// link every hole into the outer loop, producing a single-ring polygon without holes
static EarcutNode eliminateHoles(List <Vector2> data, List <int> holeIndices, EarcutNode outerNode)
{
List <EarcutNode> queue = new List <EarcutNode>();
int len = holeIndices.Count;
for (int i = 0; i < len; i++)
{
int start = holeIndices[i];
int end = i < len - 1 ? holeIndices[i + 1] : data.Count;
EarcutNode 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 (int i = 0; i < queue.Count; i++)
{
eliminateHole(queue[i], outerNode);
outerNode = filterPoints(outerNode, outerNode.next);
}
return(outerNode);
}
// go through all polygon nodes and cure small local self-intersections
static EarcutNode cureLocalIntersections(EarcutNode start, List <Int3> 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(new Int3(a.i, p.i, b.i));
// remove two nodes involved
removeNode(p);
removeNode(p.next);
p = start = b;
}
p = p.next;
} while (p != start);
return(filterPoints(p));
}
// check whether a polygon node forms a valid ear with adjacent nodes
static bool isEar(EarcutNode 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);
}
// check if two segments intersect
static bool intersects(EarcutNode p1, EarcutNode q1, EarcutNode p2, EarcutNode q2)
{
var o1 = Mathf.Sign(area(p1, q1, p2));
var o2 = Mathf.Sign(area(p1, q1, q2));
var o3 = Mathf.Sign(area(p2, q2, p1));
var o4 = Mathf.Sign(area(p2, q2, q1));
if (o1 != o2 && o3 != o4)
{
return(true); // general case
}
if (o1 == 0 && onSegment(p1, p2, q1))
{
return(true); // p1, q1 and p2 are collinear and p2 lies on p1q1
}
if (o2 == 0 && onSegment(p1, q2, q1))
{
return(true); // p1, q1 and q2 are collinear and q2 lies on p1q1
}
if (o3 == 0 && onSegment(p2, p1, q2))
{
return(true); // p2, q2 and p1 are collinear and p1 lies on p2q2
}
if (o4 == 0 && onSegment(p2, q1, q2))
{
return(true); // p2, q2 and q1 are collinear and q1 lies on p2q2
}
return(false);
}
// eliminate colinear or duplicate points
static EarcutNode filterPoints(EarcutNode start, EarcutNode 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);
}
// try splitting polygon into two and triangulate them independently
static void splitEarcut(EarcutNode start, List <Int3> triangles, float minX, float minY, float 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, 0);
earcutLinked(c, triangles, minX, minY, invSize, 0);
return;
}
b = b.next;
}
a = a.next;
} while (a != start);
}
// create a circular doubly linked list from polygon points in the specified winding order
static EarcutNode linkedList(List <Vector2> data, int start, int end, bool clockwise)
{
EarcutNode last = null;
bool isPositiveArea = signedArea(data, start, end) > 0;
if (clockwise == isPositiveArea)
{
for (int i = start; i < end; i++)
{
last = insertNode(i, data[i].X, data[i].Y, last);
}
}
else
{
for (int i = end - 1; i >= start; i--)
{
last = insertNode(i, data[i].X, data[i].Y, last);
}
}
if (last != null && equals(last, last.next))
{
removeNode(last);
last = last.next;
}
return(last);
}
// for collinear points p, q, r, check if point q lies on segment pr
static bool onSegment(EarcutNode p, EarcutNode q, EarcutNode r)
{
return(
q.x <= Mathf.Max(p.x, r.x) &&
q.x >= Mathf.Min(p.x, r.x) &&
q.y <= Mathf.Max(p.y, r.y) &&
q.y >= Mathf.Min(p.y, r.y)
);
}
public static List <Int3> Earcut(List <Vector2> data, List <int> holeIndices = null)
{
int outerLen = (holeIndices?[0]) ?? data.Count;
EarcutNode outerNode = linkedList(data, 0, outerLen, true);
List <Int3> triangles = new List <Int3>();
if (outerNode == null || outerNode.next == outerNode.prev)
{
return(triangles);
}
float minX = 0, minY = 0, maxX, maxY, x, y, invSize = 0;
if (holeIndices?.Count > 0)
{
outerNode = eliminateHoles(data, holeIndices, outerNode);
}
if (data.Count > 80)
{
minX = maxX = data[0].X;
minY = maxY = data[0].Y;
for (var i = 1; i < outerLen; i++)
{
x = data[i].X;
y = data[i].Y;
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 = Mathf.Max(maxX - minX, maxY - minY);
invSize = Mathf.IsZero(invSize) ? 0 : 1 / invSize;
}
earcutLinked(outerNode, triangles, minX, minY, invSize, 0);
return(triangles);
}
// find a bridge between vertices that connects hole with an outer ring and and link it
static void eliminateHole(EarcutNode hole, EarcutNode outerNode)
{
outerNode = findHoleBridge(hole, outerNode);
if (outerNode != null)
{
var b = splitPolygon(outerNode, hole);
// filter collinear points around the cuts
filterPoints(outerNode, outerNode.next);
filterPoints(b, b.next);
}
}
static void removeNode(EarcutNode 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;
}
}
// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
static bool isValidDiagonal(EarcutNode a, EarcutNode b)
{
return(
a.next.i != b.i &&
a.prev.i != b.i &&
!intersectsPolygon(a, b) && // dones't intersect other edges
((locallyInside(a, b) &&
locallyInside(b, a) &&
middleInside(a, b) && // locally visible
(area(a.prev, a, b.prev) != 0 || area(a, b.prev, b) != 0)) || // does not create opposite-facing sectors
(equals(a, b) &&
area(a.prev, a, a.next) > 0 &&
area(b.prev, b, b.next) > 0))
); // special zero-length case
}
// find the leftmost node of a polygon ring
static EarcutNode getLeftmost(EarcutNode start)
{
var p = start;
var leftmost = start;
do
{
if (p.x < leftmost.x || (p.x == leftmost.x && p.y < leftmost.y))
{
leftmost = p;
}
p = p.next;
} while (p != start);
return(leftmost);
}
// create a node and optionally link it with previous one (in a circular doubly linked list)
static EarcutNode insertNode(int i, float x, float y, EarcutNode last)
{
if (last == null)
{
var p = new EarcutNode(i, x, y);
p.prev = p;
p.next = p;
return(p);
}
else
{
var p = new EarcutNode(i, x, y);
p.next = last.next;
p.prev = last;
last.next.prev = p;
last.next = p;
return(p);
}
}
// interlink polygon nodes in z-order
static void indexCurve(EarcutNode start, float minX, float minY, float invSize)
{
var 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);
}
// 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 EarcutNode splitPolygon(EarcutNode a, EarcutNode b)
{
var a2 = new EarcutNode(a.i, a.x, a.y);
var b2 = new EarcutNode(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);
}
// check if a polygon diagonal intersects any polygon segments
static bool intersectsPolygon(EarcutNode a, EarcutNode b)
{
var 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 the middle point of a polygon diagonal is inside the polygon
static bool middleInside(EarcutNode a, EarcutNode b)
{
var p = a;
bool inside = false;
float px = (a.x + b.x) / 2;
float 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);
}
public EarcutNode(int i, float x, float 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
// make sure to set them!
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;
}
// main ear slicing loop which triangulates a polygon (given as a linked list)
static void earcutLinked(EarcutNode ear, List <Int3> triangles, float minX, float minY, float invSize, int pass)
{
if (ear == null)
{
return;
}
bool hasSize = !Mathf.IsZero(invSize);
if (pass == 0 && hasSize)
{
indexCurve(ear, minX, minY, invSize);
}
var stop = ear;
while (ear.prev != ear.next)
{
var prev = ear.prev;
var next = ear.next;
if (hasSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear))
{
// cut off the triangle
triangles.Add(new Int3(prev.i, ear.i, next.i));
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(filterPoints(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;
}
}
}
// Simon Tatham's linked list merge sort algorithm
// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
static EarcutNode sortLinked(EarcutNode list)
{
int numMerges;
int inSize = 1;
do
{
EarcutNode p = list;
list = null;
EarcutNode tail = null;
numMerges = 0;
while (p != null)
{
numMerges++;
var q = p;
int pSize = 0;
for (int i = 0; i < inSize; i++)
{
pSize++;
q = q.nextZ;
if (q == null)
{
break;
}
}
int qSize = inSize;
while (pSize > 0 || (qSize > 0 && q != null))
{
EarcutNode e;
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);
}
static int compareX(EarcutNode a, EarcutNode b)
{
float comp = a.x - b.x;
return(comp > 0 ? 1 : (comp < 0 ? -1 : 0));
}
static bool isEarHashed(EarcutNode ear, float minX, float minY, float 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);
}
// David Eberly's algorithm for finding a bridge between hole and outer polygon
static EarcutNode findHoleBridge(EarcutNode hole, EarcutNode outerNode)
{
var p = outerNode;
float hx = hole.x;
float hy = hole.y;
float qx = float.NegativeInfinity;
EarcutNode 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); // hole touches outer segment; pick leftmost 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;
float mx = m.x;
float my = m.y;
float tanMin = float.PositiveInfinity;
float tan;
p = m;
do
{
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 = Mathf.Abs(hy - p.y) / (hx - p.x); // tangential
if (
locallyInside(p, hole) &&
(tan < tanMin ||
(tan == tanMin &&
(p.x > m.x || (p.x == m.x && sectorContainsSector(m, p)))))
)
{
m = p;
tanMin = tan;
}
}
p = p.next;
} while (p != stop);
return(m);
}
// check if a polygon diagonal is locally inside the polygon
static bool locallyInside(EarcutNode a, EarcutNode 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);
}
// whether sector in vertex m contains sector in vertex p in the same coordinates
static bool sectorContainsSector(EarcutNode m, EarcutNode p)
{
return(area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0);
}
// signed area of a triangle
static float area(EarcutNode p, EarcutNode q, EarcutNode 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(EarcutNode p1, EarcutNode p2)
{
return(p1.x == p2.x && p1.y == p2.y);
}
