// IntersectTriangle find whether there's an intersection point between the ray and the triangle
// using barycentric coordinates and calculate the distance
func IntersectTriangle(ray *ray.Ray, A, B, C *maths.Vec3) (bool, float64) {
AB := maths.MinusVectors(B, A)
AC := maths.MinusVectors(C, A)
reverseDirection := ray.Direction.Negative()
distToA := maths.MinusVectors(&ray.Start, A)
ABxAC := maths.CrossProduct(AB, AC)
det := maths.DotProduct(ABxAC, reverseDirection)
reverseDet := 1 / det
if math.Abs(det) < maths.Epsilon {
return false, maths.Inf
}
lambda2 := maths.MixedProduct(distToA, AC, reverseDirection) * reverseDet
lambda3 := maths.MixedProduct(AB, distToA, reverseDirection) * reverseDet
gamma := maths.DotProduct(ABxAC, distToA) * reverseDet
if gamma < 0 {
return false, maths.Inf
}
if lambda2 < 0 || lambda2 > 1 || lambda3 < 0 || lambda3 > 1 || lambda2+lambda3 > 1 {
return false, maths.Inf
}
return true, gamma
}
// IntersectTriangle returns whether there's an intersection between the ray and the triangle,
// using barycentric coordinates and takes the point only if it's closer to the
// previously found intersection and the point is within the bounding box
func (m *Mesh) intersectTriangle(ray *ray.Ray, triangle *Triangle, intersection *ray.Intersection, boundingBox *BoundingBox) bool {
// lambda2 * AB + lambda3 * AC - intersectDist*rayDir = distToA
// If the triangle is ABC, this gives you A
A := &m.Vertices[triangle.Vertices[0]].Coordinates
distToA := maths.MinusVectors(&ray.Start, A)
rayDir := ray.Direction
ABxAC := triangle.ABxAC
// We will find the barycentric coordinates using Cramer's formula, so we'll need the determinant
// det is (AB^AC)*dir of the ray, but we're gonna use 1/det, so we find the recerse:
det := -maths.DotProduct(ABxAC, &rayDir)
if math.Abs(det) < maths.Epsilon {
return false
}
reverseDet := 1 / det
intersectDist := maths.DotProduct(ABxAC, distToA) * reverseDet
if intersectDist < 0 || intersectDist > intersection.Distance {
return false
}
// lambda2 = (dist^dir)*AC / det
// lambda3 = -(dist^dir)*AB / det
lambda2 := maths.MixedProduct(distToA, &rayDir, triangle.AC) * reverseDet
lambda3 := -maths.MixedProduct(distToA, &rayDir, triangle.AB) * reverseDet
if lambda2 < 0 || lambda2 > 1 || lambda3 < 0 || lambda3 > 1 || lambda2+lambda3 > 1 {
return false
}
ip := maths.AddVectors(&ray.Start, (&rayDir).Scaled(intersectDist))
// If we aren't inside the bounding box, there could be a closer intersection
// within the bounding box
if boundingBox != nil && !boundingBox.Inside(ip) {
return false
}
intersection.Point = ip
intersection.Distance = intersectDist
if triangle.Normal != nil {
intersection.Normal = triangle.Normal
} else {
// We solve intersection.normal = Anormal + AB normal * lambda2 + ACnormal * lambda 3
Anormal := &m.Vertices[triangle.Vertices[0]].Normal
Bnormal := &m.Vertices[triangle.Vertices[1]].Normal
Cnormal := &m.Vertices[triangle.Vertices[2]].Normal
ABxlambda2 := maths.MinusVectors(Bnormal, Anormal).Scaled(lambda2)
ACxlambda3 := maths.MinusVectors(Cnormal, Anormal).Scaled(lambda3)
intersection.Normal = maths.AddVectors(Anormal, maths.AddVectors(ABxlambda2, ACxlambda3))
}
uvA := &m.Vertices[triangle.Vertices[0]].UV
uvB := &m.Vertices[triangle.Vertices[1]].UV
uvC := &m.Vertices[triangle.Vertices[2]].UV
// We solve intersection.uv = uvA + uvAB * lambda2 + uvAC * lambda 3
uvABxlambda2 := maths.MinusVectors(uvB, uvA).Scaled(lambda2)
uvACxlambda3 := maths.MinusVectors(uvC, uvA).Scaled(lambda3)
uv := maths.AddVectors(uvA, maths.AddVectors(uvABxlambda2, uvACxlambda3))
intersection.U = uv.X
intersection.V = uv.Y
intersection.SurfaceOx = triangle.surfaceOx
intersection.SurfaceOy = triangle.surfaceOy
intersection.Incoming = ray
intersection.Material = triangle.Material
return true
}