三维球体上的0-1缩放

Question

我正在拍摄一个三维球面上的光线投射，我想要一种方法，它可以根据光线点(位置)从0(喷流中心)到1(圆周或球体轮廓)之间的浮点数。我怎样才能做到这一点。

我试着计算了球体位置和射线投落点之间的差异，虽然有点工作，但在代码中实现起来非常复杂。

还有其他方法吗?还是我遗漏了一些数学函数或向量函数，在这种情况下是有用的。

Answer 1

你可以取一个垂直于射线方向的Plane，穿过球体的起源，然后像这样使用Plane.Raycast将命中位置投射到球体上。

...
if(Physics.Raycast(ray, out var hit))
{
    if(hit.collider is SphereCollider hitSphere)
    {
        // This is assuming that your sphere is actually a sphere with uniform local scales
        var sphereRadius = hitSphere.radius * hitSphere.tranform.lossyScale.x;

        var hitObjectCenter = hit.collider.bounds.center;
        var plane = new Plane(-ray.diretcion, hitObjectCenter);
        if(plane.Raycast(ray, out var hitDistance))
        {
            var planeHitPoint = ray.GetPoint(hitDistance);

            var result = Vector3.Distance(hitObjectCenter, planeHitPoint) / sphereRadius;

            // now result should be your value between 0 (sphere center) and 1 (exactly on the sphere "edge" - probably never fully reached of course)
        }
    }
}

由于我们的平面使用的射线方向是正常的，你也可以用Plane.ClosestPointOnPlane近似。

var plane = new Plane(-ray.diretcion, hitObjectCenter);
var planeHitPoint = plane.ClosestPointOnPlane(hitDistance);
var result = Vector3.Distance(hitObjectCenter, planeHitPoint) / sphereRadius;

结果应该是几乎相同的，不确定哪一个更快，但我想光线投射是更精确的(我们说的差别有点像0.000001 ;)。

作为一个小演示，因为解释这是如何工作的有点复杂^^

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public class Example : MonoBehaviour
{
    public Camera mainCamera;

    private float result;
    private Ray ray;
    private Vector3 hitPoint;
    private Vector3? hitObjectCenter;
    private Vector3 planeHitPoint;

    private void Awake()
    {
        if (!mainCamera) mainCamera = Camera.main;
    }

    private void Update()
    {
        ray = mainCamera.ScreenPointToRay(Input.mousePosition);

        if (Physics.Raycast(ray, out var hit) && hit.collider is SphereCollider hitSphere)
        {
            hitPoint = hit.point;

            // This is assuming that your sphere is actually a sphere with uniform local scales
            var sphereRadius = hitSphere.radius * hitSphere.transform.lossyScale.x;

            hitObjectCenter = hit.collider.bounds.center;
            var plane = new Plane(-ray.direction, hitObjectCenter.Value);
            if(plane.Raycast(ray, out var hitDistance))
            {
                var planeHitPoint = ray.GetPoint(hitDistance);

                var result = Vector3.Distance(hitObjectCenter, planeHitPoint) / sphereRadius;
            }
        }
        else
        {
            hitObjectCenter = null;
        }
    }

    private Mesh planeMesh;

    private void OnDrawGizmos()
    {
        // if not hitting a sphere do nothing
        if (!hitObjectCenter.HasValue)
        {
            return;
        }

        // lazy initialize plan visualization
        if (!planeMesh)
        {
            planeMesh = new Mesh
            {
                vertices = new Vector3[4]
                {
                    new Vector3(-1, -1),
                    new Vector3(-1, 1),
                    new Vector3(1, 1),
                    new Vector3(1, -1)
                },
                triangles = new[]
                {
                    0, 1, 2,
                    0, 2, 3,

                    // backfaces
                    0, 2, 1,
                    0, 3, 2
                },
                normals = new Vector3[4]
                {
                    Vector3.forward,
                    Vector3.forward,
                    Vector3.forward,
                    Vector3.forward,
                }
            };
        }

        // Visualize ray
        Gizmos.color = Color.green;
        Gizmos.DrawLine(ray.origin, hitPoint);

        // Visualize hit point on sphere
        Gizmos.DrawWireSphere(hitPoint, 0.05f);

        // Visualize Plane
        Gizmos.color = Color.cyan;
        Gizmos.DrawWireMesh(planeMesh, hitObjectCenter.Value, Quaternion.LookRotation(ray.direction));

        // visualize hit point on plane
        Gizmos.DrawWireSphere(planeHitPoint, 0.05f);

        // Visualize distance
        Gizmos.color = Color.red;
        Gizmos.DrawLine(planeHitPoint, hitObjectCenter.Value);

        // print result on screen
        Handles.Label((planeHitPoint + hitObjectCenter.Value) / 2f, $"RESULT: {result:0.000}", new GUIStyle(EditorStyles.boldLabel) { alignment = TextAnchor.MiddleCenter });
    }
}