射线/AABB 交点不正确

Question

我尝试在 C# 中重新实现 Fast Graphics Gems Ray/AABB Intersection Method：

// Based on "Fast Ray-Box Intersection" algorithm by Andrew Woo, "Graphics Gems", Academic Press, 1990
public unsafe Vector? IntersectionWith(Cuboid other) {
    const int NUM_DIMENSIONS = 3;
    Assure.Equal(NUM_DIMENSIONS, 3); // If that value is ever changed, this algorithm will need some maintenance

    const byte QUADRANT_MIN = 0;
    const byte QUADRANT_MAX = 1;
    const byte QUADRANT_BETWEEN = 2;

    // Step 1: Work out which direction from the start point to test for intersection for all 3 dimensions, and the distance
    byte* quadrants = stackalloc byte[NUM_DIMENSIONS];
    float* candidatePlanes = stackalloc float[NUM_DIMENSIONS];
    float* cuboidMinPoints = stackalloc float[NUM_DIMENSIONS];
    float* cuboidMaxPoints = stackalloc float[NUM_DIMENSIONS];
    float maxDistance = Single.NegativeInfinity;
    byte maxDistanceDimension = 0;

    bool startPointIsInsideCuboid = true;

    cuboidMinPoints[0] = other.X;
    cuboidMinPoints[1] = other.Y;
    cuboidMinPoints[2] = other.Z;
    cuboidMaxPoints[0] = other.X + other.Width;
    cuboidMaxPoints[1] = other.Y + other.Height;
    cuboidMaxPoints[2] = other.Z + other.Depth;

    for (byte i = 0; i < NUM_DIMENSIONS; ++i) {
        if (StartPoint[i] < cuboidMinPoints[i]) {
            quadrants[i] = QUADRANT_MIN;
            candidatePlanes[i] = cuboidMinPoints[i];
            startPointIsInsideCuboid = false;
        }
        else if (StartPoint[i] > cuboidMaxPoints[i]) {
            quadrants[i] = QUADRANT_MAX;
            candidatePlanes[i] = cuboidMaxPoints[i];
            startPointIsInsideCuboid = false;
        }
        else {
            quadrants[i] = QUADRANT_BETWEEN;
        }
    }

    if (startPointIsInsideCuboid) return StartPoint;

    // Step 2: Find farthest dimension from cuboid
    for (byte i = 0; i < NUM_DIMENSIONS; ++i) {
        // ReSharper disable once CompareOfFloatsByEqualityOperator Exact check is desired here: Anything other than 0f is usable
        if (quadrants[i] != QUADRANT_BETWEEN && Orientation[i] != 0f) {
            float thisDimensionDist = (candidatePlanes[i] - StartPoint[i]) / Orientation[i];
            if (thisDimensionDist > maxDistance) {
                maxDistance = thisDimensionDist;
                maxDistanceDimension = i;
            }
        }
    }

    if (maxDistance < 0f) return null;

    if (maxDistance - Length > MathUtils.FlopsErrorMargin) return null;

    float* intersectionPoint = stackalloc float[NUM_DIMENSIONS];

    for (byte i = 0; i < NUM_DIMENSIONS; ++i) {
        if (maxDistanceDimension == i) {
            intersectionPoint[i] = StartPoint[i] + maxDistance * Orientation[i];
            if (cuboidMinPoints[i] - intersectionPoint[i] > MathUtils.FlopsErrorMargin || intersectionPoint[i] - cuboidMaxPoints[i] > MathUtils.FlopsErrorMargin) return null;
        }
        else intersectionPoint[i] = candidatePlanes[i];

    }

    Vector result = new Vector(intersectionPoint[0], intersectionPoint[1], intersectionPoint[2]);
    if (!IsInfiniteLength && Vector.DistanceSquared(StartPoint, result) > Length * Length) return null;
    else return result;
}

然而，虽然它有点工作，但我在单元测试的以下部分得到了不正确的结果：

Cuboid cuboid = new Cuboid(frontBottomLeft: new Vector(0f, 7.1f, 0f), width: 0f, height: 5f, depth: 0f);
Ray testRayC = new Ray(startPoint: new Vector(30f, 30f, 30f), orientation: new Vector(-1f, -1f, -1f));

Assert.AreEqual(
    null, 
    testRayC.IntersectionWith(cuboid)
);

我期待 null 来自对 testRayC.IntersectionWith(cuboid) 的调用，但它返回一个 Vector(0, 12.1, 0)，它根本不是射线上的一个点。

---

那么这只是添加最终检查计算点是否在射线上的情况吗？或者（这是我怀疑的），我在转录代码时是否出错？我进行了两次和三次检查，但没有看到任何明显的...

Answer 1

您的代码中的问题是当您执行if (maxDistanceDimension == i) { 时。原始代码检查if (whichPlane != i) {。我没有你的数据结构，但修复应该如下所示：

        for (byte i = 0; i < NUM_DIMENSIONS; ++i)
        {
            if (maxDistanceDimension != i)
            {
                intersectionPoint[i] = StartPoint[i] + maxDistance * Orientation[i];
                if (intersectionPoint[i] < cuboidMinPoints[i] - MathUtils.FlopsErrorMargin || intersectionPoint[i] > cuboidMaxPoints[i] + MathUtils.FlopsErrorMargin)
                    return null;
            }
            else
            {
                intersectionPoint[i] = candidatePlanes[i];
            }
        }

接下来，以下内容不在原始代码中。这是干什么用的？

        if (maxDistance - Length > MathUtils.FlopsErrorMargin)
            return null;

如果您尝试检查命中是否在射线范围内，这可能是一个错误。鉴于您的 Orientation 似乎没有标准化，maxDistance 不一定以长度为单位。这在原始算法中可能无关紧要，但如果您要检查 maxDistance 与其他长度，您需要规范化 Orientation（使其无量纲）以便

                thisDimensionDist = (candidatePlanes[i] - StartPoint[i]) / Orientation[i];

会有长度单位。

顺便说一句，在原文中我认为以下是错误的：

if(inside)  {
    coord = origin;
    return (TRUE);
}

假设这段代码是 c 而不是 c++，这只是将 coord 指针设置为与 origin 指针具有相同的引用，这对调用者没有影响。但是，此问题不适用于您的版本。

另外，在查看这个的过程中，我在这里对算法进行了更文字的 c# 转录：

public static class RayXCuboid
{
    enum HitQuadrant
    {
        Right = 0,
        Left = 1,
        Middle = 2,
    }

    const int Dimension = 3;

    [Conditional("DEBUG")]
    static void AssertValidArguments<TDoubleList>(params TDoubleList[] args) where TDoubleList : IList<double>
    {
        Debug.Assert(Dimension == 3);
        foreach (var list in args)
            Debug.Assert(list != null && list.Count == Dimension);
    }

    public static bool HitBoundingBox<TDoubleList>(TDoubleList minB, TDoubleList maxB, TDoubleList origin, TDoubleList dir, TDoubleList coord) where TDoubleList : IList<double>
    {
        AssertValidArguments(minB, maxB, origin, dir, coord);

        HitQuadrant[] quadrant = new HitQuadrant[Dimension];
        double[] maxT = new double[Dimension];
        double[] candidatePlane = new double[Dimension];

        /* Find candidate planes; this loop can be avoided if
        rays cast all from the eye(assume perpsective view) */
        bool inside = true;
        for (int i = 0; i < Dimension; i++)
            if (origin[i] < minB[i])
            {
                quadrant[i] = HitQuadrant.Left;
                candidatePlane[i] = minB[i];
                inside = false;
            }
            else if (origin[i] > maxB[i])
            {
                quadrant[i] = HitQuadrant.Right;
                candidatePlane[i] = maxB[i];
                inside = false;
            }
            else
            {
                quadrant[i] = HitQuadrant.Middle;
            }

        /* Ray origin inside bounding box */
        if (inside)
        {
            CopyTo(origin, coord);
            return true;
        }

        /* Calculate T distances to candidate planes */
        for (int i = 0; i < Dimension; i++)
            if (quadrant[i] != HitQuadrant.Middle && dir[i] != 0.0)
                maxT[i] = (candidatePlane[i] - origin[i]) / dir[i];
            else
                maxT[i] = -1.0;

        /* Get largest of the maxT's for final choice of intersection */
        int whichPlane = 0;
        for (int i = 1; i < Dimension; i++)
            if (maxT[whichPlane] < maxT[i])
                whichPlane = i;

        /* Check final candidate actually inside box */
        if (maxT[whichPlane] < 0.0)
        {
            FillWithDefault(coord);
            return false;
        }

        for (int i = 0; i < Dimension; i++)
            if (whichPlane != i)
            {
                coord[i] = origin[i] + maxT[whichPlane] * dir[i];
                if (coord[i] < minB[i] || coord[i] > maxB[i])
                {
                    FillWithDefault(coord);
                    return false;
                }
            }
            else
            {
                coord[i] = candidatePlane[i];
            }
        return true;                /* ray hits box */
    }

    static void FillWithDefault<T>(IList<T> list)
    {
        for (int i = 0; i < list.Count; i++)
            list[i] = default(T);
    }

    static void CopyTo<T>(IList<T> from, IList<T> to)
    {
        int arrayIndex = 0;
        foreach (var item in from)
            to[arrayIndex++] = item;
    }
}