标签：list -- count end 索引数据 描述 名称 rtl 问题
问题背景：
我这边最近需要实现动态去画多边形（不规则的），类似于高德地图中那种面积测量工具一般。
方案：
”割耳“算法实现三角化平面。
具体实现：
割耳算法类：
/*
*******************************************************
*
* 文件名称：EarCut
* 文件描述：三角化相关算法集合
*
* 版本：V1.0.0
* 支持带洞的多边形，需要保证多边形为顺时针，而洞为逆时针顺序
* *****************************************************
*/
using System;
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
namespace Tx3d.Framework
{
public class EarCut
{
#region Sub Class
///
/// “割耳”点
///
private class Node : IComparable
{
#region Members & Properties
///
/// vertice index in coordinates array
///
public int i = -1;
///
/// vertex coordinates
///
public float x = 0.0f;
public float z = 0.0f;
///
/// previous and next vertice nodes in a polygon ring
///
public Node prev = null;
public Node next = null;
///
/// z-order curve value
///
public int zOrder = -1;
///
/// previous and next nodes in z-order
///
public Node prevZ = null;
public Node nextZ = null;
///
/// indicates whether this is a steiner point
///
public bool steiner = false;
#endregion
#region IComparable Implemention
public int CompareTo(object obj)
{
try
{
Node node = obj as Node;
if (this.x > node.x)
{
return 1;
}
else
{
return 0;
}
}
catch (Exception ex)
{
throw new Exception(ex.Message);
}
}
#endregion
}
#endregion
#region Members & Properties
private static float EPSINON = 0.1f;
#endregion
#region Public Methods
///
/// “割耳”
///
public static Listint> CutEar(List data, Listint> holeIndices)
{
var triangles = new Listint>();
bool hasHoles = holeIndices != null && holeIndices.Count > 0;
int outerLength = hasHoles ? holeIndices[0] : data.Count;
Node outerNode = LinkedList(data, 0, outerLength, true);
if (outerNode == null)
{
return triangles;
}
if (hasHoles)
{
outerNode = EliminateHoles(data, holeIndices, outerNode);
}
float minX = 0.0f;
float minZ = 0.0f;
float maxX = 0.0f;
float maxZ = 0.0f;
float size = 0.0f;
// if the shape is not too simple, we‘ll use z-order curve hash later; calculate polygon bbox
// if (data.Count > 80)
if (data.Count > 100)
{
minX = maxX = data[0].x;
minZ = maxZ = data[0].z;
for (int i = 1; i )
{
float x = data[i].x;
float z = data[i].z;
if (x x;
if (z z;
if (x > maxX) maxX = x;
if (z > maxZ) maxZ = z;
}
// minX, minY and size are later used to transform coords into integers for z-order calculation
size = Mathf.Max(maxX - minX, maxZ - minZ);
}
EarCutLinked(outerNode, triangles, minX, minZ, size, 0);
return triangles;
}
#endregion
#region Private Methods
///
/// 使用多边形顶点按照指定顺序创建一个双向循环链表
///
private static Node LinkedList(List data, int start, int end, bool clockwise)
{
Node last = null;
if (clockwise == (SignedArea(data, start, end) >= 0.0))
{
for (int i = start; i )
{
last = InsertNode(i, data[i].x, data[i].z, last);
}
}
else
{
for (int i = end - 1; i >= start; i--)
{
last = InsertNode(i, data[i].x, data[i].z, last);
}
}
if (last != null && Equals(last, last.next))
{
var next = last.next;
RemoveNode(last);
last = next;
}
return last;
}
///
/// “割耳”主循环
///
///
/// main ear slicing loop which triangulates a polygon (given as a linked list)
///
private static void EarCutLinked(Node ear, Listint> triangles, float minX, float minZ, float size, int pass)
{
if (ear == null) return;
// interlink polygon nodes in z-order
if (pass == 0 && size > 0.0f)
{
IndexCurve(ear, minX, minZ, size);
}
Node stop = ear;
Node prev = null;
Node next = null;
// iterate through ears, slicing them one by one
while (ear.prev != ear.next)
{
prev = ear.prev;
next = ear.next;
if (size > 0.0f ? IsEarHashed(ear, minX, minZ, size) : IsEar(ear))
{
// cut off the triangle
triangles.Add(prev.i);
triangles.Add(ear.i);
triangles.Add(next.i);
RemoveNode(ear);
// skipping the next vertice 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, null), triangles, minX, minZ, size, 1);
}
else if (pass == 1) // if this didn‘t work, try curing all small self-intersections locally
{
ear = CureLocalIntersections(ear, triangles);
EarCutLinked(ear, triangles, minX, minZ, size, 2);
}
else if (pass == 2) // as a last resort, try splitting the remaining polygon into two
{
SplitEarCut(ear, triangles, minX, minZ, size);
}
return;
}
}
}
///
/// 尝试将多边形分割成两个，并分别进行三角化
///
private static void SplitEarCut(Node start, Listint> triangles, float minX, float minZ, float size)
{
// 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, minZ, size, 0);
EarCutLinked(c, triangles, minX, minZ, size, 0);
return;
}
b = b.next;
}
a = a.next;
} while (a != start);
}
///
/// link every hole into the outer loop, producing a single-ring polygon without holes
///
private static Node EliminateHoles(List data, Listint> holeIndices, Node outerNode)
{
var queue = new List();
for (int i = 0, len = holeIndices.Count; i )
{
var start = holeIndices[i];
var end = i 1 ? holeIndices[i + 1] : data.Count;
var list = LinkedList(data, start, end, false);
if (list == list.next)
{
list.steiner = true;
}
queue.Add(GetLeftmost(list));
}
// Sort
queue.Sort();
// process holes from left to right
for (int i = 0; i )
{
var node = EliminateHole(queue[i], outerNode);
if (node != null)
{
outerNode = FilterPoints(node, node.next);
}
}
return outerNode;
}
///
/// find a bridge between vertices that connects hole with an outer ring and and link it
///
private static Node EliminateHole(Node hole, Node outerNode)
{
outerNode = FindHoleBridge(hole, outerNode);
if (outerNode != null)
{
var b = SplitPolygon(outerNode, hole);
return FilterPoints(b, b.next);
}
return null;
}
///
/// 遍历多边形所有结点，校正局部自相交情形
///
private static Node CureLocalIntersections(Node start, Listint> 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);
triangles.Add(p.i);
triangles.Add(b.i);
var next = p.next;
// remove two nodes involved
RemoveNode(p);
RemoveNode(next);
p = start = b;
}
p = p.next;
} while (p != start);
return p;
}
///
/// 插入一个结点
///
private static Node InsertNode(int i, float x, float z, Node last)
{
var p = new Node
{
i = i,
x = x,
z = z
};
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;
}
///
/// 移除一个结点
///
private 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;
}
}
///
/// 判断两个结点是否相等
///
/// true相等，false不相等
private static bool Equals(Node p1, Node p2)
{
if (p1 == null || p2 == null)
{
Debug.Log("null");
}
return p1.x == p2.x && p1.z == p2.z;
}
///
/// 判断是否是“耳朵”
///
///
///
private static bool IsEar(Node ear)
{
var a = ear.prev;
var b = ear;
var c = ear.next;
if (Area(a, b, c) >= 0.0f)
{
// reflex, can‘t be an ear
return false;
}
// 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, b, c, p) &&
(Area(p.prev, p, p.next) >= 0.0f))
{
return false;
}
p = p.next;
}
return true;
}
///
/// 判断是否是“耳朵”散列？
///
private static bool IsEarHashed(Node ear, float minX, float minZ, float size)
{
var a = ear.prev;
var b = ear;
var c = ear.next;
if (Area(a, b, c) >= 0.0f)
{
// reflex, can‘t be an ear
return false;
}
// triangle bbox; min & max are calculated like this for speed
var minTX = a.x b.x : c.x);
var minTZ = a.z b.z : c.z);
var maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x);
var maxTZ = a.z > b.z ? (a.z > c.z ? a.z : c.z) : (b.z > c.z ? b.z : c.z);
// z-order range for the current triangle bbox;
int minZOrder = ZOrder(minTX, minTZ, minX, minZ, size);
int maxZOrder = ZOrder(maxTX, maxTZ, minX, minZ, size);
// first look for points inside the triangle in increasing z-order
var p = ear.nextZ;
while (p != null && p.zOrder maxZOrder)
{
if (p != ear.prev && p != ear.next &&
PointInTriangle(a, b, c, p) &&
Area(p.prev, p, p.next) >= 0.0f)
{
return false;
}
p = p.nextZ;
}
// then look for points in decreasing z-order
p = ear.prevZ;
while (p != null && p.zOrder >= minZOrder)
{
if (p != ear.prev && p != ear.next &&
PointInTriangle(a, b, c, p) &&
Area(p.prev, p, p.next) >= 0.0f)
{
return false;
}
p = p.prevZ;
}
return true;
}
///
/// 通过对角线分割多边形
///
///
/// 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
///
private static Node SplitPolygon(Node a, Node b)
{
var a2 = new Node
{
i = a.i,
x = a.x,
z = a.z
};
var b2 = new Node
{
i = b.i,
x = b.x,
z = b.z
};
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;
}
///
/// 对结点进行排序
///
///
/// Simon Tatham‘s linked list merge sort algorithm
///
private static Node SortLinked(Node list)
{
int numMerges = 0;
int pSize = 0;
int qSize = 0;
int inSize = 1;
Node p = null;
Node q = null;
Node e = null;
Node tail = null;
do
{
p = list;
list = null;
tail = null;
numMerges = 0;
while (p != null)
{
numMerges++;
q = p;
pSize = 0;
for (int i = 0; i )
{
pSize++;
q = q.nextZ;
if (q == null)
break;
}
qSize = inSize;
while (pSize > 0 || (qSize > 0 && q != null))
{
if (pSize == 0)
{
e = q;
q = q.nextZ;
qSize--;
}
else if (qSize == 0 || q == null)
{
e = p;
p = p.nextZ;
pSize--;
}
else if (p.zOrder q.zOrder)
{
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;
}
///
/// 相邻多边形节点次序（interlink polygon nodes in z-order）
///
private static void IndexCurve(Node start, float minX, float minZ, float size)
{
var p = start;
do
{
if (p.zOrder == -1)
{
p.zOrder = ZOrder(p.x, p.z, minX, minZ, size);
}
p.prevZ = p.prev;
p.nextZ = p.next;
p = p.next;
} while (p != start);
p.prevZ.nextZ = null;
p.prevZ = null;
SortLinked(p);
}
///
/// 判断两条线段是否相交
///
///
///
private 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) > 0.0 != Area(p1, q1, q2) > 0.0) &&
(Area(p2, q2, p1) > 0.0 != Area(p2, q2, q1) > 0.0);
}
///
/// 检测多边形的对角线是否与多边形的边相交
///
private static bool IntersectsPolygon(Node a, Node 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;
}
///
/// 查找多边形最坐标结点
///
private static Node GetLeftmost(Node start)
{
var p = start;
var leftmost = start;
do
{
if (p.x leftmost.x)
{
leftmost = p;
}
p = p.next;
} while (p != start);
return leftmost;
}
///
/// 查找多边形内部洞与外边的连接点
///
/// David Eberly‘s algorithm
private static Node FindHoleBridge(Node hole, Node outerNode)
{
var p = outerNode;
var hx = hole.x;
var hz = hole.z;
var qx = float.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 ((hz = p.next.z) ||
(hz = p.z))
{
var x = p.x + (hz - p.z) * (p.next.x - p.x) / (p.next.z - p.z);
if (x qx)
{
qx = x;
if (x == hx)
{
if (hz == p.z)
{
return p;
}
if (hz == p.next.z)
{
return p.next;
}
}
m = p.x p : p.next;
}
}
} while (p != outerNode);
if (m == null)
{
return null;
}
// hole touches outer segment; pick lower endpoint
if (hx == qx)
{
return m.prev;
}
// 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 mz = m.z;
var tanMin = float.PositiveInfinity;
p = m.next;
while (p != stop)
{
if (hx >= p.x && p.x >= mx &&
PointInTriangle(hz qx : hx, hz, p.x, p.z))
{
var tan = Mathf.Abs(hz - p.z) / (hx - p.x); // tangential
if ((tan m.x)) &&
LocallyInside(p, hole))
{
m = p;
tanMin = tan;
}
}
p = p.next;
}
return m;
}
///
/// 检测多边形的对角线是否在多边形内部
///
private static bool LocallyInside(Node a, Node b)
{
return Area(a.prev, a, a.next) != 0.0f ?
Area(a, b, a.next) >= 0.0f && Area(a, a.prev, b) >= 0.0f :
Area(a, b, a.prev) >= 0.0f && Area(a, a.next, b) 0.0f;
}
///
/// 检测多边形对角线中心点是否在多边形内部
///
private static bool MiddleInside(Node a, Node b)
{
var p = a;
var inside = false;
var px = (a.x + b.x) * 0.5f;
var pz = (a.z + b.z) * 0.5f;
do
{
if (((p.z > pz) != (p.next.z > pz)) &&
(px p.x)))
{
inside = !inside;
}
p = p.next;
} while (p != a);
return inside;
}
///
/// 判断多边形中的两点是否构成有效对角线
///
private 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);
}
///
/// 过滤掉共线或重复的结点
///
private static Node FilterPoints(Node start, Node end)
{
if (start == null) return start;
if (end == null) end = start;
var p = start;
var again = false;
do
{
again = false;
if (!p.steiner && (Equals(p, p.next) || Area(p.prev, p, p.next) == 0.0f))
{
var prev = p.prev;
RemoveNode(p);
p = end = prev;
if (p == p.next)
{
return null;
}
again = true;
}
else
{
p = p.next;
}
} while (again || p != end);
return end;
}
///
/// 计算给定坐标点和外包大小的结点z-order（z-order of a point given coords and size of the data bounding box）
///
private static int ZOrder(float x, float z, float minX, float minZ, float size)
{
// coords are transformed into non-negative 15-bit integer range
int _x = (int)(32767 * (x - minX) / size);
int _z = (int)(32767 * (z - minZ) / size);
_x = (_x | (_x 8)) & 0x00FF00FF;
_x = (_x | (_x 4)) & 0x0F0F0F0F;
_x = (_x | (_x 2)) & 0x33333333;
_x = (_x | (_x 1)) & 0x55555555;
_z = (_z | (_z 8)) & 0x00FF00FF;
_z = (_z | (_z 4)) & 0x0F0F0F0F;
_z = (_z | (_z 2)) & 0x33333333;
_z = (_z | (_z 1)) & 0x55555555;
return _x | (_z 1);
}
///
/// 判断一个点是否在三角形内
///
/// true在，false不在
private static bool PointInTriangle(Node a, Node b, Node c, Node d)
{
var SABC = Mathf.Abs(Area(a, b, c)) * 0.5f;
var SADB = Mathf.Abs(Area(a, d, b)) * 0.5f;
var SBDC = Mathf.Abs(Area(b, d, c)) * 0.5f;
var SADC = Mathf.Abs(Area(a, d, c)) * 0.5f;
var S = SABC - (SADB + SBDC + SADC);
if (S > -EPSINON && S EPSINON)
{
return true;
}
return false;
}
///
/// 判断一个点是否在三角形内
///
/// true在，false不在
private static bool PointInTriangle(float x0, float y0,
float x1, float y1,
float x2, float y2,
float x3, float y3)
{
var SABC = Mathf.Abs(Area(x0, y0, x1, y1, x2, y2)) * 0.5f;
var SADB = Mathf.Abs(Area(x0, y0, x3, y3, x1, y1)) * 0.5f;
var SBDC = Mathf.Abs(Area(x1, y1, x3, y3, x2, y2)) * 0.5f;
var SADC = Mathf.Abs(Area(x0, y0, x3, y3, x2, y2)) * 0.5f;
var S = SABC - (SADB + SBDC + SADC);
if (S > -EPSINON && S EPSINON)
{
return true;
}
return false;
}
///
/// 计算三角形有向面积（三角形面积的2倍）
///
///
/// 结果大于0.0，p、q、r按逆时针排列
/// 结果等于0.0，p、q、r在一条直线上
/// 结果小于0.0，p、q、r按顺时针排列
///
/// 三角形有向面积
private static float Area(Node p, Node q, Node r)
{
return Area(p.x, p.z, q.x, q.z, r.x, r.z);
}
///
/// 计算三角形有向面积（三角形面积2倍）
///
/// 三角形有向面积
private static float Area(float x0, float y0,
float x1, float y1,
float x2, float y2)
{
return x0 * y1 + x2 * y0 + x1 * y2 - x2 * y1 - x0 * y2 - x1 * y0;
}
///
/// 计算多边形有向面积（多边形面积的2倍）
///
/// 顶点数据
/// 起始顶点索引
/// 结束顶点索引
///
/// 结果大于等于0.0，多边形顶点按顺时针排序
/// 结果小于0.0，多边形顶点按逆时针排序
///
/// 多边形有向面积
private static float SignedArea(List data,