initial commit

2024-11-05 22:09:52 +01:00 · 2009-07-13 19:54:32 -04:00 · 2009-07-13 19:54:32 -04:00 · f461aca3dc
commit f461aca3dc
12 changed files with 1182 additions and 0 deletions
--- a/src/org/poly2tri/MonoToneMountain.scala
+++ b/src/org/poly2tri/MonoToneMountain.scala
@ -0,0 +1,138 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import scala.collection.mutable.{ArrayBuffer, Queue}
+
+class MonotoneMountain {
+
+	var tail, head: Point = null
+	var size = 0
+
+	val convexPoints = new Queue[Point]
+	val triangles = new ArrayBuffer[Array[Point]]
+ 
+	// Append
+	def +=(point: Point) {
+	  size match {
+	    case 0 => 
+	      head = point
+        case 1 =>
+          tail = point
+		  tail.prev = head
+		  head.next = tail
+        case _ =>
+          tail.next = point
+          point.prev = tail
+          tail = point
+	  }
+	  size += 1
+	}
+
+	// Remove
+	private def remove(point: Point) {
+		val next = point.next
+		val prev = point.prev
+		point.prev.next = next
+		point.next.prev = prev
+		size -= 1
+	}
+ 
+	// Determines if the inslide angle between edge v2-v3 and edge v2-v1 is convex (< PI)
+	private def angle(v1: Point, v2: Point, v3: Point) = {
+	  val a = (v2 - v1) 
+	  val b = (v2 - v3) 
+      val angle = Math.atan2(b.y,b.x).toFloat - Math.atan2(a.y,a.x).toFloat
+      angle
+    }
+
+	def lastTriangle = {
+	  assert(size == 3, "Number of points = " + size)
+	  val triangle = new Array[Point](3)
+	  var i = 0
+      var p = head
+	  while(p != null) {
+	      triangle(i) = p
+	      p = p.next
+          i += 1
+	  }
+	  triangles += triangle
+	}
+ 
+	// Partition a x-monotone mountain into triangles o(n)
+	// See "Computational Geometry in C", 2nd edition, by Joseph O'Rourke, page 52
+	def triangulate {
+	  if(size == 3) {
+	    lastTriangle
+	  } else {
+	   // Initialize internal angles at each nonbase vertex
+	   var p = head.next
+	   while(p != tail) {
+	     p.angle = Math.abs(angle(p.prev, p, p.next))
+	     println("angle = " + p.angle)
+	     // Link strictly convex vertices into a list
+	     if(p.angle > 0 && p.angle <= Math.Pi) convexPoints.enqueue(p)
+	     p = p.next
+	   }
+    
+	   while(!convexPoints.isEmpty) {
+	     val ear = convexPoints.dequeue
+	     val a = ear.prev.clone
+	     val b = ear
+	     val c = ear.next.clone
+	     val triangle = Array(a, b, c)
+	     triangles += triangle
+      
+	     // Remove ear, update angles and convex list
+	     remove(ear) 
+	     a.angle -= ear.angle
+	     if(a.angle > 0) convexPoints.enqueue(a)
+	     c.angle -= ear.angle
+	     if(c.angle > 0) convexPoints.enqueue(c)
+	   }
+    
+	   if(size == 3) lastTriangle
+	}
+   }
+ 
+	def monoPoly {
+	  val triangle = new Array[Point](size)
+	  var i = 0
+      var p = head
+	  while(p != null) {
+	      triangle(i) = p
+	      p = p.next
+          i += 1
+	  }
+	  triangles += triangle
+	  println(size)
+	}
+}
--- a/src/org/poly2tri/Node.scala
+++ b/src/org/poly2tri/Node.scala
@ -0,0 +1,59 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import collection.jcl.ArrayList
+
+// Node for a Directed Acyclic graph (DAG)
+abstract class Node(var left: Node, var right: Node) {
+
+  if(left != null) left.parentList += this
+  if(right != null) right.parentList += this
+  
+  var parentList = new ArrayList[Node]
+  
+  def locate(s: Segment): Sink
+  
+  // Replace a node in the graph with this node
+  // Make sure parent pointers are updated
+  def replace(node: Node) {
+   for(parent <- node.parentList) {
+     // Select the correct node (left or right child)
+     if(parent.left == node) {
+     	parent.left = this
+     } else {
+        parent.right = this
+     }
+     // Decouple the node
+     parentList += parent
+   }
+  }
+}
--- a/src/org/poly2tri/Point.scala
+++ b/src/org/poly2tri/Point.scala
@ -0,0 +1,58 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+class Point(val x: Float, val y: Float, var segment: Segment) {
+  
+  def this(x: Float, y: Float) = this(x, y, null)
+  
+  // Pointers to next and previous points in Monontone Mountain
+  var next, prev: Point = null
+  
+  /* Internal angle */
+  var angle = 0f
+  
+  def -(p: Point) = new Point(x - p.x, y - p.y) 
+  def +(p: Point) = new Point(x + p.x, y + p.y)
+  def +(f: Float) = new Point(x + f, y + f)
+  def *(f: Float) = new Point(x * f, y * f)
+  
+  def <(p: Point) = {
+    if(p.x == x) 
+      if(y > p.y) true
+      else false
+    else
+      (x < p.x)
+  }
+    
+  
+  override def clone = new Point(x, y)
+}
--- a/src/org/poly2tri/QueryGraph.scala
+++ b/src/org/poly2tri/QueryGraph.scala
@ -0,0 +1,97 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import collection.jcl.ArrayList
+
+// Directed Acyclic graph (DAG)
+// See "Computational Geometry", 3rd edition, by Mark de Berg et al, Chapter 6.2
+                           
+class QueryGraph(var head: Node) {
+
+  def locate(s: Segment): Trapezoid = {
+    val sink = head.locate(s)
+    return sink.trapezoid
+  }
+  
+  def followSegment(s: Segment) = {
+    val trapezoids = new ArrayList[Trapezoid]
+    trapezoids += locate(s)
+    var j = 0
+    while(s.q.x > trapezoids(j).rightPoint.x) {
+      if(s > trapezoids(j).rightPoint) {
+        trapezoids += trapezoids(j).upperRight
+      } else {
+        trapezoids += trapezoids(j).lowerRight
+      }
+      j += 1
+    }
+    trapezoids
+  }
+  
+  def replace(sink: Sink, node: Node) {
+    if(sink.parentList.size == 0) {
+      head = node
+    } else {
+      node.replace(sink)
+    }
+  }
+  
+  def case1(sink: Sink, s: Segment, tList: ArrayList[Trapezoid]) {
+    val yNode = new YNode(s, Sink.init(tList(1)), Sink.init(tList(2)))
+    val qNode = new XNode(new Point(s.q.x, s.q.y, s), yNode, Sink.init(tList(3)))
+	val pNode = new XNode(new Point(s.p.x, s.p.y, s), Sink.init(tList(0)), qNode)
+    replace(sink, pNode)
+  }
+  
+  def case2(sink: Sink, s: Segment, tList: ArrayList[Trapezoid]) {
+    val yNode = new YNode(s, Sink.init(tList(1)), Sink.init(tList(2)))
+	val pNode = new XNode(new Point(s.p.x, s.p.y, s), Sink.init(tList(0)), yNode)
+    replace(sink, pNode)
+  }
+  
+  def case3(sink: Sink, s: Segment, tList: ArrayList[Trapezoid]) {
+    val yNode = new YNode(s, Sink.init(tList(0)), Sink.init(tList(1)))
+    replace(sink, yNode)
+  }
+  
+  def case4(sink: Sink, s: Segment, tList: ArrayList[Trapezoid]) {
+    val yNode = new YNode(s, Sink.init(tList(0)), Sink.init(tList(1)))
+    if(s.left != null) {
+      val pNode = new XNode(new Point(s.p.x, s.p.y, s), Sink.init(s.left), yNode)
+      val qNode = new XNode(new Point(s.q.x, s.q.y, s), pNode, Sink.init(tList(2)))
+      replace(sink, qNode)
+    } else {
+      val qNode = new XNode(new Point(s.q.x, s.q.y, s), yNode, Sink.init(tList(2)))
+      replace(sink, qNode)
+    }
+  }
+}
--- a/src/org/poly2tri/Segment.scala
+++ b/src/org/poly2tri/Segment.scala
@ -0,0 +1,56 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import collection.jcl.ArrayList
+import scala.collection.mutable.HashSet
+
+// Represents a simple polygon's edge
+class Segment(var p: Point, var q: Point) {
+
+  // Pointer used for building trapezoidal map
+  var above, below, left: Trapezoid = null
+  
+  // Montone mountain points
+  val mPoints = HashSet(p, q)
+  
+  // Equation of a line: y = m*x + b
+  // Slope of the line (m)
+  val slope = (q.y - p.y)/(q.x - p.x)
+  // Y intercept
+  val b = p.y - (p.x * slope)
+  
+  // Determines if this segment lies above the given point
+  def > (point: Point) = (point.y < slope * point.x + b)
+  // Determines if this segment lies below the given point
+  def < (point: Point) = (point.y > slope * point.x + b) 
+
+}
--- a/src/org/poly2tri/Sink.scala
+++ b/src/org/poly2tri/Sink.scala
@ -0,0 +1,50 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+object Sink {
+  
+  def init(trapezoid: Trapezoid) = {
+    if(trapezoid.sink != null) {
+      trapezoid.sink
+    } else {
+      new Sink(trapezoid)
+    }
+  }
+  
+}
+
+class Sink(val trapezoid: Trapezoid) extends Node(null, null) {
+
+  trapezoid.sink = this
+  override def locate(s: Segment): Sink = this
+  
+}
--- a/src/org/poly2tri/Trapezoid.scala
+++ b/src/org/poly2tri/Trapezoid.scala
@ -0,0 +1,101 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+class Trapezoid(val leftPoint: Point, var rightPoint: Point, val top: Segment, val bottom: Segment) {
+
+  var sink: Sink = null
+  var outside = false
+  
+  // Neighbor pointers
+  var upperLeft: Trapezoid = null
+  var lowerLeft: Trapezoid = null
+  var upperRight: Trapezoid = null
+  var lowerRight: Trapezoid = null
+  
+  def updateNeighbors(ul: Trapezoid, ll: Trapezoid, ur: Trapezoid, lr: Trapezoid) {
+    if(upperLeft != null && upperLeft.top == top) upperLeft.upperRight = ul
+    if(lowerLeft != null && lowerLeft.bottom == bottom) lowerLeft.lowerRight = ll
+    if(upperRight != null && upperRight.top == top) upperRight.upperLeft = ur
+    if(lowerRight != null && lowerRight.bottom == bottom) lowerRight.lowerLeft = lr
+  }
+  
+  def update(ul: Trapezoid, ll: Trapezoid, ur: Trapezoid, lr: Trapezoid) {
+    upperLeft = ul
+    lowerLeft = ll
+    upperRight = ur
+    lowerRight = lr
+  }
+  
+  def markNeighbors {
+    if(upperLeft != null) upperLeft.outside = true
+    if(lowerLeft != null) lowerLeft.outside = true
+    if(upperRight != null) upperRight.outside = true
+    if(lowerRight != null) lowerRight.outside = true
+  }
+  
+  // Determines if this point lies inside the trapezoid
+  def contains(point: Point) = {
+     (point.x > leftPoint.x && point.x < rightPoint.x && top > point && bottom < point)
+  }
+  
+  def vertices: Array[Point] = {
+    val verts = new Array[Point](4)
+    verts(0) = lineIntersect(top, leftPoint.x)
+    verts(1) = lineIntersect(bottom, leftPoint.x)
+    verts(2) = lineIntersect(bottom, rightPoint.x)
+    verts(3) = lineIntersect(top, rightPoint.x)
+    return verts
+  }
+  
+  def lineIntersect(s: Segment, x: Float) = {
+    val y =  s.slope * x + s.b
+    new Point(x, y)
+  } 
+  
+  // Add points to monotone mountain
+  // Use HashSet to aboid repeats
+  def mark {
+    bottom.mPoints += leftPoint
+    bottom.mPoints += rightPoint
+    top.mPoints += leftPoint
+    top.mPoints += rightPoint
+  }
+  
+  // Clear points when dividing this trapezoid
+  def clear {
+    bottom.mPoints -= leftPoint
+    bottom.mPoints -= rightPoint
+    top.mPoints -= leftPoint
+    top.mPoints -= rightPoint
+  }
+
+}
--- a/src/org/poly2tri/TrapezoidalMap.scala
+++ b/src/org/poly2tri/TrapezoidalMap.scala
@ -0,0 +1,215 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import collection.jcl.ArrayList
+import scala.collection.mutable.{Map, HashSet}
+
+// See "Computational Geometry", 3rd edition, by Mark de Berg et al, Chapter 6.2
+
+class TrapezoidalMap {
+
+  // Trapezoid associated array
+  val map = HashSet.empty[Trapezoid]
+  // AABB margin
+  var margin = 2f
+    
+  // Bottom segment that spans multiple trapezoids
+  private var bCross: Segment = null
+  // Top segment that spans multiple trapezoids
+  private var tCross: Segment = null
+  
+  // Add a trapezoid to the map
+  def add(t: Trapezoid) {
+    map += t
+  }
+  
+  // Remove a trapezoid from the map
+  def remove(t: Trapezoid) {
+    map -=t
+  }
+  
+  def reset {
+    bCross = null
+    tCross = null
+  }
+
+  // Case 1: segment completely enclosed by trapezoid
+  //         break trapezoid into 4 smaller trapezoids
+  def case1(t: Trapezoid, s: Segment) = {
+    
+    assert(s.p.x != s.q.x)
+    
+    val trapezoids = new ArrayList[Trapezoid]
+    trapezoids += new Trapezoid(t.leftPoint, s.p, t.top, t.bottom)
+    trapezoids += new Trapezoid(s.p, s.q, t.top, s)
+    trapezoids += new Trapezoid(s.p, s.q, s, t.bottom)
+    trapezoids += new Trapezoid(s.q, t.rightPoint, t.top, t.bottom)
+    
+    trapezoids(0).update(t.upperLeft, t.lowerLeft, trapezoids(1), trapezoids(2))
+    trapezoids(1).update(trapezoids(0), null, trapezoids(3), null)
+    trapezoids(2).update(null, trapezoids(0), null, trapezoids(3))
+    trapezoids(3).update(trapezoids(1), trapezoids(2), t.upperRight, t.lowerRight)
+    
+    s.above = trapezoids(1)
+    s.below = trapezoids(2)
+    
+    t.updateNeighbors(trapezoids(0), trapezoids(0), trapezoids(3), trapezoids(3))
+    trapezoids
+  }
+
+  // Case 2: Trapezoid contains point p, q lies outside
+  //         break trapezoid into 3 smaller trapezoids
+  def case2(t: Trapezoid, s: Segment) = {
+    
+    val rp = if(s.q.x == t.rightPoint.x) s.q else t.rightPoint
+    
+    val trapezoids = new ArrayList[Trapezoid]
+    trapezoids += new Trapezoid(t.leftPoint, s.p, t.top, t.bottom)
+    trapezoids += new Trapezoid(s.p, rp, t.top, s)
+    trapezoids += new Trapezoid(s.p, rp, s, t.bottom)
+   
+    trapezoids(0).update(t.upperLeft, t.lowerLeft, trapezoids(1), trapezoids(2))
+    trapezoids(1).update(trapezoids(0), null, t.upperRight, null)
+    trapezoids(2).update(null, trapezoids(0), null, t.lowerRight)
+    
+    bCross = t.bottom
+    tCross = t.top
+    s.above = trapezoids(1)
+    s.below = trapezoids(2)
+    
+    t.updateNeighbors(trapezoids(0), trapezoids(0), trapezoids(1), trapezoids(2))
+    trapezoids
+  }
+  
+  // Case 3: Trapezoid is bisected
+  def case3(t: Trapezoid, s: Segment) = {
+    
+    assert(s.p.x != s.q.x)
+    
+    val lp = if(s.p.x == t.leftPoint.x) s.p else t.leftPoint
+    val rp = if(s.q.x == t.rightPoint.x) s.q else t.rightPoint
+    
+    val topCross = (tCross == t.top)
+    val bottomCross = (bCross == t.bottom)
+    
+    val trapezoids = new ArrayList[Trapezoid]
+    trapezoids += {if(topCross) t.upperLeft else new Trapezoid(lp, rp, t.top, s)}
+    trapezoids += {if(bottomCross) t.lowerLeft else new Trapezoid(lp, rp, s, t.bottom)}
+    
+    if(topCross) {
+      trapezoids(0).upperRight = t.upperRight
+      trapezoids(0).rightPoint = t.rightPoint
+    } else {
+      trapezoids(0).update(t.upperLeft, s.above, t.upperRight, null)
+      if(s.above != null) s.above.lowerRight = trapezoids(0)
+    }
+    
+    if(bottomCross) {
+      trapezoids(1).lowerRight = t.lowerRight
+      trapezoids(1).rightPoint = t.rightPoint
+    } else {
+      trapezoids(1).update(s.below, t.lowerLeft, null, t.lowerRight)
+      if(s.below != null) s.below.upperRight = trapezoids(1)
+    }
+    
+    bCross = t.bottom
+    tCross = t.top
+    s.above = trapezoids(0)
+    s.below = trapezoids(1)
+    
+    t.updateNeighbors(trapezoids(0), trapezoids(1), trapezoids(0), trapezoids(1))
+    trapezoids
+  }
+  
+  // Case 4: Trapezoid contains point q, p lies outside
+  //         break trapezoid into 3 smaller trapezoids
+  def case4(t: Trapezoid, s: Segment) = {
+    
+    val lp = if(s.p.x == t.leftPoint.x) s.p else t.leftPoint
+    
+    val topCross = (tCross == t.top)
+    val bottomCross = (bCross == t.bottom)
+    
+    val trapezoids = new ArrayList[Trapezoid]
+    trapezoids += {if(topCross) t.upperLeft else new Trapezoid(lp, s.q, t.top, s)}
+    trapezoids += {if(bottomCross) t.lowerLeft else new Trapezoid(lp, s.q, s, t.bottom)}
+    trapezoids += new Trapezoid(s.q, t.rightPoint, t.top, t.bottom)
+    
+    if(topCross) {
+      trapezoids(0).upperRight = trapezoids(2)
+      trapezoids(0).rightPoint = s.q
+    } else {
+      trapezoids(0).update(t.upperLeft, s.above, trapezoids(2), null)
+      if(s.above != null) s.above.lowerRight = trapezoids(0)
+    }
+    
+    if(bottomCross) {
+      trapezoids(1).lowerRight = trapezoids(2)
+      trapezoids(1).rightPoint = s.q
+    } else {
+      trapezoids(1).update(s.below, t.lowerLeft, null, trapezoids(2))
+      if(s.below != null) s.below.upperRight = trapezoids(1)
+    }
+    trapezoids(2).update(trapezoids(0), trapezoids(1), t.upperRight, t.lowerRight)
+    
+    s.above = trapezoids(0)
+    s.below = trapezoids(1)
+    
+    t.updateNeighbors(trapezoids(0), trapezoids(1), trapezoids(2), trapezoids(2))
+    trapezoids
+  }
+  
+  // Create an AABB around segments
+  def boundingBox(segments: ArrayList[Segment]): Trapezoid = {
+   
+    var max = segments(0).p + margin
+    var min = segments(0).q + margin
+
+    for(s <- segments) {
+      if(s.p.x > max.x) max = new Point(s.p.x + margin, max.y)
+      if(s.p.y > max.y) max = new Point(max.x, s.p.y + margin)
+      if(s.q.x > max.x) max = new Point(s.q.x+margin, max.y)
+      if(s.q.y > max.y) max = new Point(max.x, s.q.y+margin)
+      if(s.p.x < min.x) min = new Point(s.p.x-margin, min.y)
+      if(s.p.y < min.y) min = new Point(min.x, s.p.y-margin)
+      if(s.q.x < min.x) min = new Point(s.q.x-margin, min.y)
+      if(s.q.y < min.y) min = new Point(min.x, s.q.y-margin)
+    }
+
+    val top = new Segment(new Point(min.x, max.y), new Point(max.x, max.y))
+    val bottom = new Segment(new Point(min.x, min.y), new Point(max.x, min.y))
+    val left = bottom.p
+    val right = top.q
+    
+    return new Trapezoid(left, right, top, bottom)
+  }
+}
--- a/src/org/poly2tri/Triangulator.scala
+++ b/src/org/poly2tri/Triangulator.scala
@ -0,0 +1,155 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import collection.jcl.ArrayList
+import scala.collection.mutable.{HashSet, Map, Stack, ListBuffer}
+
+import utils.Random
+
+// Based on Raimund Seidel's paper "A simple and fast incremental randomized
+// algorithm for computing trapezoidal decompositions and for triangulating polygons"
+class Triangulator(var segments: ArrayList[Segment]) {
+  
+  // Trapezoid decomposition list
+  var trapezoids : ArrayList[Trapezoid] = null
+  // Triangle decomposition list
+  // var triangles: ArrayList[Triangle] = null
+  
+  // Build the trapezoidal map and query graph
+  def process {
+    
+    val foo = new Point(0f, 0f)
+    val foo2 = new Point(0f, 3f)
+    val foo3 = new Point(10f, 3f)
+    var bar = List(foo, foo3, foo2)
+    bar -= foo
+    
+    for(s <- segments) {
+      val traps = queryGraph.followSegment(s)
+      // Remove trapezoids from trapezoidal Map
+      traps.foreach(t => {trapezoidalMap.remove(t); t.clear})
+      for(t <- traps) {
+        var tList: ArrayList[Trapezoid] = null
+        val containsP = t.contains(s.p)
+        val containsQ = t.contains(s.q)
+        if(containsP && containsQ) {
+          // Case 1
+          tList = trapezoidalMap.case1(t,s)
+          queryGraph.case1(t.sink, s, tList)
+        } else if(containsP && !containsQ) {
+          // Case 2
+          tList = trapezoidalMap.case2(t,s) 
+          queryGraph.case2(t.sink, s, tList)
+        } else if(!containsP && !containsQ) {
+          // Case 3
+          tList = trapezoidalMap.case3(t, s)
+          queryGraph.case3(t.sink, s, tList)
+        } else {
+          // Case 4
+          tList = trapezoidalMap.case4(t, s)
+          queryGraph.case4(t.sink, s, tList)
+        }
+        // Add new trapezoids to the trapezoidal map
+        tList.foreach(trapezoidalMap.add)
+      }
+      trapezoidalMap reset
+    }
+    trapezoids = trim
+    createMountains
+  }
+  
+  def allTrapezoids = trapezoidalMap.map
+  
+  // Initialize trapezoidal map and query structure
+  private val trapezoidalMap = new TrapezoidalMap
+  private val boundingBox = trapezoidalMap.boundingBox(segments)
+  private val queryGraph = new QueryGraph(new Sink(boundingBox))
+  
+  val xMonoPoly = new ArrayList[MonotoneMountain]
+                                        
+  segments = orderSegments
+  
+  // Build a list of x-monotone mountains
+  private def createMountains {
+    for(s <- segments) {
+       if(s.mPoints.size > 2) {
+         val mountain = new MonotoneMountain
+         // TODO: Optomize sort? The number of points should be 
+         // fairly small => insertion or merge?
+         val points = s.mPoints.toList
+         for(p <- points.sort((e1,e2) => e1 < e2)) {
+           mountain += p.clone
+         }
+         if(mountain.size > 2) {
+           mountain.triangulate
+           //mountain.monoPoly
+           xMonoPoly += mountain
+         }
+       }
+    }   
+  }
+  
+  // Trim off the extraneous trapezoids surrounding the polygon
+  private def trim = {
+    val traps = new ArrayList[Trapezoid]
+    // Mark outside trapezoids
+    for(t <- trapezoidalMap.map) {
+	  if(t.top == boundingBox.top || t.bottom == boundingBox.bottom) {
+	    t.outside = true
+	    t.markNeighbors
+	  }
+    }
+    // Collect interior trapezoids
+    for(t <- trapezoidalMap.map) if(!t.outside) {
+      traps += t
+      t.mark
+    }
+    traps
+  }
+  
+  private def orderSegments = {
+    // Ignore vertical segments!
+    val segs = new ArrayList[Segment]
+    for(s <- segments) {
+      // Point p must be to the left of point q
+      if(s.p.x > s.q.x) {
+        val tmp = s.p
+        s.p = s.q
+        s.q = tmp
+        segs += s
+      } else if(s.p.x < s.q.x) {
+        segs += s
+      }
+    }
+    Random.shuffle(segs)
+  }
+}
--- a/src/org/poly2tri/Util.scala
+++ b/src/org/poly2tri/Util.scala
@ -0,0 +1,148 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+import collection.jcl.ArrayList
+
+import org.villane.vecmath.Vector2
+
+object Util {
+
+  final def rotateLeft90(v:Vector2) = new Vector2( -v.y, v.x )
+
+  final def rotateRight90(v:Vector2) = new Vector2(v.y, -v.x )
+
+  final def rotate(v:Vector2, angle:Float) = {
+    val cos = Math.cos(angle).asInstanceOf[Float]
+    val sin = Math.sin(angle).asInstanceOf[Float]
+    val u = new Vector2((cos * v.x) - (sin * v.y), (cos * v.y) + (sin * v.x))
+    u
+  }
+
+  final def clamp(a: Float, low: Float, high: Float) =
+    if (a < low) low
+    else if (a > high) high
+    else a
+    
+  final def left(a: Vector2, b: Vector2, c: Vector2) =
+    ((b.x - a.x)*(c.y - a.y) - (c.x - a.x)*(b.y - a.y) > 0)
+
+  /** Melkman's Algorithm
+   *  www.ams.sunysb.edu/~jsbm/courses/345/melkman.pdf
+   *  Return a convex hull in ccw order
+   */
+  def hull(V: Array[Vector2]) = {
+
+    val n = V.length
+    val D = new Array[Vector2](2 * n + 1)
+    var bot = n - 2
+    var top = bot + 3
+
+    D(bot) = V(2)
+    D(top) = V(2)
+
+    if (left(V(0), V(1), V(2))) {
+      D(bot+1) = V(0)
+      D(bot+2) = V(1)
+    } else {
+      D(bot+1) = V(1)
+      D(bot+2) = V(0)
+    }
+
+    var i = 3
+    while(i < n) {
+      while (left(D(bot), D(bot+1), V(i)) && left(D(top-1), D(top), V(i))) {
+        i += 1
+      }
+      while (!left(D(top-1), D(top), V(i))) top -= 1
+      top += 1; D(top) = V(i)
+      while (!left(D(bot), D(bot+1), V(i))) bot += 1
+      bot -= 1; D(bot) = V(i)
+      i += 1
+    }
+
+    val H = new Array[Vector2](top - bot)
+    var h = 0
+    while(h < (top - bot)) {
+      H(h) = D(bot + h)
+      h += 1
+    }
+    H
+  }
+
+  def svgToWorld(points: Array[Float], scale: Float) = {
+    val verts = new Array[Vector2](points.length/2)
+    var i = 0
+    while(i < verts.length) {
+      verts(i) = worldPoint(points(i*2), points(i*2+1), scale)
+      i += 1
+    }
+    verts
+  }
+
+  def worldPoint(x: Float, y: Float, scale: Float) = {
+    val p = Vector2(x*scale, y*scale)
+    p
+  }
+
+}
+
+/** The object <code>Random</code> offers a default implementation
+ *  of scala.util.Random and random-related convenience methods.
+ *
+ *  @since 2.8
+ */
+object Random extends scala.util.Random {
+  
+  /** Returns a new sequence in random order.
+   *  @param  seq   the sequence to shuffle
+   *  @return       the shuffled sequence
+   */
+  def shuffle[T](buf: ArrayList[T]): ArrayList[T] = {
+    // It would be better if this preserved the shape of its container, but I have
+    // again been defeated by the lack of higher-kinded type inference.  I can
+    // only make it work that way if it's called like
+    //   shuffle[Int,List](List.range(0,100))
+    // which nicely defeats the "convenience" portion of "convenience method".
+       
+    def swap(i1: Int, i2: Int) {
+      val tmp = buf(i1)
+      buf(i1) = buf(i2)
+      buf(i2) = tmp
+    }
+   
+    for (n <- buf.length to 2 by -1) {
+      val k = nextInt(n)
+      swap(n - 1, k)
+    }
+    buf
+  }
+}
--- a/src/org/poly2tri/XNode.scala
+++ b/src/org/poly2tri/XNode.scala
@ -0,0 +1,52 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+class XNode(point: Point, lChild: Node, rChild: Node) extends Node(lChild, rChild) {
+
+  override def locate(s: Segment): Sink = {
+    if(s.p.x > point.x) {
+      // Move to the right in the graph
+      return right.locate(s)
+    } else if(s.p.x == point.x) {
+      if(point.y > s.p.y) {
+        s.left = point.segment.below
+      } else {
+        s.left = point.segment.above
+      }
+      return right.locate(s)
+    } else {
+      // Move to the left in the graph
+      return left.locate(s)
+    } 
+  }
+
+}
--- a/src/org/poly2tri/YNode.scala
+++ b/src/org/poly2tri/YNode.scala
@ -0,0 +1,53 @@
+/* Poly2Tri
+ * Copyright (c) 2009, Mason Green
+ * http://code.google.com/p/poly2tri/
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * * Neither the name of Poly2Tri nor the names of its contributors may be
+ *   used to endorse or promote products derived from this software without specific
+ *   prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+package org.poly2tri
+
+class YNode(segment: Segment, lChild: Node, rChild: Node) extends Node(lChild, rChild) {
+
+  override def locate(s: Segment): Sink = {
+    if (segment > s.p) {
+      // Move down the graph
+      right.locate(s)
+    } else if (segment < s.p){
+      // Move up the graph
+      left.locate(s)
+    } else {
+      // s and segment share the same endpoint
+      if (s.slope < segment.slope) {
+        // Move down the graph
+        return right.locate(s)
+      } else {
+        // Move up the graph
+        return left.locate(s)
+      }
+    }
+  }
+}