static bool splitAndResume(vertex_info begin, FList <TriIdx> result)
{
vertex_info v1, v2;
if (!findDiagonal(begin, out v1, out v2))
{
return(false);
}
vertex_info v1_copy = v1.Clone();
vertex_info v2_copy = v2.Clone();
v1.next = v2;
v2.prev = v1;
v1_copy.next.prev = v1_copy;
v2_copy.prev.next = v2_copy;
v1_copy.prev = v2_copy;
v2_copy.next = v1_copy;
bool r1 = doTriangulate(v1, result);
bool r2 = doTriangulate(v1_copy, result);
return(r1 && r2);
}
static int windingNumber(vertex_info begin, vector point)
{
int wn = 0;
vertex_info v = begin;
do
{
if (v.p.Y <= point.Y)
{
if (v.next.p.Y > point.Y && orient2d(v.p, v.next.p, point) > 0)
{
++wn;
}
}
else
{
if (v.next.p.Y <= point.Y && orient2d(v.p, v.next.p, point) < 0)
{
--wn;
}
}
v = v.next;
} while (v != begin);
return(wn);
}
// 39% of execution time
public void updateVertex(vertex_info v)
{
var spre = v.score;
var qpre = v.isCandidate();
v.recompute();
var qpost = v.isCandidate();
var spost = v.score;
v.score = spre;
if (qpre)
{
if (qpost)
{
if (v.score != spre)
{
changeScore(v, spost);
}
}
else
{
remove(v);
}
}
else
{
if (qpost)
{
push(v);
}
}
}
static bool isLeft(vertex_info a, vertex_info b, vertex_info c)
{
if (a.idx < b.idx && b.idx < c.idx)
{
return(orient2d(a.p, b.p, c.p) > 0.0);
}
else if (a.idx < c.idx && c.idx < b.idx)
{
return(orient2d(a.p, c.p, b.p) < 0.0);
}
else if (b.idx < a.idx && a.idx < c.idx)
{
return(orient2d(b.p, a.p, c.p) < 0.0);
}
else if (b.idx < c.idx && c.idx < a.idx)
{
return(orient2d(b.p, c.p, a.p) > 0.0);
}
else if (c.idx < a.idx && a.idx < b.idx)
{
return(orient2d(c.p, a.p, b.p) > 0.0);
}
else
{
return(orient2d(c.p, b.p, a.p) < 0.0);
}
}
public void changeScore(vertex_info v, element score)
{
if (v.score != score)
{
v.score = score;
queue.UpdateHeap();
}
}
public void remove(vertex_info v)
{
var score = v.score;
if (v != queue.List[0])
{
v.score = queue.List[0].score + 1;
queue.UpdateHeap();
}
queue.Pop();
v.score = score;
}
public static void triangulate <T>(Project <T> project, FList <T> poly, FList <TriIdx> result)
{
var N = poly.Count;
result.Clear();
if (N < 3)
{
return;
}
result.Capacity = poly.Count - 2;
if (N == 3)
{
result.Add(new TriIdx(0, 1, 2));
return;
}
var vinfo = new vertex_info[N];
vinfo[0] = new vertex_info(project(poly[0]), 0);
for (int i = 1; i < N - 1; ++i)
{
vinfo[i] = new vertex_info(project(poly[i]), i);
vinfo[i].prev = vinfo[i - 1];
vinfo[i - 1].next = vinfo[i];
}
vinfo[N - 1] = new vertex_info(project(poly[N - 1]), N - 1);
vinfo[N - 1].prev = vinfo[N - 2];
vinfo[N - 1].next = vinfo[0];
vinfo[0].prev = vinfo[N - 1];
vinfo[N - 2].next = vinfo[N - 1];
for (int i = 0; i < N; ++i)
{
vinfo[i].recompute();
}
var begin = vinfo[0];
removeDegeneracies(ref begin, result);
doTriangulate(begin, result);
}
public static element triScore(vertex_info p, vertex_info v, vertex_info n)
{
// range: 0 - 1
element a, b, c;
bool convex = isLeft(p, v, n);
if (!convex)
{
return(-1e-5f);
}
a = (n.p - v.p).Length;
b = (p.p - n.p).Length;
c = (v.p - p.p).Length;
if (a < 1e-10 || b < 1e-10 || c < 1e-10)
{
return(0);
}
return(Math.Max(Math.Min((a + b) / c, Math.Min((a + c) / b, (b + c) / a)) - 1, 0));
}
public bool isClipable()
{
for (vertex_info v_test = next.next; v_test != prev; v_test = v_test.next)
{
if (v_test.convex)
{
continue;
}
if (v_test.p == prev.p ||
v_test.p == next.p)
{
continue;
}
if (v_test.p == p)
{
if (v_test.next.p == prev.p &&
v_test.prev.p == next.p)
{
return(false);
}
if (v_test.next.p == prev.p ||
v_test.prev.p == next.p)
{
continue;
}
}
if (pointInTriangle(prev, this, next, v_test))
{
return(false);
}
}
return(true);
}
static bool internalToAngle(vertex_info a, vertex_info b, vertex_info c, vector p)
{
return(internalToAngle(a.p, b.p, c.p, p));
}
static bool findDiagonal(vertex_info begin, out vertex_info v1, out vertex_info v2)
{
vertex_info t;
var heap = new FList <vertex_info>();
v1 = begin;
do
{
heap.Clear();
for (v2 = v1.next.next; v2 != v1.prev; v2 = v2.next)
{
if (!internalToAngle(v1.next, v1, v1.prev, v2.p) ||
!internalToAngle(v2.next, v2, v2.prev, v1.p))
{
continue;
}
PriorityQueue <vertex_info> .PushHeap(heap, v2, new vertex_info_l2norm_inc_ordering(v1));
}
while (heap.Count != 0)
{
v2 = PriorityQueue <vertex_info> .PopHeap(heap, new vertex_info_l2norm_inc_ordering(v1));
// test whether v1-v2 is a valid diagonal.
var v_min_x = Math.Min(v1.p.X, v2.p.X);
var v_max_x = Math.Max(v1.p.X, v2.p.X);
bool intersected = false;
for (t = v1.next; !intersected && t != v1.prev; t = t.next)
{
vertex_info u = t.next;
if (t == v2 || u == v2)
{
continue;
}
var l1 = orient2d(v1.p, v2.p, t.p);
var l2 = orient2d(v1.p, v2.p, u.p);
if ((l1 > 0.0 && l2 > 0.0) || (l1 < 0.0 && l2 < 0.0))
{
// both on the same side; no intersection
continue;
}
var dx13 = v1.p.X - t.p.X;
var dy13 = v1.p.Y - t.p.Y;
var dx43 = u.p.X - t.p.X;
var dy43 = u.p.Y - t.p.Y;
var dx21 = v2.p.X - v1.p.X;
var dy21 = v2.p.Y - v1.p.Y;
var ua_n = dx43 * dy13 - dy43 * dx13;
var ub_n = dx21 * dy13 - dy21 * dx13;
var u_d = dy43 * dx21 - dx43 * dy21;
if (Math.Abs(u_d) < element.Epsilon)
{
// parallel
if (Math.Abs(ua_n) < element.Epsilon)
{
// colinear
if (Math.Max(t.p.X, u.p.X) >= v_min_x && Math.Min(t.p.X, u.p.X) <= v_max_x)
{
// colinear and intersecting
intersected = true;
}
}
}
else
{
// not parallel
var ua = ua_n / u_d;
var ub = ub_n / u_d;
if (0 <= ua && ua <= 1 && 0 <= ub && ub <= 1)
{
intersected = true;
}
}
}
if (!intersected)
{
// test whether midpoint winding == 1
var mid = (v1.p + v2.p) / 2;
if (windingNumber(begin, mid) == 1)
{
// this diagonal is ok
return(true);
}
}
}
// couldn't find a diagonal from v1 that was ok.
v1 = v1.next;
} while (v1 != begin);
return(false);
}
static int removeDegeneracies(ref vertex_info begin, FList <TriIdx> result)
{
vertex_info v;
vertex_info n;
int count = 0;
int remain = 0;
v = begin;
do
{
v = v.next;
++remain;
} while (v != begin);
v = begin;
do
{
if (remain < 4)
{
break;
}
bool remove = false;
if (v.p == v.next.p)
{
remove = true;
}
else if (v.p == v.next.next.p)
{
if (v.next.p == v.next.next.next.p)
{
// a 'z' in the loop: z (a) b a b c . remove a-b-a . z (a) a b c . remove a-a-b (next loop) . z a b c
// z --(a)-- b
// /
// /
// a -- b -- d
remove = true;
}
else
{
// a 'shard' in the loop: z (a) b a c d . remove a-b-a . z (a) a b c d . remove a-a-b (next loop) . z a b c d
// z --(a)-- b
// /
// /
// a -- c -- d
// n.b. can only do this if the shard is pointing out of the polygon. i.e. b is outside z-a-c
remove = !internalToAngle(v.next.next.next, v, v.prev, v.next.p);
}
}
if (remove)
{
result.Add(new TriIdx(v.idx, v.next.idx, v.next.next.idx));
n = v.next;
if (n == begin)
{
begin = n.next;
}
n.remove();
count++;
remain--;
}
else
{
v = v.next;
}
} while (v != begin);
return(count);
}
static bool pointInTriangle(vertex_info a, vertex_info b, vertex_info c, vertex_info d)
{
return(!isLeft(a, c, d) && !isLeft(b, a, d) && !isLeft(c, b, d));
}
public void push(vertex_info v)
{
queue.Push(v);
}
static bool doTriangulate(vertex_info begin, FList <TriIdx> result)
{
var vq = new EarQueue();
var v = begin;
int remain = 0;
do
{
if (v.isCandidate())
{
vq.push(v);
}
v = v.next;
remain++;
} while (v != begin);
while (remain > 3 && vq.size() != 0)
{
var v2 = vq.pop();
if (!v2.isClipable())
{
v2.failed = true;
continue;
}
continue_clipping:
var n = v2.next;
var p = v2.prev;
result.Add(new TriIdx(v2.prev.idx, v2.idx, v2.next.idx));
v2.remove();
if (v2 == begin)
{
begin = v2.next;
}
if (--remain == 3)
{
break;
}
vq.updateVertex(n);
vq.updateVertex(p);
if (n.score < p.score)
{
var t = n;
n = p;
p = t;
}
if (n.score > 0.25 && n.isCandidate() && n.isClipable())
{
vq.remove(n);
v2 = n;
goto continue_clipping;
}
if (p.score > 0.25 && p.isCandidate() && p.isClipable())
{
vq.remove(p);
v2 = p;
goto continue_clipping;
}
}
if (remain > 3)
{
remain -= removeDegeneracies(ref begin, result);
if (remain > 3)
{
return(splitAndResume(begin, result));
}
}
if (remain == 3)
{
result.Add(new TriIdx(begin.idx, begin.next.idx, begin.next.next.idx));
}
var d = begin;
do
{
var n = d.next;
d = n;
} while (d != begin);
return(true);
}
