基于Unity利用四叉树算法实现二维碰撞检测

前言

在游戏制作过程中会经常遇到碰撞检测，假设在二维平面上有n个物体，那么检测每个物体的碰撞都要检测n-1次，如果要检测所有物体的碰撞，那么需要计算n*(n-1)/2次，时间复杂度为n的平方，四叉树算法可以将物体分到不同的区域，从而减少计算次数。关于四叉树 的概念可以参考文章四叉树与八叉树

四叉的实现

下面是用C#代码实现的四叉树算法,需要注意的是构造函数的pBounds参数，不能直接使用RectTransform.rect，这里使用的rect的参数x和y需要特殊处理，具体可以看末尾函数public static Rect GetRect(RectTransform rectTransform)。

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

public class QuadTree
{
   
   
    //节点内允许的最大对象
    private int MAX_OBJECTS = 1;
    //最大层级
    private int MAX_LEVELS = 3;
    //当前层级
    private int level;
    //当前层级内的对象
    public List<RectTransform> rectTrans;
    //rect范围
    private Rect bounds;
    //子节点
    private List<QuadTree> childs;

    public QuadTree(Rect pBounds, int pLevel = 0, int maxObjs = 1, int maxLevel = 3)
    {
   
   
        level = pLevel;
        rectTrans = new List<RectTransform>();
        bounds = pBounds;
        childs = new List<QuadTree>();
        MAX_OBJECTS = maxObjs;
        MAX_LEVELS = maxLevel;
    }
    /// <summary>
    /// 清理四叉树
    /// </summary>
    public void Clear()
    {
   
   
        rectTrans.Clear();
        for (int i = 0; i < childs.Count; i++)
        {
   
   
            childs[i].Clear();
        }
    }
    /// <summary>
    /// 分割四叉树
    /// </summary>
    public void Split()
    {
   
   
        float halfWidth = bounds.width / 2;
        float halfHeight = bounds.height / 2;
        float x = bounds.x;
        float y = bounds.y;
        childs.Add(new QuadTree(new Rect(x, y + halfHeight, halfWidth, halfHeight), level + 1, MAX_OBJECTS, MAX_LEVELS));
        childs.Add(new QuadTree(new Rect(x + halfWidth, y + halfHeight, halfWidth, halfHeight), level + 1, MAX_OBJECTS, MAX_LEVELS));
        childs.Add(new QuadTree(new Rect(x, y, halfWidth, halfHeight), level + 1, MAX_OBJECTS, MAX_LEVELS));
        childs.Add(new QuadTree(new Rect(x + halfWidth, y, halfWidth, halfHeight), level + 1, MAX_OBJECTS, MAX_LEVELS));
        //对象下沉
        for (int i = 0; i < rectTrans.Count; i++)
        {
   
   
            Insert(rectTrans[i]);
        }
        rectTrans.Clear();
    }
    /// <summary>
    /// 寻找对象所在节点列表
    /// </summary>
    /// <param name="rect">对象的rect</param>
    /// <returns></returns>
    public List<QuadTree> GetIndexes(Rect rect)
    {
   
   
        List<QuadTree> ret = new List<QuadTree>();
        FindQuad(rect, ret);
        return ret;
    }

    /// <summary>
    /// 插入对象
    /// </summary>
    /// <param name="go"></param>
    public void Insert(RectTransform go)
    {
   
   
        Rect rect = GetRect(go);
        List<QuadTree> tempList = GetIndexes(rect);
        for (int i = 0; i < tempList.Count; i++)
        {