使用耳切法将多边形三角化转

Posted 2022-11-28 mazhenyu

https://blog.csdn.net/yiwei151/article/details/87946592

效果图：

 

做法及原理可参考此链接：http://www.cnblogs.com/xignzou/p/3721494.html

 代码：

using System;
using System.Collections.Generic;
using UnityEngine;

namespace PolygonTool


#region 耳切法对简单多边形进行三角形化

/// <summary>
/// 判断凹点，凸点，耳朵的比较轴
/// </summary>
public enum CompareAxle

X,
Y,
Z


/// <summary>
/// 对多边形处理
/// </summary>
public class Triangulation


/// <summary>
/// 判断凹凸的时候的比对轴
/// </summary>
private CompareAxle _compareAxle = CompareAxle.Y;

/// <summary>
/// 多边形顶点
/// </summary>
private List<Vector3> _polygonVertexs = new List<Vector3>();

/// <summary>
/// 顶点序列
/// </summary>
private List<int> _vertexsSequence = new List<int>();

/// <summary>
/// 节点管理器
/// </summary>
private NodeManager _nodeManager = new NodeManager();

/// <summary>
/// 初始化
/// </summary>
/// <param name="polygonVertexs">多边形顶点</param>
public Triangulation(List<Vector3> polygonVertexs)

this._polygonVertexs = polygonVertexs;
_nodeManager.Init(polygonVertexs);


/// <summary>
/// 设置比较轴
/// </summary>
/// <param name="compareAxle"></param>
public void SetCompareAxle(CompareAxle compareAxle)

this._compareAxle = compareAxle;


/// <summary>
/// 获取三角形的顶点序列
/// </summary>
public int[] GetTriangles()

while (_nodeManager.LinkedListLength >= 3)

SplitResult sr = SplitPolygon();
//
if (sr == null)

Debug.Log("null");
return null;



return _vertexsSequence.ToArray();


/// <summary>
/// 计算凹顶点，凸顶点，耳朵
/// </summary>
private SplitResult SplitPolygon()

//凹点
List<Node> _concaveVertexs = new List<Node>();
//凸点
List<Node> _raisedVertexs = new List<Node>();
//耳朵
List<Node> _polygonEars = new List<Node>();
//起始节点
Node currentNode = _nodeManager.FirstNode;

#region 计算凹顶点，凸顶点

for (int i = 0; i < _nodeManager.LinkedListLength; i++)

Vector3 one = currentNode.vertex - currentNode.lastNode.vertex;
Vector3 two = currentNode.nextNode.vertex - currentNode.vertex;
Vector3 crossRes = Vector3.Cross(one, two);

if (_compareAxle == CompareAxle.Y)

if (crossRes.y > 0)

_concaveVertexs.Add(currentNode);

else

_raisedVertexs.Add(currentNode);



if (_compareAxle == CompareAxle.X)

if (crossRes.x > 0)

_concaveVertexs.Add(currentNode);

else

_raisedVertexs.Add(currentNode);



if (_compareAxle == CompareAxle.Z)

if (crossRes.z > 0)

_concaveVertexs.Add(currentNode);

else

_raisedVertexs.Add(currentNode);



_polygonEars.Add(currentNode);
currentNode = currentNode.nextNode;


for (int i = 0; i < _concaveVertexs.Count; i++)

_polygonEars.Remove(_concaveVertexs[i]);

#endregion

#region 计算耳朵
List<int> needRemoveIdList = new List<int>();
for (int i = 0; i < _polygonEars.Count; i++)

Node earNode = _polygonEars[i];
Node compareNode = earNode.nextNode.nextNode;

while (compareNode != earNode.lastNode)

bool isIn = IsIn(compareNode.vertex, earNode.lastNode.vertex, earNode.vertex,
earNode.nextNode.vertex);

if (isIn == true)

if (_polygonEars.Contains(_polygonEars[i]))

needRemoveIdList.Add(_polygonEars[i].id);

break;

compareNode = compareNode.nextNode;



for (int j = 0; j < needRemoveIdList.Count; j++)

for (int i = 0; i < _polygonEars.Count; i++)

if (_polygonEars[i].id == needRemoveIdList[j])

_polygonEars.RemoveAt(i);




#endregion

#region 打印初始化结果

Debug.Log("凸点");
for (int i = 0; i < _raisedVertexs.Count; i++)

Debug.Log(_raisedVertexs[i].id);


Debug.Log("凹点");
for (int i = 0; i < _concaveVertexs.Count; i++)

Debug.Log(_concaveVertexs[i].id);


Debug.Log("耳朵");
for (int i = 0; i < _polygonEars.Count; i++)

Debug.Log(_polygonEars[i].id);


Debug.Log("-----------------------------------------------");
#endregion

//耳朵为空说明不是简单多边形 多边形三角化失败
if (_polygonEars.Count == 0)

return null;


_vertexsSequence.Add(_polygonEars[0].lastNode.id);
_vertexsSequence.Add(_polygonEars[0].id);
_vertexsSequence.Add(_polygonEars[0].nextNode.id);
_nodeManager.RemoveNode(_polygonEars[0]);


return new SplitResult(_raisedVertexs, _concaveVertexs, _polygonEars);


/// <summary>
/// 判断一点是否在三角形内
/// </summary>
/// <param name="p">一点</param>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <returns></returns>
public bool IsIn(Vector3 p,Vector3 a,Vector3 b,Vector3 c)

Vector3 pa = p - a;
Vector3 pb = p - b;
Vector3 pc = p - c;

Vector3 t1 = Vector3.Cross(pa, pb);
Vector3 t2 = Vector3.Cross(pb, pc);
Vector3 t3 = Vector3.Cross(pc, pa);

bool isIn2 = t1.y >= 0 && t2.y >= 0 && t3.y >= 0 || t1.y <= 0 && t2.y <= 0 && t3.y <= 0;

return isIn2;


/// <summary>
/// 管理多边形 构成一个双向链表
/// </summary>
public class NodeManager


private List<Node> _nodeList = new List<Node>();

public int LinkedListLength

get return _nodeList.Count;


public Node FirstNode

get return _nodeList[0];


public void Init(List<Vector3> vertexs)


for (int i = 0; i < vertexs.Count; i++)

Node node = new Node(i, vertexs[i]);
_nodeList.Add(node);


for (int i = 0; i < LinkedListLength; i++)

if (i == 0)

_nodeList[i].lastNode = _nodeList[LinkedListLength - 1];
_nodeList[i].nextNode = _nodeList[1];

else if (i == LinkedListLength - 1)

_nodeList[i].lastNode = _nodeList[LinkedListLength - 2];
_nodeList[i].nextNode = _nodeList[0];

else

_nodeList[i].lastNode = _nodeList[i - 1];
_nodeList[i].nextNode = _nodeList[i + 1];




public void RemoveNode(Node node)

_nodeList.Remove(node);
node.lastNode.nextNode = node.nextNode;
node.nextNode.lastNode = node.lastNode;



public class Node


public int id;
public Vector3 vertex;
public Node lastNode;
public Node nextNode;

public Node(int id, Vector3 vertex)

this.id = id;
this.vertex = vertex;


public Node(int id, Vector3 vertex, Node lastNode, Node nextNode)

this.id = id;
this.vertex = vertex;
this.lastNode = lastNode;
this.nextNode = nextNode;



public class SplitResult

/// <summary>
/// 凸顶点
/// </summary>
public List<Node> raisedVertexs;

/// <summary>
/// 凹顶点
/// </summary>
public List<Node> concaveVertexs;

/// <summary>
/// 耳朵
/// </summary>
public List<Node> polygonEars;

public SplitResult(List<Node> raisedVertexs, List<Node> concaveVertexs, List<Node> polygonEars)

this.raisedVertexs = raisedVertexs;
this.concaveVertexs = concaveVertexs;
this.polygonEars = polygonEars;




#endregion

 

github地址：https://github.com/yiwei151/PolygonTriangulation