耳切法处理简单多边形三角化
耳切法处理简单多边形三角化
三维家装项目遇到一个问题，需要自定义户型，那么就遇到地板那一块是不规则的，而且后期地板还需要贴图，uv也需要处理，网上没找到适合当前项目能用的，就参考文献自己写了个简单的，在自己的项目里已经够用，在此记录一下我的理解和代码
- 拿到多边形的多有顶点，需要按照一定的顺序，顺时针逆时针都可以，构造双向链表
- 通过向量叉乘计算所有的凹点和凸点（内角是否大于180）
- 通过判断其余点是否在一个三角形内，计算出所有耳朵
- *每次以耳朵为顶点构造三角形进行剔除，每剔除一个就是一个三角形序列
- 直到剩余顶点数量为3时，说明三角形化已经完成
- 在三角形化过程中，会出现操作顶点位置，形成的多边形不是简单多边形，需要抓异常进行提示
- 下面为代码
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
///
/// 判断凹点，凸点，耳朵的比较轴
///
public enum CompareAxle {
X,
Y,
Z
}
///
/// 对多边形处理
///
public class Triangulation {
///
/// 判断凹凸的时候的比对轴
///
private CompareAxle _compareAxle = CompareAxle.Y;
///
/// 多边形顶点
///
private List _polygonVertexs = new List();
///
/// 顶点序列
///
private List _vertexsSequence = new List();
///
/// 节点管理器
///
private NodeManager _nodeManager = new NodeManager();
///
/// 初始化
///
/// 多边形顶点
public Triangulation(List polygonVertexs) {
this._polygonVertexs = polygonVertexs;
_nodeManager.Init(polygonVertexs);
}
///
/// 设置比较轴
///
///
public void SetCompareAxle(CompareAxle compareAxle) {
this._compareAxle = compareAxle;
}
///
/// 获取三角形的顶点序列
///
public int[] GetTriangles() {
while(_nodeManager.LinkedListLength >= 3) {
SplitResult sr = SplitPolygon();
//
if(sr == null) {
return null;
}
}
return _vertexsSequence.ToArray();
}
///
/// 计算凹顶点，凸顶点，耳朵
///
private SplitResult SplitPolygon() {
//凹点
List _concaveVertexs = new List();
//凸点
List _raisedVertexs = new List();
//耳朵
List _polygonEars = new List();
//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
for (int i = 0; i < _polygonEars.Count; i++) {
Node earNode = _polygonEars[i];
Node compareNode = earNode.nextNode.nextNode;
while(compareNode != earNode.lastNode) {
bool isIn = VertexIsInTriangle(compareNode.vertex, earNode.lastNode.vertex, earNode.vertex,earNode.nextNode.vertex);
if (isIn == true) {
if (_polygonEars.Contains(_polygonEars[i])) {
_polygonEars.Remove(_polygonEars[i]);
}
break;
}
compareNode = compareNode.nextNode;
}
}
#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);
//}
#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);
}
///
/// 计算凹顶点，凸顶点，耳朵
///
//private SplitResult SplitPolygon(List _polygonVertexs) {
// //凹点
// List _concaveVertexs = new List();
// //凸点
// List _raisedVertexs = new List();
// //耳朵
// List _polygonEars = new List();
// #region 计算凹顶点，凸顶点
// for (int i = 0; i < _polygonVertexs.Count; i++) {
// Vector3 one;
// Vector3 two;
// if (i == 0) {
// one = _polygonVertexs[0] - _polygonVertexs[_polygonVertexs.Count - 1];
// two = _polygonVertexs[1] - _polygonVertexs[0];
// }
// else if (i == _polygonVertexs.Count - 1) {
// one = _polygonVertexs[i] - _polygonVertexs[_polygonVertexs.Count - 2];
// two = _polygonVertexs[0] - _polygonVertexs[i];
// }
// else {
// one = _polygonVertexs[i] - _polygonVertexs[i - 1];
// two = _polygonVertexs[i + 1] - _polygonVertexs[i];
// }
// Vector3 crossRes = Vector3.Cross(one, two);
// if (_compareAxle == CompareAxle.Y) {
// if (crossRes.y < 0) {
// _concaveVertexs.Add(i);
// }
// else {
// _raisedVertexs.Add(i);
// }
// }
// if (_compareAxle == CompareAxle.X) {
// if (crossRes.x < 0) {
// _concaveVertexs.Add(i);
// }
// else {
// _raisedVertexs.Add(i);
// }
// }
// if (_compareAxle == CompareAxle.Z) {
// if (crossRes.z < 0) {
// _concaveVertexs.Add(i);
// }
// else {
// _raisedVertexs.Add(i);
// }
// }
// _polygonEars.Add(i);
// }
// for (int i = 0; i < _concaveVertexs.Count; i++) {
// _polygonEars.Remove(_concaveVertexs[i]);
// }
// #endregion
// #region 计算耳朵
// //计算耳朵
// for (int i = 0; i < _polygonEars.Count; i++) {
// if (_polygonEars[i] == 0) {
// for (int j = 0; j < _polygonVertexs.Count; j++) {
// if (j == _polygonVertexs.Count - 1 || j == 0 || j == 1) {
// continue;
// }
// else {
// bool isIn = VertexIsInTriangle(_polygonVertexs[j], _polygonVertexs[_polygonVertexs.Count - 1], _polygonVertexs[0], _polygonVertexs[1]);
// if (isIn == true) {
// if (_polygonEars.Contains(_polygonEars[i])) {
// _polygonEars.Remove(_polygonEars[i]);
// }
// }
// }
// }
// }
// else if (_polygonEars[i] == _polygonVertexs.Count - 1) {
// for (int j = 0; j < _polygonVertexs.Count; j++) {
// if (j == _polygonVertexs.Count - 2 || j == _polygonVertexs.Count - 1 || j == 0) {
// continue;
// }
// else {
// bool isIn = VertexIsInTriangle(_polygonVertexs[j], _polygonVertexs[_polygonVertexs.Count - 2], _polygonVertexs[_polygonVertexs.Count - 1], _polygonVertexs[0]);
// if (isIn == true) {
// if (_polygonEars.Contains(_polygonEars[i])) {
// _polygonEars.Remove(_polygonEars[i]);
// }
// }
// }
// }
// }
// else {
// for (int j = 0; j < _polygonVertexs.Count; j++) {
// if (j == _polygonEars[i] - 1 || j == _polygonEars[i] || j == _polygonEars[i] + 1) {
// continue;
// }
// else {
// bool isIn = VertexIsInTriangle(_polygonVertexs[j], _polygonVertexs[_polygonEars[i] - 1], _polygonVertexs[_polygonEars[i]], _polygonVertexs[_polygonEars[i] + 1]);
// if (isIn == true) {
// if (_polygonEars.Contains(_polygonEars[i])) {
// _polygonEars.Remove(_polygonEars[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]);
// //}
// //Debug.Log("凹点");
// //for (int i = 0; i < _concaveVertexs.Count; i++) {
// // Debug.Log(_concaveVertexs[i]);
// //}
// //Debug.Log("耳朵");
// //for (int i = 0; i < _polygonEars.Count; i++) {
// // Debug.Log(_polygonEars[i]);
// //}
// #endregion
// return new SplitResult(_raisedVertexs, _concaveVertexs, _polygonEars,_polygonVertexs);
//}
///
/// 判断一点是否在三角形内
///
/// 一点
///
///
///
///
/// 管理多边形 构成一个双向链表
///
public class NodeManager {
private List _nodeList = new List();
public int LinkedListLength {
get { return _nodeList.Count; }
}
public Node FirstNode {
get { return _nodeList[0]; }
}
public void Init(List 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 {
///
/// 凸顶点
///
public List raisedVertexs;
///
/// 凹顶点
///
public List concaveVertexs;
///
/// 耳朵
///
public List polygonEars;
public SplitResult(List raisedVertexs, List concaveVertexs, List polygonEars) {
this.raisedVertexs = raisedVertexs;
this.concaveVertexs = concaveVertexs;
this.polygonEars = polygonEars;
}
}
}
#endregion
}