mirror of
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CDT work; removed manual point drawing; added model; fixed bugs
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dc70f1ca78
@ -236,9 +236,9 @@
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7.85981 -0.78467
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7.79516 -0.409667
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7.49774 -0.151043
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7.84688.042924
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8.23481.314479
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8.64861.702414
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7.84688 0.042924
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8.23481 0.314479
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8.64861 0.702414
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8.70034 1.09035
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8.41585 1.42656
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8.11843 1.62053
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36
data/i.18
36
data/i.18
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0 0
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5 5
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24
data/i.snake
24
data/i.snake
@ -1,12 +1,12 @@
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10 0
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20 10
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30 0
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40 10
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50 0
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50 10
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30 10
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10
data/star.dat
Normal file
10
data/star.dat
Normal file
@ -0,0 +1,10 @@
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350 75
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379 161
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469 161
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397 215
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423 301
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350 250
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277 301
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303 215
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231 161
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321 161
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16
data/strange.dat
Normal file
16
data/strange.dat
Normal file
@ -0,0 +1,16 @@
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400 472
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500 392
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520 272
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460 232
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580 212
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480 152
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360 172
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360 52
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300 112
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200 32
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120 92
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200 72
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340 272
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208 212
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180 352
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300 312
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@ -39,6 +39,7 @@ import scala.io.Source
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import seidel.Triangulator
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import shapes.{Segment, Point, Triangle}
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import earClip.EarClip
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import cdt.CDT
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// TODO: Lots of documentation!
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@ -73,6 +74,11 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
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val nazcaMonkey = "data/nazca_monkey.dat"
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val bird = "data/bird.dat"
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val snake = "data/i.snake"
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val star = "data/star.dat"
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val strange = "data/strange.dat"
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val i18 = "data/i.18"
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var currentModel = nazcaMonkey
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def init(container: GameContainer) {
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@ -171,9 +177,10 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
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if(c == 'm') drawMap = !drawMap
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if(c == '1') {currentModel = nazcaMonkey; selectModel}
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if(c == '2') {currentModel = bird; selectModel}
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if(c == '3') {poly; earClipPoly}
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if(c == '4') snake
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if(c == '5') star
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if(c == '3') {currentModel = strange; selectModel}
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if(c == '4') {currentModel = snake; selectModel}
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if(c == '5') {currentModel = star; selectModel}
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if(c == '6') {currentModel = i18; selectModel}
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if(c == 's') drawSegs = !drawSegs
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if(c == 'e') {drawEarClip = !drawEarClip; selectModel}
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if(c == 'h') {hertelMehlhorn = !hertelMehlhorn; selectModel}
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@ -185,147 +192,26 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
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loadModel(nazcaMonkey, 4.5f, Point(400, 300), 1500)
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case "data/bird.dat" =>
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loadModel(bird, 25f, Point(400, 300), 350)
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case "data/i.snake" =>
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loadModel(snake, 10f, Point(600, 300), 10)
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case "data/star.dat" =>
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loadModel(star, -1f, Point(0f, 0f), 10)
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case "data/strange.dat" =>
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loadModel(strange, -1f, Point(0f, 0f), 15)
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case "data/i.18" =>
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loadModel(i18, 15f, Point(500f, 400f), 20)
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case _ =>
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assert(false)
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}
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}
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// Test #1
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def poly {
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val p1 = Point(400,472)
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val p2 = Point(500,392)
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val p3 = Point(520,272)
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val p4 = Point(460,232)
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val p5 = Point(580,212)
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val p6 = Point(480,152)
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val p7 = Point(360,172)
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val p8 = Point(360,52)
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val p9 = Point(300,112)
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val p10 = Point(200,32)
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val p11 = Point(120,92)
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val p12 = Point(200,72)
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val p13 = Point(340,272)
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val p14 = Point(208,212)
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val p15 = Point(180,352)
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val p16 = Point(300,312)
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segments = new ArrayBuffer[Segment]
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segments += new Segment(p16, p1)
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segments += new Segment(p9, p10)
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segments += new Segment(p13, p14)
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segments += new Segment(p5, p6)
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segments += new Segment(p2, p3)
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segments += new Segment(p1, p2)
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segments += new Segment(p4, p5)
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segments += new Segment(p7, p8)
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segments += new Segment(p8, p9)
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segments += new Segment(p10, p11)
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segments += new Segment(p11, p12)
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segments += new Segment(p12, p13)
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segments += new Segment(p3, p4)
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segments += new Segment(p15, p16)
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segments += new Segment(p14, p15)
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segments += new Segment(p6, p7)
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tesselator = new Triangulator(segments)
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tesselator.buildTriangles = hertelMehlhorn
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val t1 = System.nanoTime
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tesselator process
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val t2 = System.nanoTime
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println
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println("**Poly1**")
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println("Poly2Tri total (ms) = " + (t2-t1)*1e-6)
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}
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def star {
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val p1 = Point(350,75)
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val p2 = Point(379,161)
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val p3 = Point(469,161)
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val p4 = Point(397,215)
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val p5 = Point(423,301)
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val p6 = Point(350,250)
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val p7 = Point(277,301)
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val p8 = Point(303,215)
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val p9 = Point(231,161)
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val p10 = Point(321,161)
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segments = new ArrayBuffer[Segment]
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segments += new Segment(p1, p2)
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segments += new Segment(p2, p3)
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segments += new Segment(p3, p4)
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segments += new Segment(p4, p5)
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segments += new Segment(p5, p6)
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segments += new Segment(p6, p7)
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segments += new Segment(p7, p8)
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segments += new Segment(p8, p9)
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segments += new Segment(p9, p10)
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segments += new Segment(p10, p1)
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tesselator = new Triangulator(segments)
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tesselator.buildTriangles = hertelMehlhorn
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val t1 = System.nanoTime
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tesselator process
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val t2 = System.nanoTime
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println
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println("**Star**")
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println("Poly2Tri total (ms) = " + (t2-t1)*1e-6)
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}
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// Test #2
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def snake {
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val scale = 10.0f
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val displace = 100
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val p1 = Point(10,1)*scale+displace
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val p2 = Point(20,10)*scale+displace
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val p3 = Point(30,1)*scale+displace
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val p4 = Point(40,10)*scale+displace
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val p5 = Point(50,1)*scale+displace
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val p6 = Point(50,10)*scale+displace
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val p7 = Point(40,20)*scale+displace
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val p8 = Point(30,10)*scale+displace
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val p9 = Point(20,20)*scale+displace
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val p10 = Point(10,10)*scale+displace
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val p11 = Point(1,20)*scale+displace
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val p12 = Point(1,10)*scale+displace
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segments = new ArrayBuffer[Segment]
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segments += new Segment(p1, p2)
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segments += new Segment(p2, p3)
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segments += new Segment(p3, p4)
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segments += new Segment(p4, p5)
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segments += new Segment(p5, p6)
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segments += new Segment(p6, p7)
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segments += new Segment(p7, p8)
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segments += new Segment(p8, p9)
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segments += new Segment(p9, p10)
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segments += new Segment(p10, p11)
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segments += new Segment(p11, p12)
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segments += new Segment(p12, p1)
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tesselator = new Triangulator(segments)
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tesselator.buildTriangles = hertelMehlhorn
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val t1 = System.nanoTime
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tesselator process
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val t2 = System.nanoTime
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println
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println("**Snake**")
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println("Poly2Tri total (ms) = " + (t2-t1)*1e-6)
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}
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def loadModel(model: String, scale: Float, center: Point, maxTriangles: Int) {
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println("*** " + model + " ***")
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polyX = new ArrayBuffer[Float]
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polyY = new ArrayBuffer[Float]
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val points = new ArrayBuffer[Point]
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val angle = Math.Pi
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for (line <- Source.fromFile(model).getLines) {
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@ -337,24 +223,20 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
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// Transform the shape
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polyX += (Math.cos(angle)*x - Math.sin(angle)*y).toFloat * scale + center.x
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polyY += (Math.sin(angle)*x + Math.cos(angle)*y).toFloat * scale + center.y
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points += new Point(polyX.last, polyY.last)
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} else {
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throw new Exception("Bad input file")
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}
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}
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points.foreach(println)
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segments = new ArrayBuffer[Segment]
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var i = 0
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val numPoints = polyX.size
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while(i < polyX.size-2) {
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val p1 = new Point(polyX(i), polyY(i))
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val p2 = new Point(polyX(i+1), polyY(i+1))
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segments += new Segment(p1, p2)
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i += 1
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}
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for(i <- 0 until polyX.size-1)
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segments += new Segment(points(i), points(i+1))
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// Connect the end points
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val p1 = segments(0).p
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val p2 = segments(segments.length-1).q
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segments += new Segment(p2, p1)
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segments += new Segment(points.first, points.last)
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val cdt = CDT.init(points)
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println(cdt.points.size + "," + cdt.segments.size)
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println("Number of points = " + polyX.size)
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println
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@ -379,8 +261,14 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
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earClipResults = new Array[poly2tri.earClip.Triangle](maxTriangles)
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for(i <- 0 until earClipResults.size) earClipResults(i) = new poly2tri.earClip.Triangle
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val xVerts = polyX.toArray.reverse
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val yVerts = polyY.toArray.reverse
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var xVerts = polyX.toArray
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var yVerts = polyY.toArray
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if(currentModel != strange) {
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xVerts = xVerts.reverse
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yVerts = yVerts.reverse
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}
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val t1 = System.nanoTime
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earClip.triangulatePolygon(xVerts, yVerts, xVerts.size, earClipResults)
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@ -391,55 +279,5 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
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println("Number of triangles = " + earClip.numTriangles)
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}
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}
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def earClipPoly {
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val polyX = Array(400f, 500f, 520f, 460f, 580f, 480f, 360f, 360f, 300f, 200f, 120f, 200f, 340f, 208f, 180f, 300f)
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val polyY = Array(472f, 392f, 272f, 232f, 212f, 152f, 172f, 52f, 112f, 32f, 92f, 72f, 272f, 212f, 352f, 312f)
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val earClipResults = new Array[poly2tri.earClip.Triangle](14)
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for(i <- 0 until earClipResults.size) earClipResults(i) = new poly2tri.earClip.Triangle
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val t1 = System.nanoTime
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earClip.triangulatePolygon(polyX, polyY, polyX.size, earClipResults)
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val t2 = System.nanoTime
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println("Earclip total (ms) = " + (t2-t1)*1e-6)
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}
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def earClipSnake {
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val polyX = Array(200f, 300f, 400f, 500f, 600f, 600f, 500f, 400f, 300f, 200f, 110f, 110f)
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val polyY = Array(110f, 200f, 110f, 200f, 110f, 200f, 300f, 200f, 300f, 200f, 300f, 200f)
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val earClipResults = new Array[poly2tri.earClip.Triangle](14)
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for(i <- 0 until earClipResults.size) earClipResults(i) = new poly2tri.earClip.Triangle
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val t1 = System.nanoTime
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earClip.triangulatePolygon(polyX, polyY, polyX.size, earClipResults)
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val t2 = System.nanoTime
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println("Earclip total (ms) = " + (t2-t1)*1e-6)
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}
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def earClipStar {
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val p1 = Point(350,75)
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val p2 = Point(379,161)
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val p3 = Point(469,161)
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val p4 = Point(397,215)
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val p5 = Point(423,301)
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val p6 = Point(350,250)
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val p7 = Point(277,301)
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val p8 = Point(303,215)
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val p9 = Point(231,161)
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val p10 = Point(321,161)
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val polyX = Array(350f, 379f, 469f, 397f, 423f, 350f, 277f, 303f, 231f, 321f)
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val polyY = Array(75f, 161f, 161f, 215f, 301f, 250f, 301f,215f, 161f, 161f)
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val earClipResults = new Array[poly2tri.earClip.Triangle](14)
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for(i <- 0 until earClipResults.size) earClipResults(i) = new poly2tri.earClip.Triangle
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val t1 = System.nanoTime
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earClip.triangulatePolygon(polyX, polyY, polyX.size, earClipResults)
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val t2 = System.nanoTime
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println("Earclip total (ms) = " + (t2-t1)*1e-6)
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}
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}
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@ -40,69 +40,73 @@ import utils.Util
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* See: Domiter, V. and Žalik, B.(2008)'Sweep-line algorithm for constrained Delaunay triangulation',
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* International Journal of Geographical Information Science,22:4,449 — 462
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*/
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class CDT(segments: ArrayBuffer[Segment]) {
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object CDT {
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// Inital triangle factor
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val ALPHA = 0.3f
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def init(points: ArrayBuffer[Point]): CDT = {
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var xmax, xmin = 0f
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var ymax, ymin = 0f
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// Calculate bounds
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for(i <- 0 until points.size) {
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points(i) = shearTransform(points(i))
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val p = points(i)
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if(p.x > xmax) xmax = p.x
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if(p.x < xmin) xmin = p.x
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if(p.y > ymax) ymax = p.x
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if(p.y < ymin) ymin = p.x
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}
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val deltaX = ALPHA * (xmax - xmin)
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val deltaY = ALPHA * (ymax - ymin)
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val p1 = Point(xmin - deltaX, ymin - deltaY)
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val p2 = Point(xmax - deltaX, ymin - deltaY)
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val initialTriangle = new Triangle(Array(p2, points(0), p1), null)
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val segments = initSegments(points)
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val sortedPoints = pointSort(points)
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new CDT(sortedPoints, segments, initialTriangle)
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}
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// Create segments and connect end points
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private def initSegments(points: ArrayBuffer[Point]): List[Segment] = {
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var segments = List[Segment]()
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for(i <- 0 until points.size-1)
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segments = new Segment(points(i), points(i+1)) :: segments
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segments = new Segment(points.first, points.last) :: segments
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segments
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}
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// Insertion sort is one of the fastest algorithms for sorting arrays containing
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// fewer than ten elements, or for lists that are already mostly sorted.
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// Merge sort: O(n log n)
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private def pointSort(pts: ArrayBuffer[Point]): List[Point] = {
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if(pts.size < 10)
|
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Util.insertSort((p1: Point, p2: Point) => p1 > p2)(pts).toList
|
||||
else
|
||||
Util.msort((p1: Point, p2: Point) => p1 > p2)(pts.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
|
||||
//val SHEER = 0.0001f
|
||||
private def shearTransform(point: Point) = Point(point.x, point.y + point.x * 0.0001f)
|
||||
|
||||
}
|
||||
|
||||
// The initial triangle
|
||||
var initialTriangle: Triangle = null
|
||||
// The point list
|
||||
val points = init
|
||||
class CDT(val points: List[Point], val segments: List[Segment], initialTriangle: Triangle) {
|
||||
|
||||
// The triangle mesh
|
||||
val mesh = new Mesh(initialTriangle)
|
||||
|
||||
// Used to compute inital triangle
|
||||
private val ALPHA = 0.3f
|
||||
|
||||
|
||||
// Sweep points; build mesh
|
||||
sweep
|
||||
// Finalize triangulation
|
||||
finalization
|
||||
|
||||
// Initialize and sort point list
|
||||
private def init: List[Point] = {
|
||||
|
||||
var xmax, xmin = segments(0).p.x
|
||||
var ymax, ymin = segments(0).p.y
|
||||
val pts = new ArrayBuffer[Point]
|
||||
|
||||
for(i <- 0 until segments.size) {
|
||||
|
||||
val p = segments(i).p
|
||||
val q = segments(i).q
|
||||
|
||||
if(p.x > xmax) xmax = p.x
|
||||
if(q.x > xmax) xmax = q.x
|
||||
if(p.x < xmin) xmin = p.x
|
||||
if(q.x < xmin) xmin = q.x
|
||||
|
||||
if(p.y > ymax) ymax = p.x
|
||||
if(q.y > ymax) ymax = q.x
|
||||
if(p.y < ymin) ymin = p.x
|
||||
if(q.y < ymin) ymin = q.x
|
||||
|
||||
pts += shearTransform(p)
|
||||
pts += shearTransform(q)
|
||||
}
|
||||
|
||||
var points: List[Point] = null
|
||||
|
||||
if(pts.size < 10)
|
||||
// Insertion sort is one of the fastest algorithms for sorting arrays containing
|
||||
// fewer than ten elements, or for lists that are already mostly sorted.
|
||||
points = Util.insertSort((p1: Point, p2: Point) => p1 > p2)(pts).toList
|
||||
else
|
||||
// Merge sort: O(n log n)
|
||||
points = Util.msort((p1: Point, p2: Point) => p1 > p2)(pts.toList)
|
||||
|
||||
val deltaX = ALPHA * (xmax - xmin)
|
||||
val deltaY = ALPHA * (ymax - ymin)
|
||||
|
||||
val p1 = Point(xmin - deltaX, ymin - deltaY)
|
||||
val p2 = Point(xmax - deltaX, ymin - deltaY)
|
||||
|
||||
initialTriangle = new Triangle(Array(p2, points(0), p1), null)
|
||||
points
|
||||
}
|
||||
|
||||
// Implement sweep-line paradigm
|
||||
private def sweep {
|
||||
}
|
||||
@ -110,8 +114,5 @@ class CDT(segments: ArrayBuffer[Segment]) {
|
||||
private def finalization {
|
||||
}
|
||||
|
||||
// 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
|
||||
//val SHEER = 0.0001f
|
||||
def shearTransform(point: Point) = Point(point.x, point.y + point.x * 0.0001f)
|
||||
def triangles = mesh.map
|
||||
}
|
||||
|
||||
@ -32,7 +32,7 @@ package org.poly2tri.cdt
|
||||
|
||||
import scala.collection.mutable.HashSet
|
||||
|
||||
import shapes.Point
|
||||
import shapes.{Point, Triangle}
|
||||
|
||||
class Mesh(initialTriangle: Triangle) {
|
||||
|
||||
|
||||
@ -30,18 +30,16 @@
|
||||
*/
|
||||
package org.poly2tri.shapes
|
||||
|
||||
object Event extends Enumeration {
|
||||
val point, edge = Value
|
||||
}
|
||||
|
||||
case class Point(val x: Float, val y: Float) {
|
||||
|
||||
// Pointers to next and previous points in Monontone Mountain
|
||||
var next, prev: Point = null
|
||||
// The setment this point belongs to
|
||||
var segment: Segment = null
|
||||
// Point type for CDT
|
||||
var eventType: Event.Value = _
|
||||
// Edge event pointer for CDT
|
||||
var eEvent: Segment = null
|
||||
// Point event pointer for CDT
|
||||
var pEvent: Segment = null
|
||||
|
||||
@inline def -(p: Point) = Point(x - p.x, y - p.y)
|
||||
@inline def +(p: Point) = Point(x + p.x, y + p.y)
|
||||
|
||||
@ -34,10 +34,7 @@ import scala.collection.mutable.{ArrayBuffer}
|
||||
|
||||
// Represents a simple polygon's edge
|
||||
class Segment(var p: Point, var q: Point) {
|
||||
|
||||
p.segment = this
|
||||
q.segment = this
|
||||
|
||||
|
||||
// Pointers used for building trapezoidal map
|
||||
var above, below: Trapezoid = null
|
||||
// Montone mountain points
|
||||
@ -53,27 +50,4 @@ class Segment(var p: Point, var q: Point) {
|
||||
// Determines if this segment lies below the given point
|
||||
def < (point: Point) = (Math.floor(point.y) > Math.floor(slope * point.x + b))
|
||||
|
||||
// Assign point type for CDT
|
||||
if(p.y > q.y)
|
||||
pEdge
|
||||
else if (p.y < q.y)
|
||||
pPoint
|
||||
else
|
||||
if(p.x < q.x)
|
||||
pPoint
|
||||
else if (p.x > q.x)
|
||||
pEdge
|
||||
else
|
||||
throw new Exception("Invalid segment")
|
||||
|
||||
private def pPoint {
|
||||
p.eventType = Event.point
|
||||
q.eventType = Event.edge
|
||||
}
|
||||
|
||||
private def pEdge {
|
||||
p.eventType = Event.edge
|
||||
q.eventType = Event.point
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
@ -30,8 +30,6 @@
|
||||
*/
|
||||
package org.poly2tri.shapes
|
||||
|
||||
import shapes.Point
|
||||
|
||||
// Triangle-based data structures are know to have better performance than quad-edge structures
|
||||
// See: J. Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator"
|
||||
// "Triangulations in CGAL"
|
||||
|
||||
Loading…
Reference in New Issue
Block a user