游戏中的2DOBB碰撞模型的碰撞算法介绍和实践前⾔上⼀篇博⽂说道，射线与场景中模型上的所有三⾓形求交时，会⼤幅度影响效率且花费⽐较多的时间，因此会采取使⽤包围盒的形式，进⾏⼀个加速求交。
在此⽂中介绍OBB碰撞模型的碰撞算法OBB的碰撞模型有没有想过为什么需要⽤到OBB模型呢，假设⼀个场景内两个⼈物相撞了，你怎么判断它们是否相撞呢，⼤概就是它们的碰撞体接触在了⼀起就相撞了。
那怎么算碰撞在⼀起呢（此处只讨论2D规则的包围盒模型）？⽅向包围盒OBB"("Oriented Bounding Box)是⽬前⽐较流⾏的⼀种包围盒，OBB最⼤的特点是其⽅向的任意性，这使得可以根据被包围的对象的形状特点尽可能紧密地包围对象，Unity中的BoxCollider的其实就是OBB模型，它不是轴对称模型，⽽是有⽅向的OBB模型与之相反的是AABB模型，是轴对称模型，即它的边⼀定与坐标轴平⾏，算法简单，但使⽤的局限性⽐较⼤，更多还是使⽤OBB模型碰撞算法分析想要判断两个OBB模型碰撞，也就是两个矩形相交，我们分为⼏个步骤，⾸先先转换问题，什么时候两个矩形不相交，两个矩形相离可看成有多个直线可将它们之间分开。
当逐渐移动某个矩形，使得某个时刻，两个矩形只有⼀个交点，交点属于矩形的某条边上，此时为临界状态，当且仅当只有⼀条直线将他们两个分开，此时这条直线必定与某条边平⾏。
所以我们只需找两个矩形的四条边分别作为轴，两个矩形的xVt、yVt分别进⾏投影，看投影后的两个线段是否相离，如果相离则在这个轴上可以将这两个进⾏分开，故此时两个矩形不相交，反之若相交，则继续接着其他轴进⾏判断，若所有轴都不能分开，则这两个矩形相交我们观察 AB proj 与 boxA、boxB 的 xVt proj 、yVt proj 之间的关系，可以得出结论：AB proj > sum(Vt proj) ，则矩形相离AB proj = sum(Vt proj) ，则矩形相切AB proj < sum(Vt proj) ，则矩形相交参考⽹上某⼤佬的代码参考博⽂:分别取两个矩形的两个边，总共进⾏四次投影对称，作为对称轴axis1 = (P1 - P0).normalized;axis2 = (P3 - P0).normalized;axis3 = (other.P1 - other.P0).normalized;axis4 = (other.P3 - other.P0).normalized;mDebugInternalAxisIndex = 0;bool isNotIntersect = false;isNotIntersect |= ProjectionIsNotIntersect(this, other, axis1);isNotIntersect |= ProjectionIsNotIntersect(this, other, axis2);isNotIntersect |= ProjectionIsNotIntersect(this, other, axis3);isNotIntersect |= ProjectionIsNotIntersect(this, other, axis4);这⾥是取带符号的长度，⽤来⽐较投影后的线段是否相交float x_p0 = xProject_P0.magnitude * Mathf.Sign(Vector3.Dot(xProject_P0, axis));float x_p1 = xProject_P1.magnitude * Mathf.Sign(Vector3.Dot(xProject_P1, axis));float x_p2 = xProject_P2.magnitude * Mathf.Sign(Vector3.Dot(xProject_P2, axis));float x_p3 = xProject_P3.magnitude * Mathf.Sign(Vector3.Dot(xProject_P3, axis));相交判断：if (yMin >= xMin && yMin <= xMax) return false;if (yMax >= xMin && yMax <= xMax) return false;简约的⽰例图using UnityEngine;// OBB.cspublic class OBB : MonoBehaviour{public bool enableDebug;public int debug_axisIndex;int mDebugInternalAxisIndex;public Vector2 size;public Color gizmosColor = Color.white;Vector2 P0 { get { return transform.localToWorldMatrix.MultiplyPoint3x4(-size * 0.5f); } }Vector2 P1 { get { return transform.localToWorldMatrix.MultiplyPoint3x4(new Vector3(size.x * 0.5f, -size.y * 0.5f, 0)); } } Vector2 P2 { get { return transform.localToWorldMatrix.MultiplyPoint3x4(size * 0.5f); } }Vector2 P3 { get { return transform.localToWorldMatrix.MultiplyPoint3x4(new Vector3(-size.x * 0.5f, size.y * 0.5f, 0)); } } Vector2 axis1, axis2, axis3, axis4;// 较参考博⽂添加以下变量，⽤来缓存向量减少gcVector3 xProject_P0;Vector3 xProject_P1;Vector3 xProject_P2;Vector3 xProject_P3;Vector3 yProject_P0;Vector3 yProject_P1;Vector3 yProject_P2;Vector3 yProject_P3;public bool Intersects(OBB other){axis1 = (P1 - P0).normalized;axis2 = (P3 - P0).normalized;axis3 = (other.P1 - other.P0).normalized;axis4 = (other.P3 - other.P0).normalized;mDebugInternalAxisIndex = 0;bool isNotIntersect = false;isNotIntersect |= ProjectionIsNotIntersect(this, other, axis1);isNotIntersect |= ProjectionIsNotIntersect(this, other, axis2);isNotIntersect |= ProjectionIsNotIntersect(this, other, axis3);isNotIntersect |= ProjectionIsNotIntersect(this, other, axis4);return isNotIntersect ? false : true;}bool ProjectionIsNotIntersect(OBB x, OBB y, Vector2 axis){xProject_P0 = Vector3.Project(x.P0, axis);xProject_P1 = Vector3.Project(x.P1, axis);xProject_P2 = Vector3.Project(x.P2, axis);xProject_P3 = Vector3.Project(x.P3, axis);float x_p0 = xProject_P0.magnitude * Mathf.Sign(Vector3.Dot(xProject_P0, axis));float x_p1 = xProject_P1.magnitude * Mathf.Sign(Vector3.Dot(xProject_P1, axis));float x_p2 = xProject_P2.magnitude * Mathf.Sign(Vector3.Dot(xProject_P2, axis));float x_p3 = xProject_P3.magnitude * Mathf.Sign(Vector3.Dot(xProject_P3, axis));yProject_P0 = Vector3.Project(y.P0, axis);yProject_P1 = Vector3.Project(y.P1, axis);yProject_P2 = Vector3.Project(y.P2, axis);yProject_P3 = Vector3.Project(y.P3, axis);float y_p0 = yProject_P0.magnitude * Mathf.Sign(Vector3.Dot(yProject_P0, axis));float y_p1 = yProject_P1.magnitude * Mathf.Sign(Vector3.Dot(yProject_P1, axis));float y_p2 = yProject_P2.magnitude * Mathf.Sign(Vector3.Dot(yProject_P2, axis));float y_p3 = yProject_P3.magnitude * Mathf.Sign(Vector3.Dot(yProject_P3, axis));float xMin = Mathf.Min(x_p0, x_p1, x_p2, x_p3);float xMax = Mathf.Max(x_p0, x_p1, x_p2, x_p3);float yMin = Mathf.Min(y_p0, y_p1, y_p2, y_p3);float yMax = Mathf.Max(y_p0, y_p1, y_p2, y_p3);if (enableDebug){if (debug_axisIndex == mDebugInternalAxisIndex){Debug.DrawRay(Vector3.Project(x.P0, axis), Vector3.one * 0.1f);Debug.DrawRay(Vector3.Project(x.P2, axis), Vector3.one * 0.1f);Debug.DrawRay(Vector3.Project(y.P0, axis), Vector3.one * 0.1f, Color.white * 0.9f);Debug.DrawRay(Vector3.Project(y.P2, axis), Vector3.one * 0.1f, Color.white * 0.9f);Debug.DrawRay(Vector3.zero, Vector3.one * 0.1f, Color.black);Debug.DrawRay(Vector3.zero, axis, Color.yellow);Debug.DrawRay(xMin * Vector3.right, Vector3.one * 0.1f, Color.blue);Debug.DrawRay(xMax * Vector3.right, Vector3.one * 0.1f, Color.cyan);Debug.DrawRay(yMin * Vector3.right, Vector3.one * 0.1f, Color.red * 0.5f);Debug.DrawRay(yMax * Vector3.right, Vector3.one * 0.1f, Color.red * 0.5f);Debug.Log("(yMin >= xMin && yMin <= xMax): " + (yMin >= xMin && yMin <= xMax) + " frame count: " + Time.frameCount); Debug.Log("(yMax >= xMin && yMax <= xMax): " + (yMax >= xMin && yMax <= xMax) + " frame count: " + Time.frameCount); Debug.Log("(xMin >= yMin && xMin <= yMax): " + (xMin >= yMin && xMin <= yMax) + " frame count: " + Time.frameCount); Debug.Log("(xMax >= yMin && xMax <= yMax): " + (xMax >= yMin && xMax <= yMax) + " frame count: " + Time.frameCount); }mDebugInternalAxisIndex++;}if (yMin >= xMin && yMin <= xMax) return false;if (yMax >= xMin && yMax <= xMax) return false;// 此处只需做两次判断即可，参考博⽂做了四次判断// if (xMin >= yMin && xMin <= yMax) return false;// if (xMax >= yMin && xMax <= yMax) return false;return true;}void OnDrawGizmos(){Gizmos.matrix = transform.localToWorldMatrix;Gizmos.color = gizmosColor;Gizmos.DrawWireCube(Vector3.zero, new Vector3(size.x, size.y, 1f));}}using System.Collections;using System.Collections.Generic;using UnityEngine;// OBBTest.cspublic class OBBTest : MonoBehaviour{public OBB a;public OBB b;void Update(){var isIntersects = a.Intersects(b);if (isIntersects){a.gizmosColor = Color.red;b.gizmosColor = Color.red;}else{a.gizmosColor = Color.white;b.gizmosColor = Color.white;}}}效果。
