From e1fdc7f4e6e178bf2d390189d64c3be48a2eaaa3 Mon Sep 17 00:00:00 2001
From: "A. Kolmogorov" <akolmogorov@lmu>
Date: Tue, 21 Apr 2020 00:29:06 +0200
Subject: [PATCH] sample vertex

---
 R/generateSierpinski.R | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/R/generateSierpinski.R b/R/generateSierpinski.R
index b09ad86..8e68e8c 100644
--- a/R/generateSierpinski.R
+++ b/R/generateSierpinski.R
@@ -17,7 +17,11 @@ generateSierpinski <- function(rows) {
 # n: number of vertices (e.g. n=3: Triangle)
 # Return a vector of length 2 with x and y coordinates
 sampleVertex <- function(n) {
-  c(x=0, y=0)
+  midpoint = c(x=0.5, y=0.5 / tan(pi / n))
+  radius = 0.5 / sin(pi / n)
+  angle = 2 * pi / n * (sample(n, 1))
+
+  midpoint + radius * c(sin(angle), cos(angle))
 }
 
 # Create a point that is a step from `from` to `to`