diff --git a/core/Shape.cpp b/core/Shape.cpp
index 9c8b256..3f495ab 100644
--- a/core/Shape.cpp
+++ b/core/Shape.cpp
@@ -38,6 +38,17 @@ bool Shape::validate() const {
 
 void Shape::normalize() {
     for (std::vector<Contour>::iterator contour = contours.begin(); contour != contours.end(); ++contour) {
+        // First, erase all degenerate edges.
+        std::vector<EdgeHolder>::iterator edge_it = contour->edges.begin();
+        while( edge_it != contour->edges.end() ) {
+            if( (*edge_it)->isDegenerate() ) {
+                edge_it = contour->edges.erase(edge_it);
+            }
+            else {
+                edge_it++;
+            }
+        }
+        
         if (contour->edges.size() == 1) {
             EdgeSegment *parts[3] = { };
             contour->edges[0]->splitInThirds(parts[0], parts[1], parts[2]);
diff --git a/core/edge-segments.cpp b/core/edge-segments.cpp
index 169f2bb..e2cef2c 100644
--- a/core/edge-segments.cpp
+++ b/core/edge-segments.cpp
@@ -295,5 +295,17 @@ void CubicSegment::splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeS
         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.), p[2] == p[3] ? p[3] : mix(p[2], p[3], 2/3.), p[3], color);
 }
+    
+bool LinearSegment::isDegenerate() const {
+    return p[0].same(p[1]);
+}
+    
+bool QuadraticSegment::isDegenerate() const {
+    return p[0].same(p[2]);
+}
+
+bool CubicSegment::isDegenerate() const {
+    return p[0].same(p[3]) && (p[0].same(p[1]) || p[2].same(p[1]));
+}
 
 }
diff --git a/core/edge-segments.h b/core/edge-segments.h
index d201ab8..6b0b4dd 100644
--- a/core/edge-segments.h
+++ b/core/edge-segments.h
@@ -38,6 +38,8 @@ public:
     virtual void moveEndPoint(Point2 to) = 0;
     /// Splits the edge segments into thirds which together represent the original edge.
     virtual void splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const = 0;
+    
+    virtual bool isDegenerate() const = 0;
 
 };
 
@@ -57,6 +59,8 @@ public:
     void moveStartPoint(Point2 to);
     void moveEndPoint(Point2 to);
     void splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const;
+    
+    bool isDegenerate() const;
 
 };
 
@@ -77,6 +81,8 @@ public:
     void moveEndPoint(Point2 to);
     void splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const;
 
+    bool isDegenerate() const;
+
 };
 
 /// A cubic Bezier curve.
@@ -96,6 +102,8 @@ public:
     void moveEndPoint(Point2 to);
     void splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const;
 
+    bool isDegenerate() const;
+
 };
 
 }