using System;
using System.Collections.Generic;
namespace EarcutNet
{
public class Earcut
{
public static List<int> Tessellate(IList<double> data, IList<int> holeIndices)
{
var hasHoles = holeIndices.Count > 0;
var outerLen = hasHoles ? holeIndices[0] * 2 : data.Count;
var outerNode = LinkedList(data, 0, outerLen, true);
var triangles = new List<int>();
if (outerNode == null)
{
return triangles;
}
var minX = double.PositiveInfinity;
var minY = double.PositiveInfinity;
var maxX = double.NegativeInfinity;
var maxY = double.NegativeInfinity;
var invSize = default(double);
if (hasHoles)
{
outerNode = EliminateHoles(data, holeIndices, outerNode);
}
// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
if (data.Count > 80 * 2)
{
for (int i = 0; i < outerLen; i += 2)
{
double x = data[i];
double y = data[i + 1];
if (x < minX)
{
minX = x;
}
if (y < minY)
{
minY = y;
}
if (x > maxX)
{
maxX = x;
}
if (y > maxY)
{
maxY = y;
}
}
// minX, minY and invSize are later used to transform coords into integers for z-order calculation
invSize = Math.Max(maxX - minX, maxY - minY);
invSize = invSize != 0 ? 1 / invSize : 0;
}
EarcutLinked(outerNode, triangles, minX, minY, invSize, 0);
return triangles;
}
// Creates a circular doubly linked list from polygon points in the specified winding order.
static Node LinkedList(IList<double> data, int start, int end, bool clockwise)
{
var last = default(Node);
if (clockwise == (SignedArea(data, start, end) > 0))
{
for (int i = start; i < end; i += 2)
{
last = InsertNode(i, data[i], data[i + 1], last);
}
}
else
{
for (int i = end - 2; i >= start; i -= 2)
{
last = InsertNode(i, data[i], data[i + 1], last);
}
}
if (last != null && Equals(last, last.next))
{
RemoveNode(last);
last = last.next;
}
return last;
}
// eliminate colinear or duplicate points
static Node FilterPoints(Node start, Node end = null)
{
if (start == null)
{
return start;
}
if (end == null)
{
end = start;
}
var p = start;
bool again;
do
{
again = false;
if (!p.steiner && (Equals(p, p.next) || Area(p.prev, p, p.next) == 0))
{
RemoveNode(p);
p = end = p.prev;
if (p == p.next)
{
break;
}
again = true;
}
else
{
p = p.next;
}
} while (again || p != end);
return end;
}
// main ear slicing loop which triangulates a polygon (given as a linked list)
static void EarcutLinked(Node ear, IList<int> triangles, double minX, double minY, double invSize, int pass = 0)
{
if (ear == null)
{
return;
}
// interlink polygon nodes in z-order
if (pass == 0 && invSize != 0)
{
IndexCurve(ear, minX, minY, invSize);
}
var stop = ear;
Node prev;
Node next;
// iterate through ears, slicing them one by one
while (ear.prev != ear.next)
{
prev = ear.prev;
next = ear.next;
if (invSize != 0 ? IsEarHashed(ear, minX, minY, invSize) : IsEar(ear))
{
// cut off the triangle
triangles.Add(prev.i / 2);
triangles.Add(ear.i / 2);
triangles.Add(next.i / 2);
RemoveNode(ear);
// skipping the next vertex leads to less sliver triangles
ear = next.next;
stop = next.next;
continue;
}
ear = next;
// if we looped through the whole remaining polygon and can't find any more ears
if (ear == stop)
{
// try filtering points and slicing again
if (pass == 0)
{
EarcutLinked(FilterPoints(ear), triangles, minX, minY, invSize, 1);
// if this didn't work, try curing all small self-intersections locally
}
else if (pass == 1)
{
ear = CureLocalIntersections(ear, triangles);
EarcutLinked(ear, triangles, minX, minY, invSize, 2);
// as a last resort, try splitting the remaining polygon into two
}
else if (pass == 2)
{
SplitEarcut(ear, triangles, minX, minY, invSize);
}
break;
}
}
}
// check whether a polygon node forms a valid ear with adjacent nodes
static bool IsEar(Node ear)
{
var a = ear.prev;
var b = ear;
var c = ear.next;
if (Area(a, b, c) >= 0)
{
return false; // reflex, can't be an ear
}
// now make sure we don't have other points inside the potential ear
var p = ear.next.next;
while (p != ear.prev)
{
if (PointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
Area(p.prev, p, p.next) >= 0)
{
return false;
}
p = p.next;
}
return true;
}
static bool IsEarHashed(Node ear, double minX, double minY, double invSize)
{
var a = ear.prev;
var b = ear;
var c = ear.next;
if (Area(a, b, c) >= 0)
{
return false; // reflex, can't be an ear
}
// triangle bbox; min & max are calculated like this for speed
var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x);
var minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y);
var maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x);
var maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y);
// z-order range for the current triangle bbox;
var minZ = ZOrder(minTX, minTY, minX, minY, invSize);
var maxZ = ZOrder(maxTX, maxTY, minX, minY, invSize);
var p = ear.prevZ;
var n = ear.nextZ;
// look for points inside the triangle in both directions
while (p != null && p.z >= minZ && n != null && n.z <= maxZ)
{
if (p != ear.prev && p != ear.next &&
PointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
Area(p.prev, p, p.next) >= 0)
{
return false;
}
p = p.prevZ;
if (n != ear.prev && n != ear.next &&
PointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&
Area(n.prev, n, n.next) >= 0)
{
return false;
}
n = n.nextZ;
}
// look for remaining points in decreasing z-order
while (p != null && p.z >= minZ)
{
if (p != ear.prev && p != ear.next &&
PointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
Area(p.prev, p, p.next) >= 0)
{
return false;
}
p = p.prevZ;
}
// look for remaining points in increasing z-order
while (n != null && n.z <= maxZ)
{
if (n != ear.prev && n != ear.next &&
PointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&
Area(n.prev, n, n.next) >= 0)
{
return false;
}
n = n.nextZ;
}
return true;
}
// go through all polygon nodes and cure small local self-intersections
static Node CureLocalIntersections(Node start, IList<int> triangles)
{
var p = start;
do
{
var a = p.prev;
var b = p.next.next;
if (!Equals(a, b) && Intersects(a, p, p.next, b) && LocallyInside(a, b) && LocallyInside(b, a))
{
triangles.Add(a.i / 2);
triangles.Add(p.i / 2);
triangles.Add(b.i / 2);
// remove two nodes involved
RemoveNode(p);
RemoveNode(p.next);
p = start = b;
}
p = p.next;
} while (p != start);
return p;
}
// try splitting polygon into two and triangulate them independently
static void SplitEarcut(Node start, IList<int> triangles, double minX, double minY, double invSize)
{
// look for a valid diagonal that divides the polygon into two
var a = start;
do
{
var b = a.next.next;
while (b != a.prev)
{
if (a.i != b.i && IsValidDiagonal(a, b))
{
// split the polygon in two by the diagonal
var c = SplitPolygon(a, b);
// filter colinear points around the cuts
a = FilterPoints(a, a.next);
c = FilterPoints(c, c.next);
// run earcut on each half
EarcutLinked(a, triangles, minX, minY, invSize);
EarcutLinked(c, triangles, minX, minY, invSize);
return;
}
b = b.next;
}
a = a.next;
} while (a != start);
}
// link every hole into the outer loop, producing a single-ring polygon without holes
static Node EliminateHoles(IList<double> data, IList<int> holeIndices, Node outerNode)
{
var queue = new List<Node>();
var len = holeIndices.Count;
for (var i = 0; i < len; i++)
{
var start = holeIndices[i] * 2;
var end = i < len - 1 ? holeIndices[i + 1] * 2 : data.Count;
var list = LinkedList(data, start, end, false);
if (list == list.next)
{
list.steiner = true;
}
queue.Add(GetLeftmost(list));
}
queue.Sort(CompareX);
// process holes from left to right
for (var i = 0; i < queue.Count; i++)
{
EliminateHole(queue[i], outerNode);
outerNode = FilterPoints(outerNode, outerNode.next);
}
return outerNode;
}
static int CompareX(Node a, Node b)
{
return Math.Sign(a.x - b.x);
}
// find a bridge between vertices that connects hole with an outer ring and and link it
static void EliminateHole(Node hole, Node outerNode)
{
outerNode = FindHoleBridge(hole, outerNode);
if (outerNode != null)
{
var b = SplitPolygon(outerNode, hole);
FilterPoints(b, b.next);
}
}
// David Eberly's algorithm for finding a bridge between hole and outer polygon
static Node FindHoleBridge(Node hole, Node outerNode)
{
var p = outerNode;
var hx = hole.x;
var hy = hole.y;
var qx = double.NegativeInfinity;
Node m = null;
// find a segment intersected by a ray from the hole's leftmost point to the left;
// segment's endpoint with lesser x will be potential connection point
do
{
if (hy <= p.y && hy >= p.next.y && p.next.y != p.y)
{
var x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y);
if (x <= hx && x > qx)
{
qx = x;
if (x == hx)
{
if (hy == p.y)
{
return p;
}
if (hy == p.next.y)
{
return p.next;
}
}
m = p.x < p.next.x ? p : p.next;
}
}
p = p.next;
} while (p != outerNode);
if (m == null)
{
return null;
}
if (hx == qx)
{
return m.prev; // hole touches outer segment; pick lower endpoint
}
// look for points inside the triangle of hole point, segment intersection and endpoint;
// if there are no points found, we have a valid connection;
// otherwise choose the point of the minimum angle with the ray as connection point
var stop = m;
var mx = m.x;
var my = m.y;
var tanMin = double.PositiveInfinity;
double tan;
p = m.next;
while (p != stop)
{
if (hx >= p.x && p.x >= mx && hx != p.x && PointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y))
{
tan = Math.Abs(hy - p.y) / (hx - p.x); // tangential
if ((tan < tanMin || (tan == tanMin && p.x > m.x)) && LocallyInside(p, hole))
{
m = p;
tanMin = tan;
}
}
p = p.next;
}
return m;
}
// interlink polygon nodes in z-order
static void IndexCurve(Node start, double minX, double minY, double invSize)
{
Node p = start;
do
{
if (p.z == null)
{
p.z = ZOrder(p.x, p.y, minX, minY, invSize);
}
p.prevZ = p.prev;
p.nextZ = p.next;
p = p.next;
} while (p != start);
p.prevZ.nextZ = null;
p.prevZ = null;
SortLinked(p);
}
// Simon Tatham's linked list merge sort algorithm
// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
static Node SortLinked(Node list)
{
int i;
Node p;
Node q;
Node e;
Node tail;
int numMerges;
int pSize;
int qSize;
int inSize = 1;
do
{
p = list;
list = null;
tail = null;
numMerges = 0;
while (p != null)
{
numMerges++;
q = p;
pSize = 0;
for (i = 0; i < inSize; i++)
{
pSize++;
q = q.nextZ;
if (q == null)
{
break;
}
}
qSize = inSize;
while (pSize > 0 || (qSize > 0 && q != null))
{
if (pSize != 0 && (qSize == 0 || q == null || p.z <= q.z))
{
e = p;
p = p.nextZ;
pSize--;
}
else
{
e = q;
q = q.nextZ;
qSize--;
}
if (tail != null)
{
tail.nextZ = e;
}
else
{
list = e;
}
e.prevZ = tail;
tail = e;
}
p = q;
}
tail.nextZ = null;
inSize *= 2;
} while (numMerges > 1);
return list;
}
// z-order of a point given coords and inverse of the longer side of data bbox
static int ZOrder(double x, double y, double minX, double minY, double invSize)
{
// coords are transformed into non-negative 15-bit integer range
int intX = (int)(32767 * (x - minX) * invSize);
int intY = (int)(32767 * (y - minY) * invSize);
intX = (intX | (intX << 8)) & 0x00FF00FF;
intX = (intX | (intX << 4)) & 0x0F0F0F0F;
intX = (intX | (intX << 2)) & 0x33333333;
intX = (intX | (intX << 1)) & 0x55555555;
intY = (intY | (intY << 8)) & 0x00FF00FF;
intY = (intY | (intY << 4)) & 0x0F0F0F0F;
intY = (intY | (intY << 2)) & 0x33333333;
intY = (intY | (intY << 1)) & 0x55555555;
return intX | (intY << 1);
}
// find the leftmost node of a polygon ring
static Node GetLeftmost(Node start)
{
Node p = start;
Node leftmost = start;
do
{
if (p.x < leftmost.x)
{
leftmost = p;
}
p = p.next;
} while (p != start);
return leftmost;
}
// check if a point lies within a convex triangle
static bool PointInTriangle(double ax, double ay, double bx, double by, double cx, double cy, double px, double py)
{
return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
(ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
(bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;
}
// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
static bool IsValidDiagonal(Node a, Node b)
{
return a.next.i != b.i && a.prev.i != b.i && !IntersectsPolygon(a, b) &&
LocallyInside(a, b) && LocallyInside(b, a) && MiddleInside(a, b);
}
// signed area of a triangle
static double Area(Node p, Node q, Node r)
{
return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
}
// check if two points are equal
static bool Equals(Node p1, Node p2)
{
return p1.x == p2.x && p1.y == p2.y;
}
// check if two segments intersect
static bool Intersects(Node p1, Node q1, Node p2, Node q2)
{
if ((Equals(p1, q1) && Equals(p2, q2)) ||
(Equals(p1, q2) && Equals(p2, q1)))
{
return true;
}
return Area(p1, q1, p2) > 0 != Area(p1, q1, q2) > 0 &&
Area(p2, q2, p1) > 0 != Area(p2, q2, q1) > 0;
}
// check if a polygon diagonal intersects any polygon segments
static bool IntersectsPolygon(Node a, Node b)
{
Node p = a;
do
{
if (p.i != a.i && p.next.i != a.i && p.i != b.i && p.next.i != b.i &&
Intersects(p, p.next, a, b))
{
return true;
}
p = p.next;
} while (p != a);
return false;
}
// check if a polygon diagonal is locally inside the polygon
static bool LocallyInside(Node a, Node b)
{
return Area(a.prev, a, a.next) < 0 ?
Area(a, b, a.next) >= 0 && Area(a, a.prev, b) >= 0 :
Area(a, b, a.prev) < 0 || Area(a, a.next, b) < 0;
}
// check if the middle point of a polygon diagonal is inside the polygon
static bool MiddleInside(Node a, Node b)
{
var p = a;
var inside = false;
var px = (a.x + b.x) / 2;
var py = (a.y + b.y) / 2;
do
{
if (((p.y > py) != (p.next.y > py)) && p.next.y != p.y &&
(px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x))
{
inside = !inside;
}
p = p.next;
} while (p != a);
return inside;
}
// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two;
// if one belongs to the outer ring and another to a hole, it merges it into a single ring
static Node SplitPolygon(Node a, Node b)
{
var a2 = new Node(a.i, a.x, a.y);
var b2 = new Node(b.i, b.x, b.y);
var an = a.next;
var bp = b.prev;
a.next = b;
b.prev = a;
a2.next = an;
an.prev = a2;
b2.next = a2;
a2.prev = b2;
bp.next = b2;
b2.prev = bp;
return b2;
}
// create a node and optionally link it with previous one (in a circular doubly linked list)
static Node InsertNode(int i, double x, double y, Node last)
{
var p = new Node(i, x, y);
if (last == null)
{
p.prev = p;
p.next = p;
}
else
{
p.next = last.next;
p.prev = last;
last.next.prev = p;
last.next = p;
}
return p;
}
static void RemoveNode(Node p)
{
p.next.prev = p.prev;
p.prev.next = p.next;
if (p.prevZ != null)
{
p.prevZ.nextZ = p.nextZ;
}
if (p.nextZ != null)
{
p.nextZ.prevZ = p.prevZ;
}
}
class Node
{
public int i;
public double x;
public double y;
public int? z;
public Node prev;
public Node next;
public Node prevZ;
public Node nextZ;
public bool steiner;
public Node(int i, double x, double y)
{
// vertex index in coordinates array
this.i = i;
// vertex coordinates
this.x = x;
this.y = y;
// previous and next vertex nodes in a polygon ring
this.prev = null;
this.next = null;
// z-order curve value
this.z = null;
// previous and next nodes in z-order
this.prevZ = null;
this.nextZ = null;
// indicates whether this is a steiner point
this.steiner = false;
}
}
static double SignedArea(IList<double> data, int start, int end)
{
var sum = default(double);
for (int i = start, j = end - 2; i < end; i += 2)
{
sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
j = i;
}
return sum;
}
// return a percentage difference between the polygon area and its triangulation area;
// used to verify correctness of triangulation
public static double Deviation(IList<double> data, IList<int> holeIndices, IList<int> triangles)
{
var hasHoles = holeIndices.Count > 0;
var outerLen = hasHoles ? holeIndices[0] * 2 : data.Count;
var polygonArea = Math.Abs(SignedArea(data, 0, outerLen));
if (hasHoles)
{
var len = holeIndices.Count;
for (var i = 0; i < len; i++)
{
var start = holeIndices[i] * 2;
var end = i < len - 1 ? holeIndices[i + 1] * 2 : data.Count;
polygonArea -= Math.Abs(SignedArea(data, start, end));
}
}
var trianglesArea = default(double);
for (var i = 0; i < triangles.Count; i += 3)
{
var a = triangles[i] * 2;
var b = triangles[i + 1] * 2;
var c = triangles[i + 2] * 2;
trianglesArea += Math.Abs(
(data[a] - data[c]) * (data[b + 1] - data[a + 1]) -
(data[a] - data[b]) * (data[c + 1] - data[a + 1]));
}
return polygonArea == 0 && trianglesArea == 0 ? 0 :
Math.Abs((trianglesArea - polygonArea) / polygonArea);
}
}
}