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fixed circumcircle test

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This commit is contained in:
zzzzrrr 2009-08-16 13:25:06 -04:00
parent cd7d09ee8a
commit 47eb8c6f6c
4 changed files with 170 additions and 74 deletions
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2
src/org/poly2tri/Poly2Tri.scala
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@ -87,7 +87,7 @@ class Poly2TriDemo extends BasicGame("Poly2Tri") {
val i18 = "data/i.18"
val tank = "data/tank.dat"
var currentModel = nazcaMonkey
var currentModel = strange
var doCDT = true
var mouseButton = 0

24
src/org/poly2tri/cdt/AFront.scala
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@ -98,8 +98,6 @@ class AFront(iTriangle: Triangle) {
val point1 = edge.q
val point2 = edge.p
var edgeTri1: Triangle = null
var edgeTri2: Triangle = null
var marked = false
// Scan the advancing front and update Node triangle pointers
@ -108,29 +106,19 @@ class AFront(iTriangle: Triangle) {
T2.foreach(t => {
if(t.contains(node.point, node.next.point))
node.triangle = t
if(!marked && t.contains(point1, point2)) {
edgeTri2 = t
edgeTri2 markEdge(point1, point2)
marked = true
}
})
marked = false
T1.foreach(t => {
if(t.contains(node.point, node.next.point))
node.triangle = t
if(!marked && t.contains(point1, point2)) {
edgeTri1 = t
edgeTri1 markEdge(point1, point2)
marked = true
}
})
if(!marked)
T1.foreach(t => {
if(t.contains(node.point, node.next.point))
node.triangle = t
})
node = node.next
}
edgeTri1.markNeighbor(edgeTri2)
T1.last.markNeighbor(T2.last)
}

82
src/org/poly2tri/cdt/CDT.scala
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@ -34,6 +34,7 @@ import scala.collection.mutable.{ArrayBuffer, Set}
import shapes.{Segment, Point, Triangle}
import utils.Util
import seidel.MonotoneMountain
/**
* Sweep-line, Constrained Delauney Triangulation (CDT)
@ -242,6 +243,10 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
aFront.constrainedEdge(sNode, eNode, T1, T2, edge)
// Mark constrained edge
T1.last markEdge(point1, point2)
T2.last markEdge(point1, point2)
} else if(firstTriangle == null) {
// No triangles are intersected by the edge; edge must lie outside the mesh
@ -251,7 +256,7 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
val point1 = if(ahead) edge.q else edge.p
val point2 = if(ahead) edge.p else edge.q
var pNode = aFront.locatePoint(point1)
var pNode = if(ahead) node else aFront.locatePoint(point1)
val first = pNode
val points = new ArrayBuffer[Point]
@ -266,30 +271,19 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
nTriangles += pNode.triangle
pNode = pNode.next
}
// Triangulate empty areas.
val T = new ArrayBuffer[Triangle]
triangulate(points.toArray, List(point1, point2), T)
//T.foreach(t => mesh.debug += t)
// Select edge triangle
var edgeTri: Triangle = null
var i = 0
while(edgeTri == null) {
if(T(i).contains(point1, point2))
edgeTri = T(i)
i += 1
}
// Update advancing front
aFront link (first, pNode, edgeTri)
// Update neighbors
edgeNeighbors(nTriangles, T)
// Update advancing front
aFront link (first, pNode, T.last)
// Mark constrained edge
edgeTri markEdge(point1, point2)
T.last markEdge(point1, point2)
} else if(firstTriangle.contains(edge.q, edge.p)) {
// Mark constrained edge
@ -297,7 +291,6 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
firstTriangle.finalized = true
} else {
throw new Exception("Triangulation error")
//null
}
}
@ -316,18 +309,18 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
}
// Marc Vigo Anglada's triangulate pseudo-polygon algo
// See "An improved incremental algorithm for constructing restricted Delaunay triangulations"
private def triangulate(P: Array[Point], ab: List[Point], T: ArrayBuffer[Triangle]) {
val a = ab.first
val b = ab.last
val a = ab(0)
val b = ab(1)
var i = 0
if(P.size > 1) {
var c = P.first
var c = P(0)
for(j <- 1 until P.size) {
if(illegal(a, c, b, P(j))) {
if(illegal(a, b, c, P(j))) {
c = P(j)
i = j
}
@ -389,31 +382,18 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
angle
}
// Do edges need to be swapped? Robust CircumCircle test
// See section 3.7 from "Triangulations and Applications" by O. Hjelle & M. Deahlen
private def illegal(p1: Point, p2: Point, p3: Point, p4:Point): Boolean = {
// Circumcircle test.
// Determines if point d lies inside triangle abc's circumcircle
def illegal(a: Point, b: Point, c: Point, d: Point): Boolean = {
val ccw = Util.orient2d(a, b, c) > 0
// Make sure abc is oriented counter-clockwise
if(ccw)
Util.incircle(a, b, c, d)
else
Util.incircle(a, c, b, d)
val v1 = p3 - p2
val v2 = p1 - p2
val v3 = p1 - p4
val v4 = p3 - p4
val cosA = v1 dot v2
val cosB = v3 dot v4
if(cosA < 0 && cosB < 0)
return true
if(cosA > 0 && cosB > 0)
return false
val sinA = v1 cross v2
val sinB = v3 cross v4
if((cosA*sinB + sinA*cosB) < 0f)
true
else
false
}
// Ensure adjacent triangles are legal
@ -424,10 +404,8 @@ class CDT(val points: List[Point], val segments: List[Segment], iTriangle: Trian
val point = t1.points(0)
val oPoint = t2 oppositePoint t1
val collinear = t1.collinear(oPoint) || t2.collinear(oPoint, point)
if(illegal(t1.points(1), oPoint, t1.points(2), t1.points(0)) && !t2.finalized) {
if(illegal(t1.points(1), t1.points(0), t1.points(2), oPoint) && !t2.finalized) {
// Flip edge and rotate everything clockwise
t1.legalize(oPoint)

136
src/org/poly2tri/utils/Util.scala
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@ -12,7 +12,8 @@ object Util {
val epsilon = exactinit
val ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon
val iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon
// From "Scala By Example," by Martin Odersky
def msort[A](less: (A, A) => Boolean)(xs: List[A]): List[A] = {
def merge(xs1: List[A], xs2: List[A]): List[A] =
@ -120,7 +121,7 @@ object Util {
return det
}
val errbound = Util.ccwerrboundA * detsum
val errbound = ccwerrboundA * detsum
if ((det >= errbound) || (-det >= errbound)) {
return det
} else {
@ -129,7 +130,136 @@ object Util {
return orient2d(pa, pb, c)
}
}
}
// Returns triangle circumcircle point and radius
def circumCircle(a: Point, b: Point, c: Point): Tuple2[Point, Float] = {
val A = det(a, b, c)
val C = detC(a, b, c)
val bx1 = Point(a.x*a.x + a.y*a.y, a.y)
val bx2 = Point(b.x*b.x + b.y*b.y, b.y)
val bx3 = Point(c.x*c.x + c.y*c.y, c.y)
val bx = det(bx1, bx2, bx3)
val by1 = Point(a.x*a.x + a.y*a.y, a.x)
val by2 = Point(b.x*b.x + b.y*b.y, b.x)
val by3 = Point(c.x*c.x + c.y*c.y, c.x)
val by = det(by1, by2, by3)
val x = bx / (2*A)
val y = by / (2*A)
val center = Point(x, y)
val radius = Math.sqrt(bx*bx + by*by - 4*A*C).toFloat / (2*Math.abs(A))
(center, radius)
}
def det(p1: Point, p2: Point, p3: Point): Float = {
val a11 = p1.x
val a12 = p1.y
val a13,a23,a33 = 1f
val a21 = p2.x
val a22 = p2.y
val a31 = p3.x
val a32 = p3.y
a11*(a22*a33-a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32-a22*a31)
}
def detC(p1: Point, p2: Point, p3: Point): Float = {
val a11 = p1.x*p1.x + p1.y*p1.y
val a12 = p1.x
val a13 = p1.y
val a21 = p2.x*p2.x + p2.y*p2.y
val a22 = p2.x
val a23 = p2.y
val a31 = p3.x*p3.x + p3.y*p3.y
val a32 = p3.x
val a33 = p3.y
a11*(a22*a33-a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32-a22*a31)
}
/* Approximate 2D incircle test. Nonrobust. By Jonathan Shewchuk
* Return a positive value if the point pd lies inside the
* circle passing through pa, pb, and pc; a negative value if
* it lies outside; and zero if the four points are cocircular.
* The points pa, pb, and pc must be in counterclockwise
* order, or the sign of the result will be reversed.
*/
def incirclefast(pa: Point, pb: Point, pc: Point, pd: Point): Boolean = {
val adx = pa.x - pd.x
val ady = pa.y - pd.y
val bdx = pb.x - pd.x
val bdy = pb.y - pd.y
val cdx = pc.x - pd.x
val cdy = pc.y - pd.y
val abdet = adx * bdy - bdx * ady
val bcdet = bdx * cdy - cdx * bdy
val cadet = cdx * ady - adx * cdy
val alift = adx * adx + ady * ady
val blift = bdx * bdx + bdy * bdy
val clift = cdx * cdx + cdy * cdy
alift * bcdet + blift * cadet + clift * abdet >= 0
}
/* Robust 2D incircle test, modified. Original By Jonathan Shewchuk
* Return a positive value if the point pd lies inside the
* circle passing through pa, pb, and pc; a negative value if
* it lies outside; and zero if the four points are cocircular.
* The points pa, pb, and pc must be in counterclockwise
* order, or the sign of the result will be reversed.
*/
def incircle(pa: Point, pb: Point, pc: Point, pd: Point): Boolean = {
val adx = pa.x - pd.x
val bdx = pb.x - pd.x
val cdx = pc.x - pd.x
val ady = pa.y - pd.y
val bdy = pb.y - pd.y
val cdy = pc.y - pd.y
val bdxcdy = bdx * cdy
val cdxbdy = cdx * bdy
val alift = adx * adx + ady * ady
val cdxady = cdx * ady
val adxcdy = adx * cdy
val blift = bdx * bdx + bdy * bdy
val adxbdy = adx * bdy
val bdxady = bdx * ady
val clift = cdx * cdx + cdy * cdy
val det = alift * (bdxcdy - cdxbdy) +
blift * (cdxady - adxcdy) +
clift * (adxbdy - bdxady)
val permanent = (Math.abs(bdxcdy) + Math.abs(cdxbdy)) * alift +
(Math.abs(cdxady) + Math.abs(adxcdy)) * blift +
(Math.abs(adxbdy) + Math.abs(bdxady)) * clift
val errbound = iccerrboundA * permanent
if ((det > errbound) || (-det > errbound)) {
return det >= 0
} else {
throw new Exception("Points nearly collinear")
}
}
}