用AABBTree加速碰撞检测
AABBTree加速碰撞检测的原理？
减少碰撞检测的执行次数。怎么减少呢？排除那些不可能发生碰撞的形状间的检测。
最简单粗暴的碰撞检测就是两个for循环嵌套
void ForLoopCheckIntersect() { for (int i = 0; i < m_RectList.Count; ++i) { var shape = m_ShapeList[i]; for (int j = i + 1; j < m_RectList.Count; ++j) { var shape_2 = m_ShapeList[j]; if (shape == shape_2) continue; if (!shape.GetBounds().Overlaps(shape_2.GetBounds())) //包围盒粗检测 continue; if (Shape2DHelper.IsShapeIntersect(verts, verts_2)) //细检测 Debug.Log($"Intersect"); } } }
但好多形状根本不可能发生碰撞，也再参与检测，明显是执行了很多无效的检测。
AABBTree如何排除那些不可能发生的碰撞？
1) 使用2叉树结构。
2) 使用了层次包围盒(BVH)的组织方式，就是形状只保存在叶子节点上，叶子节点的父节点用包围盒包住2个叶子节点，祖父节点再用包围盒包住其子节点，以此类推。
3) 跟二叉查找树有点类似, AABB树的也通过查找规则确定是走left-child还是right-child，每次都可以减少一半查找量。
效果
同样的耗时50ms
1) 暴力检测的话可以支持250个OBBRect参与，执行了3112次检测
2) 用AABBTree支持890个OBBRect参与，执行了7834次检测
using UnityEngine; public partial class MyAABBTree { public class Node { private Node m_Parent; private Node m_Left; private Node m_Right; public Rect m_Bounds; //节点包围盒: 有Shape等于Shape的包围盒大小, 没Shape等于包住两个子节点的包围盒的大小 public IShape m_Shape; //叶子节点才有Shape public Node() { } public void RemoveFromParent() { if (null != m_Parent) { if (m_Parent.IsLeft(this)) m_Parent.Left = null; else m_Parent.Right = null; m_Parent = null; } } public bool IsLeft(Node n) { return (null != m_Left && n == m_Left); } public Node Parent { get { return m_Parent; } } public Rect GetBounds() { return m_Bounds; } public Node Left { get { return m_Left; } set { if (null == value) { if (null != m_Left) { m_Left.m_Parent = null; m_Left = null; } } else { m_Left = value; value.m_Parent = this; } } } public Node Right { get { return m_Right; } set { if (null == value) { if (null != m_Right) { m_Right.m_Parent = null; m_Right = null; } } else { m_Right = value; value.m_Parent = this; } } } public bool IsLeaf() { return (null == m_Left) && (null == m_Right); } } }
using System.Collections.Generic; using UnityEngine; public partial class MyAABBTree { public interface IShape { Rect GetBounds(); string GetShapeName(); } private Node m_Root; private Dictionary<IShape, Node> m_NodeDict = new Dictionary<IShape, Node>(); public Node Root { get { return m_Root; } } //添加 public void AddShape(IShape shape) { var shapeBounds = shape.GetBounds(); //如果树是空的, 直接创建根节点 if (null == m_Root) { m_Root = CreateNode(shape, ref shapeBounds); return; } Node node = m_Root; while (!node.IsLeaf()) { var isLeft = IsLeftChild(node.Left.GetBounds(), node.Right.GetBounds(), shapeBounds); node = isLeft ? node.Left : node.Right; } //将原来的变成父节点(包围盒节点), 原来的shape新建left-child, 新的shape新建right-child var leftChild = CreateNode(node.m_Shape, ref node.m_Bounds); node.Left = leftChild; node.m_Shape = null; var rightChild = CreateNode(shape, ref shapeBounds); node.Right = rightChild; UpdateAncestorBounds(node); } private Node CreateNode(IShape shape, ref Rect bounds) { var node = new Node(); m_NodeDict[shape] = node; node.m_Shape = shape; node.m_Bounds = bounds; return node; } //根据查找规则确定是否是用left-child private bool IsLeftChild(Rect left, Rect right, Rect cur) { var mergeRect1 = MergeRect(ref left, ref cur); float area1 = mergeRect1.width * mergeRect1.height + right.width * right.height; var mergeRect2 = MergeRect(ref right, ref cur); float area2 = mergeRect2.width * mergeRect2.height + left.width * left.height; if (area1 < area2) return true; if (area1 > area2) return false; //面积相同时: 选中心点距离近的 var toLeft = cur.center - left.center; var toRight = cur.center - right.center; return toLeft.sqrMagnitude < toRight.sqrMagnitude; } public static Rect MergeRect(ref Rect a, ref Rect b) { float xMin = Mathf.Min(a.xMin, b.xMin); float yMin = Mathf.Min(a.yMin, b.yMin); float xMax = Mathf.Max(a.xMax, b.xMax); float yMax = Mathf.Max(a.yMax, b.yMax); var result = new Rect(xMin, yMin, xMax - xMin, yMax - yMin); return result; } //更新所有祖先节点的包围盒 private void UpdateAncestorBounds(Node node) { while (null != node) { var leftBounds = node.Left.GetBounds(); var rightBounds = node.Right.GetBounds(); node.m_Bounds = MergeRect(ref leftBounds, ref rightBounds); node = node.Parent; } } //删除 public bool RemoveShape(IShape shape) { if (!m_NodeDict.TryGetValue(shape, out var node)) return false; m_NodeDict.Remove(shape); if (m_Root == node) { m_Root = null; return true; } var parent = node.Parent; var sibling = parent.IsLeft(node) ? parent.Right : parent.Left; if (parent == m_Root) { m_Root = sibling; } else //删掉一个Shape节点后, 用兄弟节点替换掉父节点 { parent.Left = null; parent.Right = null; parent.m_Shape = sibling.m_Shape; parent.m_Bounds = sibling.m_Bounds; UpdateAncestorBounds(parent.Parent); } return true; } //更新 public bool UpdateShape(IShape shape) { if (!m_NodeDict.TryGetValue(shape, out var node)) return false; if (RectContains(node.m_Bounds, shape.GetBounds())) //还在原来的包围盒范围内 return false; RemoveShape(shape); AddShape(shape); return true; } private static bool RectContains(Rect a, Rect b) { return !(b.xMin < a.xMin || b.xMax > a.xMax || b.yMin < a.yMin || b.yMax > a.yMax); } //查找: 返回与指定区域相交的所有形状 public List<IShape> Query(Rect bounds) { if (null == m_Root) return null; var resultList = new List<IShape>(); var stack = new Stack<Node>(); stack.Push(m_Root); do { var node = stack.Pop(); if (!node.m_Bounds.Overlaps(bounds)) continue; if (node.IsLeaf()) { resultList.Add(node.m_Shape); continue; } stack.Push(node.Left); stack.Push(node.Right); } while (stack.Count > 0); return resultList; } }
还需要优化的地方：
1) 不是平衡树，频繁添加、删除后可能退化成链表，可以考虑改成用红黑树来优化。
测试代码
using UnityEngine; public class OBBRect : MonoBehaviour, MyAABBTree.IShape { public float m_Width = 0.2f; public float m_Height = 0.1f; private Vector2[] m_Verts = new Vector2[4]; public static Rect GetBounds(Vector2[] verts) { float xMin = float.MaxValue; float yMin = float.MaxValue; float xMax = float.MinValue; float yMax = float.MinValue; for (int i = 0; i < 4; ++i) { var vert = verts[i]; xMin = Mathf.Min(xMin, vert.x); yMin = Mathf.Min(yMin, vert.y); xMax = Mathf.Max(xMax, vert.x); yMax = Mathf.Max(yMax, vert.y); } return new Rect(xMin, yMin, xMax - xMin, yMax - yMin); } public Rect GetBounds() { var verts = GetVerts(); return GetBounds(verts); } public Vector2[] GetVerts() { var localMin = new Vector2(-m_Width * 0.5f, -m_Height * 0.5f); var localMax = new Vector2(m_Width * 0.5f, m_Height * 0.5f); var localLeftTop = new Vector2(localMin.x, localMax.y); var localRightBottom = new Vector2(localMax.x, localMin.y); m_Verts[0] = this.transform.TransformPoint(localMin); //min m_Verts[1] = this.transform.TransformPoint(localLeftTop); //left-top m_Verts[2] = this.transform.TransformPoint(localMax); //max m_Verts[3] = this.transform.TransformPoint(localRightBottom); //right-bottom return m_Verts; } public string GetShapeName() { return "Rect"; } #if UNITY_EDITOR public Color m_GizmosColor = Color.white; private void OnDrawGizmos() { if (m_Width <= 0 || m_Height <= 0) return; var center = transform.position; Gizmos.color = m_GizmosColor; var verts = GetVerts(); for (int i = 0; i < 4; ++i) { Gizmos.DrawLine(verts[i], verts[(i+1)%4]); } Gizmos.color = Color.white; } #endif }
using System; using System.Collections.Generic; using UnityEngine; public class MyAABBTreeTest : MonoBehaviour { public Transform m_ShapesRoot; public GameObject m_RectTemplate; [Range(0, 9)] public int m_ApiType = 1; public bool m_Benchmark = false; //测试多少个shape参与碰撞检测时, 执行耗时超过50ms [Range(0, 999)] public int m_TestShapeCount = 1; public int m_CostTime = 0; public int m_CheckCount = 0; private List<OBBRect> m_RectList = new List<OBBRect>(); private MyAABBTree m_Tree; void Start() { m_Tree = new MyAABBTree(); for (int i = 0; i < m_ShapesRoot.childCount; ++i) { var shape = m_ShapesRoot.GetChild(i).GetComponent<OBBRect>(); if (null == shape) continue; m_RectList.Add(shape); m_Tree.AddShape(shape); } } void Update() { for (int i = 0; i < 10; ++i) { if (m_RectList.Count >= m_TestShapeCount) break; CreateRect(); } switch (m_ApiType) { case 1: ForLoopCheckIntersect(); break; case 2: AABBTreeCheckIntersect(); break; } CheckTimeCost(); } void ForLoopCheckIntersect() { for (int i = 0; i < m_RectList.Count; ++i) { var shape = m_RectList[i]; shape.m_GizmosColor = Color.white; } var t = DateTime.Now; m_CheckCount = 0; for (int i = 0; i < m_RectList.Count; ++i) { var shape = m_RectList[i]; for (int j = i + 1; j < m_RectList.Count; ++j) { var shape_2 = m_RectList[j]; if (null == shape_2 || shape == shape_2) continue; m_CheckCount++; var verts = shape.GetVerts(); var verts_2 = shape_2.GetVerts(); if (!OBBRect.GetBounds(verts).Overlaps(OBBRect.GetBounds(verts_2))) //包围盒粗检测 continue; if (Shape2DHelper.IsPolygonIntersect(verts, verts_2)) { shape.m_GizmosColor = Color.red; shape_2.m_GizmosColor = Color.red; } } } m_CostTime = (int)(DateTime.Now - t).TotalMilliseconds; } void AABBTreeCheckIntersect() { for (int i = 0; i < m_RectList.Count; ++i) { var shape = m_RectList[i]; shape.m_GizmosColor = Color.white; m_Tree.UpdateShape(shape); } var t = DateTime.Now; m_CheckCount = 0; for (int i = 0; i < m_RectList.Count; ++i) { var shape = m_RectList[i]; var intersectList = m_Tree.Query(shape.GetBounds()); if (null != intersectList) { for (int j = 0; j < intersectList.Count; ++j) { var shape_2 = intersectList[j] as OBBRect; if (null == shape_2 || shape == shape_2) continue; m_CheckCount++; if (Shape2DHelper.IsPolygonIntersect(shape.GetVerts(), shape_2.GetVerts())) { shape.m_GizmosColor = Color.red; shape_2.m_GizmosColor = Color.red; } } } } m_CostTime = (int)(DateTime.Now - t).TotalMilliseconds; } protected void CheckTimeCost() { if (m_CostTime >= 100) //防止卡住 { for (int i = 1; i <= 10; ++i) { var childIndex = m_ShapesRoot.childCount - i; if (childIndex < 0) break; m_ShapesRoot.GetChild(childIndex).gameObject.SetActive(false); } } if (m_Benchmark) { if (m_CostTime >= 50) { Debug.Log($"type:{m_ApiType}, shapeCount:{m_RectList.Count}, totalMs:{m_CostTime}, checkCount:{m_CheckCount}"); if (m_ApiType >= 2) { m_ApiType = 1; m_Benchmark = false; } else m_ApiType++; } else { if (m_RectList.Count >= m_TestShapeCount) { m_TestShapeCount++; } } } } private void CreateRect() { var go = GameObject.Instantiate(m_RectTemplate, m_ShapesRoot, false); go.name = $"Rect ({m_RectList.Count})"; var trans = go.transform; trans.position = new Vector2(UnityEngine.Random.Range(-5, 5), UnityEngine.Random.Range(-5, 5)); trans.localEulerAngles = new Vector3(0, 0, UnityEngine.Random.Range(-30, 30)); var shape = go.GetComponent<OBBRect>(); shape.m_Width = UnityEngine.Random.Range(0.1f, 0.5f); shape.m_Height = shape.m_Width * UnityEngine.Random.Range(0.6f, 0.8f); m_RectList.Add(shape); m_Tree.AddShape(shape); } #if UNITY_EDITOR public Color[] m_NodeDepthColors = new Color[] { new Color(0, 1, 0, 0.5f) }; public Color m_LeafColor = new Color(0, 0, 1, 0.5f); private Stack<MyAABBTree.Node> m_DrawStack = new Stack<MyAABBTree.Node>(); private void OnDrawGizmos() { switch (m_ApiType) { case 1: DrawGizmos_ForLoop(); break; case 2: DrawGizmos_AABBTree(); break; } } private void DrawGizmos_AABBTree() { if (null != m_Tree && null != m_Tree.Root) { Gizmos.color = Color.green; int nodeNum = 1; var node = m_Tree.Root; m_DrawStack.Push(node); DrawNodeBounds(node, nodeNum); do { node = m_DrawStack.Pop(); var left = node.Left; if (null != left) { nodeNum++; DrawNodeBounds(left, nodeNum); m_DrawStack.Push(left); } var right = node.Right; if (null != right) { nodeNum++; DrawNodeBounds(right, nodeNum); m_DrawStack.Push(right); } } while (m_DrawStack.Count > 0); Gizmos.color = Color.white; } } private void DrawNodeBounds(MyAABBTree.Node node, int nodeNum) { if (node.IsLeaf()) Gizmos.color = m_LeafColor; else { int depth = (int)Mathf.Log(nodeNum, 2); Gizmos.color = m_NodeDepthColors[depth % m_NodeDepthColors.Length]; } var bounds = node.m_Bounds; var min = bounds.min; var max = bounds.max; var leftTop = new Vector2(min.x, max.y); var rightBottom = new Vector2(max.x, min.y); Gizmos.DrawLine(min, leftTop); Gizmos.DrawLine(leftTop, max); Gizmos.DrawLine(max, rightBottom); Gizmos.DrawLine(rightBottom, min); } private void DrawGizmos_ForLoop() { Gizmos.color = m_LeafColor; for (int i = 0; i < m_RectList.Count; ++i) { var rect = m_RectList[i]; var bounds = rect.GetBounds(); var min = bounds.min; var max = bounds.max; var leftTop = new Vector2(min.x, max.y); var rightBottom = new Vector2(max.x, min.y); Gizmos.DrawLine(min, leftTop); Gizmos.DrawLine(leftTop, max); Gizmos.DrawLine(max, rightBottom); Gizmos.DrawLine(rightBottom, min); } Gizmos.color = Color.white; } #endif }
参考
