❤️UNITY实战进阶-三维AABB包围盒详解-6_欲望如海水，越喝越渴。-CSDN博客前言碰撞检测问题在虚拟现实、计算机辅助设计与制造、游戏、机器人等方面都有着广泛的应用，而包围盒算法是进行碰撞检测的重要方法之一。而常见的包围盒有：AABB包围盒（Axis-aligned bounding box）包围球（Sphere）OBB包围盒（Oriented bounding box）凸包包围盒（Convex Hull）...在Unity中的Collider包含：介绍在游戏中，为了简化物体之间的碰...https://blog.csdn.net/flj135792468/article/details/120654391在前文中，我们可以通过2个点来确定一个立方体。在此基础上添加3个轴向

        public Vector3 XAxis { get { return transform.right; } }public Vector3 YAxis { get { return transform.up; } }public Vector3 ZAxis { get { return transform.forward; } }

已知一个点的坐标和物体的四元数，我们就可以得知旋转完的点

public void GetCorners()
{// 朝着Z轴正方向的面// 左上顶点坐标m_Corners[0].Set(m_RealCalcMin.x, m_RealCalcMax.y, m_RealCalcMax.z);// 左下顶点坐标m_Corners[1].Set(m_RealCalcMin.x, m_RealCalcMin.y, m_RealCalcMax.z);// 右下顶点坐标m_Corners[2].Set(m_RealCalcMax.x, m_RealCalcMin.y, m_RealCalcMax.z);// 右上顶点坐标m_Corners[3].Set(m_RealCalcMax.x, m_RealCalcMax.y, m_RealCalcMax.z);// 朝着Z轴负方向的面// 右上顶点坐标m_Corners[4].Set(m_RealCalcMax.x, m_RealCalcMax.y, m_RealCalcMin.z);// 右下顶点坐标.m_Corners[5].Set(m_RealCalcMax.x, m_RealCalcMin.y, m_RealCalcMin.z);// 左下顶点坐标.m_Corners[6].Set(m_RealCalcMin.x, m_RealCalcMin.y, m_RealCalcMin.z);// 左上顶点坐标.m_Corners[7].Set(m_RealCalcMin.x, m_RealCalcMax.y, m_RealCalcMin.z);// 根据旋转修改8个点的坐标for (int i = 0; i < m_Corners.Length; i++){Vector3 dis = m_Corners[i] - transform.position;m_Corners[i] = transform.position + transform.localRotation * dis;}
}

这样一个可以跟着旋转的8个顶点坐标就算出来了

OBB包围盒的碰撞检测方法

检测方法常采用的是分离轴定理。说白了就是去检测并判断两个图形之间是否有间隙。

找到一个轴，两个凸形状在该轴上的投影不重叠，则这两个形状不相交。如果这个轴不存在，并且那些形状是凸形的，则可以确定两个形状相交。

在算法上就是取两个OBB的坐标轴各3个以及垂直于每个轴的9个轴。

1.先将点投影到坐标抽上

/// <summary>
/// 将点投影到坐标轴
/// </summary>
/// <param name="point"></param>
/// <param name="axis"></param>
/// <returns>投影的坐标</returns>
private float ProjectPoint(Vector3 point, Vector3 axis)
{Vector3 projectPoint = Vector3.Project(point, axis);float result = projectPoint.magnitude * Mathf.Sign(Vector3.Dot(projectPoint, axis));return result;
}

2.获取8个点在轴上投影的最大值和最小值

/// <summary>
/// 计算最大最小投影值
/// </summary>
/// <param name="corners"></param>
/// <param name="axis"></param>
/// <param name="min"></param>
/// <param name="max"></param>
private void GetInterval(Vector3[] corners, Vector3 axis, out float min, out float max)
{float value;//分别投影八个点，取最大和最小值min = max = ProjectPoint(corners[0], axis);for (int i = 1; i < corners.Length; i++){value = ProjectPoint(corners[i], axis);min = Mathf.Min(min, value);max = Mathf.Max(max, value);}
}

3.判断是不是交叉点

/// <summary>
/// 预测是不是交叉点
/// </summary>
/// <param name="aCorners"></param>
/// <param name="bCorners"></param>
/// <param name="axis"></param>
/// <returns></returns>
private bool AxisProjection(Vector3[] aCorners, Vector3[] bCorners, Vector3 axis)
{GetInterval(aCorners, axis, out float xMin, out float xMax);GetInterval(bCorners, axis, out float yMin, out float yMax);if (yMin >= xMin && yMin <= xMax) return false;if (yMax >= xMin && yMax <= xMax) return false;if (xMin >= yMin && xMin <= yMax) return false;if (xMax >= yMin && xMax <= yMax) return false;return true;
}

4.根据2个包围盒的3个轴以及垂直于每个轴的9个轴判断是否有交集

public bool Intersects(IMathAABB aabb)
{m_IsNotIntersect = false;m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, XAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, YAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, ZAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, aabb.XAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, aabb.YAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, aabb.ZAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(XAxis, aabb.XAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(XAxis, aabb.YAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(XAxis, aabb.ZAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(YAxis, aabb.XAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(YAxis, aabb.YAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(YAxis, aabb.ZAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(ZAxis, aabb.XAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(ZAxis, aabb.YAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(ZAxis, aabb.ZAxis).normalized);return !m_IsNotIntersect;
}

完整代码

public class OBB : MonoBehaviour, IMathAABB{//修改此值控制m_CalcMin[SerializeField, AABBModify("MinVector")]private Vector3 m_Min = -Vector3.one;//修改此值控制m_CalcMax[SerializeField, AABBModify("MaxVector")]private Vector3 m_Max = Vector3.one;/// <summary>/// 中心点/// </summary>[SerializeField, AABBDisable]private Vector3 m_Center = Vector3.zero;/// <summary>/// 保存包围盒八个顶点/// </summary>[SerializeField, AABBDisable]private Vector3[] m_Corners = new Vector3[8];#if UNITY_EDITOR[SerializeField]private Color m_DebugLineColor = Color.green;
#endifpublic Vector3 MinVector{set{SetMinMax(m_Min, m_Max);}get{return m_RealCalcMin;}}public Vector3 MaxVector{set{SetMinMax(m_Min, m_Max);}get{return m_RealCalcMax;}}public Vector3[] Corners{get{return m_Corners;}}public Vector3 Center{get{return m_Center;}}public Vector3 XAxis { get { return transform.right; } }public Vector3 YAxis { get { return transform.up; } }public Vector3 ZAxis { get { return transform.forward; } }/// <summary>/// 实际计算的最小值/// </summary>private Vector3 m_RealCalcMin;/// <summary>/// 实际计算的最大值/// </summary>private Vector3 m_RealCalcMax;private bool m_IsNotIntersect = false;/// <summary>/// 防止在update之前产生碰撞/// </summary>private void Awake(){SetMinMax(m_Min, m_Max);}// Update is called once per frameprivate void Update(){SetMinMax(m_Min, m_Max);}#if UNITY_EDITORvoid OnDrawGizmos(){//// draw linesGizmos.color = m_DebugLineColor;Gizmos.DrawLine(Corners[0], Corners[1]);Gizmos.DrawLine(Corners[1], Corners[2]);Gizmos.DrawLine(Corners[2], Corners[3]);Gizmos.DrawLine(Corners[3], Corners[0]);Gizmos.DrawLine(Corners[4], Corners[5]);Gizmos.DrawLine(Corners[5], Corners[6]);Gizmos.DrawLine(Corners[6], Corners[7]);Gizmos.DrawLine(Corners[7], Corners[4]);Gizmos.DrawLine(Corners[0], Corners[7]);Gizmos.DrawLine(Corners[1], Corners[6]);Gizmos.DrawLine(Corners[2], Corners[5]);Gizmos.DrawLine(Corners[3], Corners[4]);}
#endifpublic Vector3 GetCenter(){m_Center.x = 0.5f * (m_RealCalcMin.x + m_RealCalcMax.x);m_Center.y = 0.5f * (m_RealCalcMin.y + m_RealCalcMax.y);m_Center.z = 0.5f * (m_RealCalcMin.z + m_RealCalcMax.z);return m_Center;}public void GetCorners(){// 朝着Z轴正方向的面// 左上顶点坐标m_Corners[0].Set(m_RealCalcMin.x, m_RealCalcMax.y, m_RealCalcMax.z);// 左下顶点坐标m_Corners[1].Set(m_RealCalcMin.x, m_RealCalcMin.y, m_RealCalcMax.z);// 右下顶点坐标m_Corners[2].Set(m_RealCalcMax.x, m_RealCalcMin.y, m_RealCalcMax.z);// 右上顶点坐标m_Corners[3].Set(m_RealCalcMax.x, m_RealCalcMax.y, m_RealCalcMax.z);// 朝着Z轴负方向的面// 右上顶点坐标m_Corners[4].Set(m_RealCalcMax.x, m_RealCalcMax.y, m_RealCalcMin.z);// 右下顶点坐标.m_Corners[5].Set(m_RealCalcMax.x, m_RealCalcMin.y, m_RealCalcMin.z);// 左下顶点坐标.m_Corners[6].Set(m_RealCalcMin.x, m_RealCalcMin.y, m_RealCalcMin.z);// 左上顶点坐标.m_Corners[7].Set(m_RealCalcMin.x, m_RealCalcMax.y, m_RealCalcMin.z);// 根据旋转修改8个点的坐标for (int i = 0; i < m_Corners.Length; i++){Vector3 dis = m_Corners[i] - transform.position;m_Corners[i] = transform.position + transform.localRotation * dis;}}public bool Intersects(IMathAABB aabb){m_IsNotIntersect = false;m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, XAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, YAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, ZAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, aabb.XAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, aabb.YAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, aabb.ZAxis);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(XAxis, aabb.XAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(XAxis, aabb.YAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(XAxis, aabb.ZAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(YAxis, aabb.XAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(YAxis, aabb.YAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(YAxis, aabb.ZAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(ZAxis, aabb.XAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(ZAxis, aabb.YAxis).normalized);m_IsNotIntersect |= AxisProjection(this.Corners, aabb.Corners, Vector3.Cross(ZAxis, aabb.ZAxis).normalized);return !m_IsNotIntersect;}public bool ContainPoint(Vector3 point){m_IsNotIntersect = false;m_IsNotIntersect |= AxisProjection(this.Corners, point, XAxis);m_IsNotIntersect |= AxisProjection(this.Corners, point, YAxis);m_IsNotIntersect |= AxisProjection(this.Corners, point, ZAxis);return !m_IsNotIntersect;}public void Merge(IMathAABB box){throw new System.NotImplementedException("Please ingore 'Merge(IMathAABB box)' function !");}public void SetMinMax(Vector3 min, Vector3 max){this.m_RealCalcMin = min * 0.5f + transform.position;this.m_RealCalcMax = max * 0.5f + transform.position;GetCenter();GetCorners();}public bool IsEmpty(){return m_RealCalcMin.x > m_RealCalcMax.x || m_RealCalcMin.y > m_RealCalcMax.y || m_RealCalcMin.z > m_RealCalcMax.z;}public void ResetMinMax(){m_RealCalcMin.Set(-1, -1, -1);m_RealCalcMax.Set(1, 1, 1);GetCenter();GetCorners();}/// <summary>/// 预测是不是交叉点/// </summary>/// <param name="aCorners"></param>/// <param name="bCorners"></param>/// <param name="axis"></param>/// <returns></returns>private bool AxisProjection(Vector3[] aCorners, Vector3[] bCorners, Vector3 axis){GetInterval(aCorners, axis, out float xMin, out float xMax);GetInterval(bCorners, axis, out float yMin, out float yMax);if (yMin >= xMin && yMin <= xMax) return false;if (yMax >= xMin && yMax <= xMax) return false;if (xMin >= yMin && xMin <= yMax) return false;if (xMax >= yMin && xMax <= yMax) return false;return true;}/// <summary>/// 预测是不是交叉点/// </summary>/// <param name="aCorners"></param>/// <param name="point"></param>/// <param name="axis"></param>/// <returns></returns>private bool AxisProjection(Vector3[] aCorners, Vector3 point, Vector3 axis){GetInterval(aCorners, axis, out float xMin, out float xMax);float yMin = ProjectPoint(point, axis);float yMax = ProjectPoint(point, axis);if (yMin >= xMin && yMin <= xMax) return false;if (yMax >= xMin && yMax <= xMax) return false;if (xMin >= yMin && xMin <= yMax) return false;if (xMax >= yMin && xMax <= yMax) return false;return true;}/// <summary>/// 计算最大最小投影值/// </summary>/// <param name="corners"></param>/// <param name="axis"></param>/// <param name="min"></param>/// <param name="max"></param>private void GetInterval(Vector3[] corners, Vector3 axis, out float min, out float max){float value;//分别投影八个点，取最大和最小值min = max = ProjectPoint(corners[0], axis);for (int i = 1; i < corners.Length; i++){value = ProjectPoint(corners[i], axis);min = Mathf.Min(min, value);max = Mathf.Max(max, value);}}/// <summary>/// 将点投影到坐标轴/// </summary>/// <param name="point"></param>/// <param name="axis"></param>/// <returns>投影的坐标</returns>private float ProjectPoint(Vector3 point, Vector3 axis){Vector3 projectPoint = Vector3.Project(point, axis);float result = projectPoint.magnitude * Mathf.Sign(Vector3.Dot(projectPoint, axis));return result;}}

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❤️UNITY实战进阶-OBB包围盒详解-6

OBB包围盒的碰撞检测方法

完整代码

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