// Vec3Hemi returns a random unit vector in the hemisphere defined by normal
func (r *Random) Vec3Hemi(normal *maths.Vec3) *maths.Vec3 {
vec := r.Vec3Sphere()
if maths.DotProduct(vec, normal) < 0 {
vec.Negate()
}
return vec
}
// Shade returns the emitted colour after intersecting the material
func (m *RefractiveMaterial) Shade(intersection *ray.Intersection, raytracer Raytracer) *hdrcolour.Colour {
incoming := &intersection.Incoming.Direction
normal := intersection.Normal
ior := m.IOR.GetFac(intersection)
colour := m.Colour.GetColour(intersection)
refracted := &maths.Vec3{}
startPoint := &maths.Vec3{}
if maths.DotProduct(incoming, normal) < 0 {
refracted = maths.Refract(incoming, normal, 1/ior)
} else {
refracted = maths.Refract(incoming, normal.Negative(), ior)
}
if refracted != nil {
// regular refraction - push the starting point a tiny bit
// through the surface
startPoint = maths.MinusVectors(
intersection.Point, normal.FaceForward(incoming).Scaled(maths.Epsilon),
)
} else {
// total inner reflection
refracted = incoming.Reflected(normal.FaceForward(incoming))
// push the starting point a tiny bit away from the surface
startPoint = maths.AddVectors(
intersection.Point, normal.FaceForward(incoming).Scaled(maths.Epsilon),
)
}
newRay := &ray.Ray{Depth: intersection.Incoming.Depth + 1}
newRay.Start = *startPoint
newRay.Direction = *refracted
return hdrcolour.MultiplyColours(raytracer.Raytrace(newRay), colour)
}
func TestVectors(t *testing.T) {
assert := assert.New(t)
rnd := New(42)
vec := rnd.Vec3Sphere()
assert.InDelta(1, vec.Length(), maths.Epsilon, "Random unit vector's length should be 1")
norm := vec
vec = rnd.Vec3Hemi(norm)
if maths.DotProduct(vec, norm) < 0 {
t.Error("Random hemi vector is in the wrong hemisphere")
}
vec = rnd.Vec3HemiCos(norm)
if maths.DotProduct(vec, norm) < 0 {
t.Error("Random cosine-weighed hemi vector is in the wrong hemisphere")
}
}
// 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 checks if the bounding box intersects with a triangle
// 1) To have a vertex in the box
// 2) The edge of the triangle intersects with the box
// 3) The middle of the triangle to be inside the box, while the vertices aren't
func (b *BoundingBox) IntersectTriangle(A, B, C *maths.Vec3) bool {
if b.Inside(A) || b.Inside(B) || b.Inside(C) {
return true
}
// we construct the ray from A->B, A->C, etc and check whether it intersects with the box
triangle := [3]*maths.Vec3{A, B, C}
ray := &ray.Ray{}
for rayStart := 0; rayStart < 3; rayStart++ {
for rayEnd := rayStart + 1; rayEnd < 3; rayEnd++ {
ray.Start = *(triangle[rayStart])
ray.Direction = *maths.MinusVectors(triangle[rayEnd], triangle[rayStart])
ray.Init()
// Check if there's intersection between AB and the box (example)
if b.Intersect(ray) {
// we check whether there's intersection between BA and the Box too
// to be sure the edge isn't outside the box
// _____
// | | <----AB there is intersection, but BA----->
// |____|
ray.Start = *triangle[rayEnd]
ray.Direction = *maths.MinusVectors(triangle[rayStart], triangle[rayEnd])
ray.Init()
if b.Intersect(ray) {
return true
}
}
}
}
// we have to check if the inside of the triangle intersects with the box
AB := maths.MinusVectors(B, A)
AC := maths.MinusVectors(C, A)
ABxAC := maths.CrossProduct(AB, AC)
distance := maths.DotProduct(A, ABxAC)
rayEnd := &maths.Vec3{}
for edgeMask := 0; edgeMask < 7; edgeMask++ {
for axis := uint(0); axis < 3; axis++ {
if edgeMask&(1<<axis) != 0 {
continue
}
if edgeMask&1 != 0 {
ray.Start.X = b.MaxVolume[0]
} else {
ray.Start.X = b.MinVolume[0]
}
if edgeMask&2 != 0 {
ray.Start.Y = b.MaxVolume[1]
} else {
ray.Start.Y = b.MinVolume[1]
}
if edgeMask&4 != 0 {
ray.Start.Z = b.MaxVolume[2]
} else {
ray.Start.Z = b.MinVolume[2]
}
*rayEnd = ray.Start
rayEnd.SetDimension(int(axis), b.MaxVolume[axis])
if (maths.DotProduct(&ray.Start, ABxAC)-distance)*(maths.DotProduct(rayEnd, ABxAC)-distance) <= 0 {
ray.Direction = *maths.MinusVectors(rayEnd, &ray.Start)
ray.Init()
intersected, distance := IntersectTriangle(ray, A, B, C)
if intersected && distance < 1.0000001 {
return true
}
}
}
}
return false
}
// 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
}