fixed nemerical robustness issue in triangulation

src/org/poly2tri/MonoToneMountain.scala

@@ -39,8 +39,13 @@ class MonotoneMountain {
 	var size = 0
 
 	val convexPoints = new Queue[Point]
+    // Monotone mountain points
+	val monoPoly = new ArrayBuffer[Point]
+    // Triangles that constitute the mountain
 	val triangles = new ArrayBuffer[Array[Point]]
 	      
+	var angle = 0f
+ 
 	// Append a point to the list
 	def +=(point: Point) {
 	  size match {
@@ -71,6 +76,9 @@ class MonotoneMountain {
 	// See "Computational Geometry in C", 2nd edition, by Joseph O'Rourke, page 52
 	def triangulate {
 	
+	  // create monotone polygon - for dubug purposes
+	  genMonoPoly
+   
 	  if(size == 3) {
 	    lastTriangle
 	  } else {
@@ -97,28 +105,29 @@ class MonotoneMountain {
          if(c.prev != null && convex(c)) convexPoints.enqueue(c)
 
 	   }    
+	   assert(size <= 3, "Triangulation bug")
 	   if(size == 3)lastTriangle
 	}
    }
  
 	// Return the monotone polygon 
-	def monoPoly: Array[Point] = {
+	private def genMonoPoly { 
-	  val poly = new Array[Point](size)
-	  var i = 0
       var p = head
 	  while(p != null) {
-	      poly(i) = p
+	      monoPoly += p
 	      p = p.next
-          i += 1
 	  }
-	  poly
 	}
  
 	// Determines if the inslide angle between edge v2-v3 and edge v2-v1 is convex 
 	private def convex(p: Point) = {
 	  val a = (p.next - p) 
 	  val b = (p.prev - p) 
-      var angle = Math.atan2(b.y,b.x).toFloat - Math.atan2(a.y,a.x).toFloat
+      angle = Math.atan2(b.y,b.x).toFloat - Math.atan2(a.y,a.x).toFloat
+      if(angle < 0) while(angle < -Math.Pi) angle += Math.Pi.toFloat
+      if(angle > 0) while(angle > Math.Pi) angle -= Math.Pi.toFloat
+      // For numerical robustness....
+      angle = 0.01f * Math.round( angle * 10.0f)
       if(p.y >= head.y) {
         (angle < 0)
       } else {

src/org/poly2tri/Poly2Tri.scala

@@ -38,7 +38,7 @@ package org.poly2tri
 import org.newdawn.slick.{BasicGame, GameContainer, Graphics, Color, AppGameContainer}
 import org.newdawn.slick.geom.{Polygon, Circle}
 
-import collection.jcl.ArrayList
+import scala.collection.mutable.ArrayBuffer
 
 // TODO: Lots of documentation!
 
@@ -61,9 +61,6 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
   var drawMap = false
   
   def init(container: GameContainer) {
-    // TODO: Add text file point loader
-    //poly
-    //poly2
     snake
   }
   
@@ -79,7 +76,7 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
     val yellow = new Color(1f, 1f, 0f)
     
    if(debug) {
-	   val draw = if(drawMap) tesselator.allTrapezoids else tesselator.trapezoids
+	   val draw = if(drawMap) tesselator.trapezoidMap else tesselator.trapezoids
 	   for(t <- draw) {
 	     val polygon = new Polygon()
 	     for(v <- t.vertices) {
@@ -88,32 +85,37 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
 	     val lCirc = new Circle(t.leftPoint.x, t.leftPoint.y, 4)
 	     g.setColor(blue); g.draw(lCirc); g.fill(lCirc)
 	     val rCirc = new Circle(t.rightPoint.x, t.rightPoint.y, 6)
-	     g.setColor(yellow); g.draw(rCirc); g.fill(rCirc)
+	     //g.setColor(yellow); g.draw(rCirc); g.fill(rCirc)
 	     g.setColor(red)
 	     g.draw(polygon)
 	    }
    }
    
-    var i = 0
+   if(!debug) {
-    for(x <- tesselator.xMonoPoly) {
+    for(t <- tesselator.triangles) {
-      var t = x.triangles
+        val triangle = new Polygon
-      var j = 0
-      for(t <- x.triangles) { 
-        val triangle = new Polygon()
         t.foreach(p => triangle.addPoint(p.x, p.y))
-        val color = if(i == 0 && j == 3) blue else green
+        g.setColor(red)
-        g.setColor(color)
         g.draw(triangle)
-        j += 1
       }
-      i += 1
+   } else {
+    for(mp <- tesselator.monoPolies) {
+      val poly = new Polygon
+      mp.foreach(p => poly.addPoint(p.x, p.y))
+      g.setColor(yellow)
+      g.draw(poly)
+      }
     }
+    
   }
   
   override def keyPressed(key:Int, c:Char) {
     if(key == 1) quit = true
     if(key == 57) debug = !debug
     if(c == 'm') drawMap = !drawMap
+    if(c == '1') poly
+    if(c == '2') snake
+    if(c == '3') star
   }
   
   // Test #1
@@ -127,7 +129,7 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
     val p5 = new Point(400,300)*scale
     val p6 = new Point(650,250)*scale
     
-    val segments = new ArrayList[Segment]
+    val segments = new ArrayBuffer[Segment]
     segments += new Segment(p1, p2)
     segments += new Segment(p3, p4)
     segments += new Segment(p1, p3)
@@ -139,7 +141,7 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
     tesselator.process
    }
   
-  def poly2 {
+  def star {
 	
 	val scale = 1.0f
     val displace = 0f
@@ -154,7 +156,7 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
     val p9 = new Point(231,161)*scale+displace
     val p10 = new Point(321,161)*scale+displace
     
-    val segments = new ArrayList[Segment]
+    val segments = new ArrayBuffer[Segment]
     segments += new Segment(p1, p2)
     segments += new Segment(p2, p3)
     segments += new Segment(p3, p4)
@@ -187,7 +189,7 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
     val p11 = new Point(1,20)*scale+displace
     val p12 = new Point(1,10)*scale+displace
     
-    val segments = new ArrayList[Segment]
+    val segments = new ArrayBuffer[Segment]
     segments += new Segment(p1, p2)
     segments += new Segment(p2, p3)
     segments += new Segment(p3, p4)

src/org/poly2tri/QueryGraph.scala

@@ -30,29 +30,30 @@
  */
 package org.poly2tri
 
-import collection.jcl.ArrayList
+import scala.collection.mutable.ArrayBuffer
 
 // 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 = {
+  def locate(s: Segment) = head.locate(s).trapezoid
-    val sink = head.locate(s)
-    return sink.trapezoid
-  }
   
   def followSegment(s: Segment) = {
-    val trapezoids = new ArrayList[Trapezoid]
+    val trapezoids = new ArrayBuffer[Trapezoid]
     trapezoids += locate(s)
     var j = 0
-    while(s.q.x > trapezoids(j).rightPoint.x) {
+    try {
-      if(s > trapezoids(j).rightPoint) {
+	    while(s.q.x > trapezoids(j).rightPoint.x) {
-        trapezoids += trapezoids(j).upperRight
+	      if(s > trapezoids(j).rightPoint) {
-      } else {
+	        trapezoids += trapezoids(j).upperRight
-        trapezoids += trapezoids(j).lowerRight
+	      } else {
-      }
+	        trapezoids += trapezoids(j).lowerRight
-      j += 1
+	      }
+	      j += 1
+	    }
+    } catch {
+      case e => println("# of Trapezoids = " + j)
     }
     trapezoids
   }
@@ -65,25 +66,25 @@ class QueryGraph(var head: Node) {
     }
   }
   
-  def case1(sink: Sink, s: Segment, tList: ArrayList[Trapezoid]) {
+  def case1(sink: Sink, s: Segment, tList: ArrayBuffer[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]) {
+  def case2(sink: Sink, s: Segment, tList: ArrayBuffer[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]) {
+  def case3(sink: Sink, s: Segment, tList: ArrayBuffer[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]) {
+  def case4(sink: Sink, s: Segment, tList: ArrayBuffer[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)

src/org/poly2tri/TrapezoidalMap.scala

@@ -30,8 +30,7 @@
  */
 package org.poly2tri
 
-import collection.jcl.ArrayList
+import scala.collection.mutable.{Map, HashSet, ArrayBuffer}
-import scala.collection.mutable.{Map, HashSet}
 
 // See "Computational Geometry", 3rd edition, by Mark de Berg et al, Chapter 6.2
 
@@ -68,7 +67,7 @@ class TrapezoidalMap {
     
     assert(s.p.x != s.q.x)
     
-    val trapezoids = new ArrayList[Trapezoid]
+    val trapezoids = new ArrayBuffer[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)
@@ -92,7 +91,7 @@ class TrapezoidalMap {
     
     val rp = if(s.q.x == t.rightPoint.x) s.q else t.rightPoint
     
-    val trapezoids = new ArrayList[Trapezoid]
+    val trapezoids = new ArrayBuffer[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)
@@ -121,7 +120,7 @@ class TrapezoidalMap {
     val topCross = (tCross == t.top)
     val bottomCross = (bCross == t.bottom)
     
-    val trapezoids = new ArrayList[Trapezoid]
+    val trapezoids = new ArrayBuffer[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)}
     
@@ -159,7 +158,7 @@ class TrapezoidalMap {
     val topCross = (tCross == t.top)
     val bottomCross = (bCross == t.bottom)
     
-    val trapezoids = new ArrayList[Trapezoid]
+    val trapezoids = new ArrayBuffer[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)
@@ -189,7 +188,7 @@ class TrapezoidalMap {
   }
   
   // Create an AABB around segments
-  def boundingBox(segments: ArrayList[Segment]): Trapezoid = {
+  def boundingBox(segments: ArrayBuffer[Segment]): Trapezoid = {
    
     var max = segments(0).p + margin
     var min = segments(0).q + margin

src/org/poly2tri/Triangulator.scala

@@ -30,17 +30,16 @@
  */
 package org.poly2tri
 
-import collection.jcl.ArrayList
+import scala.collection.mutable.ArrayBuffer
-import scala.collection.mutable.{HashSet, Map, Stack, ListBuffer}
 
 // 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]) {
+class Triangulator(var segments: ArrayBuffer[Segment]) {
   
   // Trapezoid decomposition list
-  var trapezoids : ArrayList[Trapezoid] = null
+  var trapezoids : ArrayBuffer[Trapezoid] = null
   // Triangle decomposition list
-  // var triangles: ArrayList[Triangle] = null
+  var triangles = new ArrayBuffer[Array[Point]]
   
   // Build the trapezoidal map and query graph
   def process {
@@ -50,7 +49,7 @@ class Triangulator(var segments: ArrayList[Segment]) {
       // Remove trapezoids from trapezoidal Map
       traps.foreach(trapezoidalMap.remove)
       for(t <- traps) {
-        var tList: ArrayList[Trapezoid] = null
+        var tList: ArrayBuffer[Trapezoid] = null
         val containsP = t.contains(s.p)
         val containsQ = t.contains(s.q)
         if(containsP && containsQ) {
@@ -77,39 +76,48 @@ class Triangulator(var segments: ArrayList[Segment]) {
     }
     trapezoids = trim
     createMountains
+    
+    // Extract all the triangles into a single list
+    for(i <- 0 until xMonoPoly.size)
+      for(t <- xMonoPoly(i).triangles)
+    	  triangles += t
   }
   
-  def allTrapezoids = trapezoidalMap.map
+  // For debugging
+  def trapezoidMap = trapezoidalMap.map
+  // Monotone polygons - these are monotone mountains
+  def monoPolies: ArrayBuffer[ArrayBuffer[Point]] = {
+    val polies = new ArrayBuffer[ArrayBuffer[Point]]
+    for(i <- 0 until xMonoPoly.size)
+     polies += xMonoPoly(i).monoPoly
+    return polies
+  }
   
   // 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))
-  
+  private val xMonoPoly = new ArrayBuffer[MonotoneMountain]
-  val xMonoPoly = new ArrayList[MonotoneMountain]
                                         
   segments = orderSegments
   
   // Build a list of x-monotone mountains
   private def createMountains {
     for(s <- segments) {
-       if(s.mPoints.size > 0) {
          val mountain = new MonotoneMountain
          val k = Util.msort((x: Point, y: Point) => x < y)(s.mPoints.toList)
          val points = s.p :: k ::: List(s.q)
          points.foreach(p => 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]
+    val traps = new ArrayBuffer[Trapezoid]
     // Mark outside trapezoids
     for(t <- trapezoidalMap.map) {
 	  if(t.top == boundingBox.top || t.bottom == boundingBox.bottom) {
@@ -127,7 +135,7 @@ class Triangulator(var segments: ArrayList[Segment]) {
   
   private def orderSegments = {
     // Ignore vertical segments!
-    val segs = new ArrayList[Segment]
+    val segs = new ArrayBuffer[Segment]
     for(s <- segments) {
       // Point p must be to the left of point q
       if(s.p.x > s.q.x) {

src/org/poly2tri/Util.scala

@@ -1,7 +1,7 @@
 
 package org.poly2tri
 
-import collection.jcl.ArrayList
+import scala.collection.mutable.ArrayBuffer
 
 object Util {
   
@@ -30,7 +30,7 @@ object Random extends scala.util.Random {
    *  @param  seq   the sequence to shuffle
    *  @return       the shuffled sequence
    */
-  def shuffle[T](buf: ArrayList[T]): ArrayList[T] = {
+  def shuffle[T](buf: ArrayBuffer[T]): ArrayBuffer[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