胶囊体边界点的计算及获取

(注意 取的是中心点位置来计算边界点，而非投影点位置。可以自行修改为投影点)

 

之前想做一些体积碰撞的效果但是遇到点问题，胶囊边界点检测这个涉及到球体的交点检测以及圆柱的交点检测

觉得可以放上来，相交检测的代码逻辑来源于网络。

 

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

public class CapsuleTest : MonoBehaviour
{
    public enum DirectionEnum { X, Y, Z }
    public Vector3 center;
    public float height = 1f;
    public float radius = 1f;
    public DirectionEnum direction = DirectionEnum.Y;
    public Transform testOutsidePoint;


    Vector3 Test(Vector3 outsidePoint)
    {
        var localMassPoint = center;
        var localOutsidePoint = transform.worldToLocalMatrix.MultiplyPoint3x4(outsidePoint);

        var centerPoint = localMassPoint + center;

        var up = Vector3.up;
        var right = Vector3.right;
        var forward = Vector3.forward;

        switch (direction)
        {
            case DirectionEnum.X:
                up = Vector3.right;
                right = Vector3.forward;
                forward = Vector3.up;
                break;
            case DirectionEnum.Z:
                up = Vector3.forward;
                right = Vector3.up;
                forward = Vector3.right;
                break;
        }

        var remainHeight = Mathf.Max(height - radius * 2f, 0) + 0.01f;
        var remainHeightHalf = remainHeight * 0.5f;
        var pillarOrigin = centerPoint + up * -remainHeightHalf;
        var pillarEnd = centerPoint + up * remainHeightHalf;

        var insectPoint = Vector3.zero;
        var isHitCylinder = CylinderVSline(localOutsidePoint, (centerPoint - localOutsidePoint).normalized, pillarOrigin, pillarEnd, radius, out insectPoint);

        if (isHitCylinder)
        {
            return transform.localToWorldMatrix.MultiplyPoint3x4(insectPoint);
        }
        else
        {
            var spherePoint1 = centerPoint + up * remainHeightHalf;
            var spherePoint2 = centerPoint + (-up) * remainHeightHalf;
            var finalSpherePoint = spherePoint1;

            if (Vector3.Distance(localOutsidePoint, spherePoint2) < Vector3.Distance(localOutsidePoint, spherePoint1))
            {
                finalSpherePoint = spherePoint2;
            }

            BetweenLineAndSphere(finalSpherePoint, radius, centerPoint, localOutsidePoint, out spherePoint1, out spherePoint2);

            if (Vector3.Distance(spherePoint1, centerPoint) > Vector3.Distance(spherePoint2, centerPoint))
                return transform.localToWorldMatrix.MultiplyPoint3x4(spherePoint1);
            else
                return transform.localToWorldMatrix.MultiplyPoint3x4(spherePoint2);
        }
    }

    void OnDrawGizmos()
    {
        var cacheColor = Gizmos.color;
        var cacheMatrix = Gizmos.matrix;

        if (testOutsidePoint != null)
        {
            var edgePoint = Test(testOutsidePoint.position);
            Gizmos.DrawWireSphere(edgePoint, 0.2f);
        }

        Gizmos.color = Color.Lerp(Color.green, Color.gray, 0.5f);
        Gizmos.matrix = transform.localToWorldMatrix;

        var remainHeight = Mathf.Max(height - radius * 2f, 0);
        var remainHeightHalf = remainHeight * 0.5f;

        var up = Vector3.up;
        var right = Vector3.right;
        var forward = Vector3.forward;

        switch (direction)
        {
            case DirectionEnum.X:
                up = Vector3.right;
                right = Vector3.forward;
                forward = Vector3.up;
                break;
            case DirectionEnum.Z:
                up = Vector3.forward;
                right = Vector3.up;
                forward = Vector3.right;
                break;
        }

        var lastPoint1 = (Vector3?)null;
        var lastPoint2 = (Vector3?)null;
        for (var i = 0f; i <= 180f; i += 9f)
        {
            var point1 = up * -remainHeightHalf + Quaternion.AngleAxis(i, right) * forward * radius;
            var point2 = up * -remainHeightHalf + Quaternion.AngleAxis(i, -forward) * right * radius;

            Gizmos.DrawLine(center + lastPoint1.GetValueOrDefault(point1), center + point1);
            Gizmos.DrawLine(center + lastPoint2.GetValueOrDefault(point2), center + point2);

            lastPoint1 = point1;
            lastPoint2 = point2;
        }

        lastPoint1 = (Vector3?)null;
        for (var i = 0f; i <= 360f; i += 9f)
        {
            var point1 = up * -remainHeightHalf + Quaternion.AngleAxis(i, up) * forward * radius;

            Gizmos.DrawLine(center + lastPoint1.GetValueOrDefault(point1), center + point1);

            lastPoint1 = point1;
        }

        Gizmos.DrawLine(center + forward * radius + up * -remainHeightHalf, center + forward * radius + up * remainHeightHalf);
        Gizmos.DrawLine(center + -forward * radius + up * -remainHeightHalf, center + -forward * radius + up * remainHeightHalf);

        Gizmos.DrawLine(center + right * radius + up * -remainHeightHalf, center + right * radius + up * remainHeightHalf);
        Gizmos.DrawLine(center + -right * radius + up * -remainHeightHalf, center + -right * radius + up * remainHeightHalf);

        lastPoint1 = (Vector3?)null;
        lastPoint2 = (Vector3?)null;
        for (var i = 0f; i <= 180f; i += 9f)
        {
            var point1 = up * remainHeightHalf + Quaternion.AngleAxis(i, -right) * forward * radius;
            var point2 = up * remainHeightHalf + Quaternion.AngleAxis(i, forward) * right * radius;

            Gizmos.DrawLine(center + lastPoint1.GetValueOrDefault(point1), center + point1);
            Gizmos.DrawLine(center + lastPoint2.GetValueOrDefault(point2), center + point2);

            lastPoint1 = point1;
            lastPoint2 = point2;
        }

        lastPoint1 = (Vector3?)null;
        for (var i = 0f; i <= 360f; i += 9f)
        {
            var point1 = up * remainHeightHalf + Quaternion.AngleAxis(i, up) * forward * radius;

            Gizmos.DrawLine(center + lastPoint1.GetValueOrDefault(point1), center + point1);

            lastPoint1 = point1;
        }

        Gizmos.color = cacheColor;
        Gizmos.matrix = cacheMatrix;
    }

    bool BetweenLineAndSphere(
        Vector3 circleCenter, float circleRadius,
        Vector3 point1, Vector3 point2,
        out Vector3 intersection1, out Vector3 intersection2)
    {
        float t;

        var dx = point2.x - point1.x;
        var dy = point2.y - point1.y;
        var dz = point2.z - point1.z;

        var a = dx * dx + dy * dy + dz * dz;
        var b = 2 * (dx * (point1.x - circleCenter.x) + dy * (point1.y - circleCenter.y) + dz * (point1.z - circleCenter.z));
        var c = (point1.x - circleCenter.x) * (point1.x - circleCenter.x)
            + (point1.y - circleCenter.y) * (point1.y - circleCenter.y)
            + (point1.z - circleCenter.z) * (point1.z - circleCenter.z) - circleRadius * circleRadius;

        var determinate = b * b - 4 * a * c;

        // Two solutions.
        t = (float)((-b + Mathf.Sqrt(determinate)) / (2 * a));
        intersection1 = new Vector3(point1.x + t * dx, point1.y + t * dy, point1.z + t * dz);
        t = (float)((-b - Mathf.Sqrt(determinate)) / (2 * a));
        intersection2 = new Vector3(point1.x + t * dx, point1.y + t * dy, point1.z + t * dz);

        if (intersection1.normalized == Vector3.zero && intersection2.normalized == Vector3.zero)
            return false;
        else
            return true;
    }

    bool CylinderVSline(Vector3 start, Vector3 dir, Vector3 aVec, Vector3 bVec, float radius, out Vector3 intersectPoint)
    {
        intersectPoint = Vector3.zero;

        // Solution : http://www.gamedev.net/community/forums/topic.asp?topic_id=467789

        var ab = bVec - aVec;
        var ao = start - aVec;
        var aoxAb = Vector3.Cross(ao, ab);
        var vxAb = Vector3.Cross(dir, ab);
        var ab2 = Vector3.Dot(ab, ab);
        var a = Vector3.Dot(vxAb, vxAb);
        var b = 2 * Vector3.Dot(vxAb, aoxAb);
        var c = Vector3.Dot(aoxAb, aoxAb) - (radius * radius * ab2);
        var d = b * b - 4 * a * c;
        if (d < 0) return false;
        float time = (-b - Mathf.Sqrt(d)) / (2 * a);
        if (time < 0) return false;

        intersectPoint = start + dir * time;

        var projectionPoint = aVec + Vector3.Project(intersectPoint - aVec, ab.normalized);
        var distance1 = Mathf.Max(Vector3.Distance(projectionPoint, aVec), Vector3.Distance(projectionPoint, bVec));
        var distance2 = Vector3.Distance(aVec, bVec);

        if (distance1 >= distance2)
            return false;

        return true;
    }
}