// 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)
}
// Shade returns the emitted colour after intersecting the material
func (m *LambertMaterial) Shade(intersection *ray.Intersection, raytracer Raytracer) *hdrcolour.Colour {
randomRayDir := *raytracer.RandomGen().Vec3HemiCos(intersection.Normal)
randomRayStart := *maths.AddVectors(intersection.Point, intersection.Normal.Scaled(maths.Epsilon))
ray := &ray.Ray{Start: randomRayStart, Direction: randomRayDir, Depth: intersection.Incoming.Depth + 1}
colour := raytracer.Raytrace(ray)
colour.MultiplyBy(m.Colour.GetColour(intersection))
return colour
}
// Shade returns the emitted colour after intersecting the material
func (m *ReflectiveMaterial) Shade(intersection *ray.Intersection, raytracer Raytracer) *hdrcolour.Colour {
incoming := intersection.Incoming
colour := m.Colour.GetColour(intersection)
reflectedRay := &ray.Ray{Depth: incoming.Depth + 1}
reflectedRay.Direction = *incoming.Direction.Reflected(intersection.Normal)
reflectedRay.Start = *maths.AddVectors(intersection.Point, intersection.Normal.Scaled(maths.Epsilon))
return hdrcolour.MultiplyColours(raytracer.Raytrace(reflectedRay), colour)
}
// Init of Mesh sets the Triangle indices in the Faces array, calculates the bounding box
// and KD tree, sets the surfaceOx and Oy and Cross Products of the sides of each triangle
func (m *Mesh) Init() {
allIndices := make([]int, len(m.Faces))
for i := range allIndices {
allIndices[i] = i
}
m.BoundingBox = m.GetBoundingBox()
m.tree = m.newKDtree(m.BoundingBox, allIndices, 0)
for i := range m.Faces {
triangle := &m.Faces[i]
A := &m.Vertices[triangle.Vertices[0]].Coordinates
B := &m.Vertices[triangle.Vertices[1]].Coordinates
C := &m.Vertices[triangle.Vertices[2]].Coordinates
AB := maths.MinusVectors(B, A)
AC := maths.MinusVectors(C, A)
triangle.AB = AB
triangle.AC = AC
triangle.ABxAC = maths.CrossProduct(AB, AC)
surfaceA := &m.Vertices[triangle.Vertices[0]].UV
surfaceB := &m.Vertices[triangle.Vertices[1]].UV
surfaceC := &m.Vertices[triangle.Vertices[2]].UV
surfaceAB := maths.MinusVectors(surfaceB, surfaceA)
surfaceAC := maths.MinusVectors(surfaceC, surfaceA)
// Solve using Cramer:
// |surfaceAB.X * px + surfaceAX.X *qx + 1 = 0
// |surfaceAB.Y * px + surfaceAX.Y *qx = 0
// and
// surfaceAB.X * py + surfaceAX.X *qy = 0
// surfaceAB.X * py + surfaceAX.X *qy + 1 = 0
px, qx := maths.SolveEquation(surfaceAB, surfaceAC, maths.NewVec3(1, 0, 0))
py, qy := maths.SolveEquation(surfaceAB, surfaceAC, maths.NewVec3(0, 1, 0))
triangle.surfaceOx = maths.AddVectors(AB.Scaled(px), AC.Scaled(qx))
triangle.surfaceOy = maths.AddVectors(AB.Scaled(py), AC.Scaled(qy))
}
}
// 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
}