diff --git a/src/org/poly2tri/cdt/CDT.scala b/src/org/poly2tri/cdt/CDT.scala
index f741e09..165fe4a 100644
--- a/src/org/poly2tri/cdt/CDT.scala
+++ b/src/org/poly2tri/cdt/CDT.scala
@@ -44,19 +44,16 @@ object CDT {
   
   // Inital triangle factor
   val ALPHA = 0.3f
-  val SHEER = 0.0001
-  
   var clearPoint = 0
   
   // Triangulate simple polygon
   def init(points: ArrayBuffer[Point]): CDT = {
     
-    var xmax, xmin = shearTransform(points.first).x
-    var ymax, ymin = shearTransform(points.first).y
+    var xmax, xmin = points.first.x
+    var ymax, ymin = points.first.y
     
     // Calculate bounds
     for(i <- 0 until points.size) { 
-      points(i) = shearTransform(points(i))
       val p = points(i)
       if(p.x > xmax) xmax = p.x
       if(p.x < xmin) xmin = p.x
@@ -98,11 +95,7 @@ object CDT {
     else
       Util.msort((p1: Point, p2: Point) => p1 > p2)(points.toList)
   }
-  
-  // Prevents any two distinct endpoints from lying on a common horizontal line, and avoiding
-  // the degenerate case. See Mark de Berg et al, Chapter 6.3
-  private def shearTransform(point: Point) = Point(point.x, point.y + point.x * 0.001f)
-  
+ 
 }
 
 class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Triangle) {
@@ -351,9 +344,6 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
     } 
     
     if(!P.isEmpty) {
-      //val ccw = Util.orient2d(a, b, P(i)) > 0
-      //val pB = if(ccw) P(i) else b
-      //val pC = if(ccw) b else P(i)
       val points = Array(a, P(i), b)
       T += new Triangle(points)
       T.last.finalized = true
@@ -439,6 +429,8 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
     val point = t1.points(0)
     val oPoint = t2 oppositePoint t1
     
+    val collinear = t1.collinear(oPoint) || t2.collinear(oPoint, point)
+    
     if(illegal(t1.points(1), oPoint, t1.points(2), t1.points(0)) && !t2.finalized) {
       
         // Flip edge and rotate everything clockwise
diff --git a/src/org/poly2tri/shapes/Point.scala b/src/org/poly2tri/shapes/Point.scala
index fba52e0..662c340 100644
--- a/src/org/poly2tri/shapes/Point.scala
+++ b/src/org/poly2tri/shapes/Point.scala
@@ -53,8 +53,21 @@ case class Point(val x: Float, val y: Float) {
   @inline def normalize = this / length  
   // Sort along x axis
   @inline def <(p: Point) = (x < p.x)
+  
   // Sort along y axis
-  @inline def >(p: Point) = (y < p.y) 
+  @inline def >(p: Point) = {
+    if(y < p.y) 
+      true
+    else if(y > p.y)
+      false
+    else {
+      if(x < p.x)
+        true
+      else 
+        false
+    }
+   }
+  
   @inline def !(p: Point) = !(p.x == x && p.y == y)
   @inline override def clone = Point(x, y)
   
diff --git a/src/org/poly2tri/utils/Util.scala b/src/org/poly2tri/utils/Util.scala
index 5c5e2fc..4957c29 100644
--- a/src/org/poly2tri/utils/Util.scala
+++ b/src/org/poly2tri/utils/Util.scala
@@ -43,7 +43,7 @@ object Util {
   // Tests if the given points are collinear
   def collinear(p1: Point, p2: Point, p3: Point): Boolean = {
 
-    val d = orient2d(p1, p2, p3)
+    val d = Math.abs((p2-p1) cross (p1-p3))
     
     if(Math.abs(d) <= COLLINEAR_SLOP) 
       true
@@ -123,9 +123,9 @@ object Util {
 	   val errbound = Util.ccwerrboundA * detsum
 	   if ((det >= errbound) || (-det >= errbound)) {
 	     return det
-	   } else {
+	   } else {    
 	     // Cheat a little bit.... we have a degenerate triangle
-	     val c = pc * 0.1e-5f
+	     val c = pc * 0.1e-6f
          return orient2d(pa, pb, c)
 	   }