Fast Graphics Gems Ray/AABB Intersection Methodを C# で再実装しようとしました。
// 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;
}
ただし、ある程度は機能しますが、単体テストの次の部分で誤った結果が得られます。
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)
);
nullへの呼び出しを期待してtestRayC.IntersectionWith(cuboid)いますが、代わりに を返しますVector(0, 12.1, 0)。これは光線上の点ではありません。
では、計算された点が光線上にあるかどうかの最終チェックを追加するだけの場合ですか? または (これは私が疑っていることです)、コードの転記に誤りがありましたか? ダブルチェックとトリプルチェックしましたが、明らかなものは何も見られませんでした...