游戏编程精粹学习 - 线段与非无限平面相交检测

参考自《游戏编程精粹1》多边形相交部分，用该方法除了知道是否相交以外还可以得到相交点，从而用于其他判断。

 

 

原文用到了平面方程的基本式Ax+By+Cz+D=0，求出线段2点p0和p1的D值，用D值转换成比值最后插值得到坐标

不用平面方程其实也可以用向量投影解释。

其中一些公式计算直接做了优化，没有生搬硬套。

这里直接使用平面，然后再拿相交点和平面所占区域进行判断，以下为Unity中的实现代码：

using UnityEngine;

public class Practice : MonoBehaviour
{
    public Transform p0;
    public Transform p1;
    public Transform planeLocation;
    public float size = 5f;


    void OnDrawGizmos()
    {
        if (p0 == null) return;
        if (p1 == null) return;
        if (planeLocation == null) return;

        var cacheColor = Gizmos.color;

        var r = GetIntersectPoint(planeLocation.forward, planeLocation.position, p0.position, p1.position);

        if (r != null)
        {
            var matrix = Matrix4x4.TRS(planeLocation.position, Quaternion.FromToRotation(planeLocation.forward, Vector3.forward), planeLocation.localScale);
            var temp = matrix.inverse.MultiplyPoint(r.Value);
            var sizeHalf = size * 0.5f;

            if (temp.x <= sizeHalf
                && temp.x >= -sizeHalf
                && temp.y <= sizeHalf
                && temp.y >= -sizeHalf)
            {
                Gizmos.color = Color.red;
            }

            Gizmos.DrawWireSphere(r.Value, 0.1f);
        }

        var cacheMatrix = Gizmos.matrix;
        Gizmos.matrix = Matrix4x4.TRS(planeLocation.position, planeLocation.rotation, Vector3.one);
        Gizmos.DrawWireCube(Vector3.zero, new Vector3(size, size, 0f));
        Gizmos.matrix = cacheMatrix;
        Gizmos.color = cacheColor;
    }

    /// <summary>
    /// 检测相交点的原始函数，没有相交点返回空，否则返回相交点。
    /// </summary>
    /// <param name="planeNormal">平面的法线朝向</param>
    /// <param name="planePosition">平面的位置</param>
    /// <param name="p0">线段点0</param>
    /// <param name="p1">线段点1</param>
    Vector3? GetIntersectPoint(Vector3 planeNormal, Vector3 planePosition, Vector3 p0, Vector3 p1)
    {
        var sign1 = Mathf.Sign(Vector3.Dot(planeNormal, planePosition - p0));
        var sign2 = Mathf.Sign(Vector3.Dot(planeNormal, planePosition - p1));
        if (Mathf.Approximately(sign1, sign2)) return null;//同侧异侧.

        var a = planeNormal.x;
        var b = planeNormal.y;
        var c = planeNormal.z;
        var d = -a * planePosition.x - b * planePosition.y - c * planePosition.z;

        var i0 = a * p0.x + b * p0.y + c * p0.z;
        var i1 = a * p1.x + b * p1.y + c * p1.z;
        var final_t = -(i1 + d) / (i0 - i1);

        var finalPoint = new Vector3()
        {
            x = p0.x * final_t + p1.x * (1 - final_t),
            y = p0.y * final_t + p1.y * (1 - final_t),
            z = p0.z * final_t + p1.z * (1 - final_t),
        };

        return finalPoint;
    }
}