func MakeViewRay(u, v, k float64) geometry.Ray {
//var d1 float64 = math.Sqrt(1/(2+4*sinθ2))
// = math.Sqrt(5/14)
const d1 float64 = 0.5976143046671968
//var d2 float64 = -2*sinθ*d1
const d2 float64 = -2 * sinθ * d1
// = -math.Sqrt(2/7)
d := geometry.MakeVector(d1, d2, d1)
bu := geometry.MakeVector(1.0/math.Sqrt(2), 0, -1.0/math.Sqrt(2))
var bv1 float64 = math.Sqrt(1.0 / 7.0) //math.Sqrt(1/(2 + 1/sinθ2))
var bv2 float64 = math.Sqrt(5.0 / 7.0) //bv1/sinθ
bv := geometry.MakeVector(bv1, bv2, bv1)
//fmt.Println(bu.Dot(d), bv.Dot(d), bu.Dot(bv))
o := (bu.Mul(u)).Add(bv.Mul(v)).Add(d.Mul(k))
return geometry.MakeRay(o, d)
}
func calculateColour(r geometry.Ray,
depth float64,
scene geometry.Object,
object geometry.Object,
mat geometry.Material,
recursionLimit uint) (colour geometry.Vector) {
colour = mat.BaseColour.Mul(mat.CBase)
if mat.CReflectance != 0 && recursionLimit != 0 {
//calculate normal
normal := object.Normal(r, depth)
dir_proj := normal.Mul(normal.Dot(r.GetDirectionVector()))
reflectedDirection := dir_proj.Mul(2).Sub(r.GetDirectionVector())
incidence := r.Point(depth)
reflectedRay := geometry.MakeRay(incidence.Add(reflectedDirection.Mul(0.01)), reflectedDirection) //add a small amount so that it doesn't intersect the mirror
_, reflectedColour := castRay(reflectedRay, scene, recursionLimit-1)
colour = colour.Add(reflectedColour.Mul(mat.CReflectance))
}
return
}