diff --git a/src/renderer/sw_engine/tvgSwMath.cpp b/src/renderer/sw_engine/tvgSwMath.cpp
index 09044280..428e3e04 100644
--- a/src/renderer/sw_engine/tvgSwMath.cpp
+++ b/src/renderer/sw_engine/tvgSwMath.cpp
@@ -50,11 +50,17 @@ bool mathSmallCubic(const SwPoint* base, SwFixed& angleIn, SwFixed& angleMid, Sw
     auto d2 = base[1] - base[2];
     auto d3 = base[0] - base[1];
 
+    if (d1 == d2 || d2 == d3) {
+        if (d3.small()) angleIn = angleMid = angleOut = 0;
+        else angleIn = angleMid = angleOut = mathAtan(d3);
+        return true;
+    }
+
     if (d1.small()) {
         if (d2.small()) {
             if (d3.small()) {
-                //basically a point.
-                //do nothing to retain original direction
+                angleIn = angleMid = angleOut = 0;
+                return true;
             } else {
                 angleIn = angleMid = angleOut = mathAtan(d3);
             }
@@ -205,7 +211,14 @@ SwFixed mathLength(const SwPoint& pt)
     if (pt.y == 0) return abs(pt.x);
 
     auto v = pt.toPoint();
-    return static_cast<SwFixed>(sqrtf(v.x * v.x + v.y * v.y) / 64.0f);
+    //return static_cast<SwFixed>(sqrtf(v.x * v.x + v.y * v.y) * 65536.0f);
+
+    /* approximate sqrt(x*x + y*y) using alpha max plus beta min algorithm.
+       With alpha = 1, beta = 3/8, giving results with the largest error less
+       than 7% compared to the exact value. */
+    if (v.x < 0) v.x = -v.x;
+    if (v.y < 0) v.y = -v.y;
+    return (v.x > v.y) ? (v.x + v.y * 0.375f) : (v.y + v.x * 0.375f);
 }
 
 
@@ -216,22 +229,22 @@ void mathSplitCubic(SwPoint* base)
     base[6].x = base[3].x;
     c = base[1].x;
     d = base[2].x;
-    base[1].x = a = (base[0].x + c) / 2;
-    base[5].x = b = (base[3].x + d) / 2;
-    c = (c + d) / 2;
-    base[2].x = a = (a + c) / 2;
-    base[4].x = b = (b + c) / 2;
-    base[3].x = (a + b) / 2;
+    base[1].x = a = (base[0].x + c) >> 1;
+    base[5].x = b = (base[3].x + d) >> 1;
+    c = (c + d) >> 1;
+    base[2].x = a = (a + c) >> 1;
+    base[4].x = b = (b + c) >> 1;
+    base[3].x = (a + b) >> 1;
 
     base[6].y = base[3].y;
     c = base[1].y;
     d = base[2].y;
-    base[1].y = a = (base[0].y + c) / 2;
-    base[5].y = b = (base[3].y + d) / 2;
-    c = (c + d) / 2;
-    base[2].y = a = (a + c) / 2;
-    base[4].y = b = (b + c) / 2;
-    base[3].y = (a + b) / 2;
+    base[1].y = a = (base[0].y + c) >> 1;
+    base[5].y = b = (base[3].y + d) >> 1;
+    c = (c + d) >> 1;
+    base[2].y = a = (a + c) >> 1;
+    base[4].y = b = (b + c) >> 1;
+    base[3].y = (a + b) >> 1;
 }