diff --git a/core/edge-segments.cpp b/core/edge-segments.cpp
index b9fd166..169f2bb 100644
--- a/core/edge-segments.cpp
+++ b/core/edge-segments.cpp
@@ -288,12 +288,12 @@ void QuadraticSegment::splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, E
 }
 
 void CubicSegment::splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const {
-    part1 = new CubicSegment(p[0], mix(p[0], p[1], 1/3.), mix(mix(p[0], p[1], 1/3.), mix(p[1], p[2], 1/3.), 1/3.), point(1/3.), color);
+    part1 = new CubicSegment(p[0], p[0] == p[1] ? p[0] : mix(p[0], p[1], 1/3.), mix(mix(p[0], p[1], 1/3.), mix(p[1], p[2], 1/3.), 1/3.), point(1/3.), color);
     part2 = new CubicSegment(point(1/3.),
         mix(mix(mix(p[0], p[1], 1/3.), mix(p[1], p[2], 1/3.), 1/3.), mix(mix(p[1], p[2], 1/3.), mix(p[2], p[3], 1/3.), 1/3.), 2/3.),
         mix(mix(mix(p[0], p[1], 2/3.), mix(p[1], p[2], 2/3.), 2/3.), mix(mix(p[1], p[2], 2/3.), mix(p[2], p[3], 2/3.), 2/3.), 1/3.),
         point(2/3.), color);
-    part3 = new CubicSegment(point(2/3.), mix(mix(p[1], p[2], 2/3.), mix(p[2], p[3], 2/3.), 2/3.), mix(p[2], p[3], 2/3.), p[3], color);
+    part3 = new CubicSegment(point(2/3.), mix(mix(p[1], p[2], 2/3.), mix(p[2], p[3], 2/3.), 2/3.), p[2] == p[3] ? p[3] : mix(p[2], p[3], 2/3.), p[3], color);
 }
 
 }