad \mbox{\emph{where}} \\
+\mbox{arm length} & = \tfrac{5}{12}(\cos \theta_a - 0.2\cos 3\theta_a), \quad \mbox{\emph{where}} \\
 \theta_a & = \theta_0 - 0.3 \sin (2\theta_1 - 0.4\sin 2\theta_1) \\
 \end{aligned}
 \]