func (p *Plane) RayInteraction(r *gnr.Ray) []*gnr.InteractionResult {
// Ray: {P | P = r.Origin + t * r.Direction}
// Plane: {P | P * p.Normal + p.Distance = 0}
// Substitute: (r.Origin + t * r.Direction) * p.Normal + p.Distance = 0
t := -(p.Distance + gnr.VectorProduct(r.Origin, p.Normal)) / gnr.VectorProduct(r.Direction, p.Normal)
if t < 0 {
return []*gnr.InteractionResult{}
}
impact := gnr.CopyVector3f(r.Direction).ScalarMultiply(t).Add(r.Origin)
return []*gnr.InteractionResult{{
Color: gnr.ColorWhite,
PointOfImpact: impact,
Normal: gnr.CopyVector3f(p.Normal),
Distance: gnr.VectorDifference(impact, r.Origin).Magnitude(),
}}
}
func (s *Sphere) RayInteraction(r *gnr.Ray) []*gnr.InteractionResult {
// Ray: {P | P = r.Origin + t * r.Direction}
// Sphere: {P | mag(P - s.Center)^2 - s.Radius^2 = 0}
// substitution
// mag(r.Origin + t * r.Direction)^2 - s.Radius^2 = 0
d := gnr.VectorDifference(r.Origin, s.Center)
p := 2 * gnr.VectorProduct(r.Direction, d)
q := math.Pow(d.Magnitude(), 2) - math.Pow(s.Radius, 2)
p2 := math.Pow(p, 2)
inSqrt := p2/4 - q
if inSqrt < 0 {
return []*gnr.InteractionResult{}
}
sqrt := math.Sqrt(inSqrt)
t1 := -p/2 + sqrt
t2 := -p/2 - sqrt
P1 := gnr.VectorSum(r.Origin, gnr.CopyVector3f(r.Direction).ScalarMultiply(t1))
P2 := gnr.VectorSum(r.Origin, gnr.CopyVector3f(r.Direction).ScalarMultiply(t2))
irs := []*gnr.InteractionResult{
{Color: gnr.ColorWhite},
{Color: gnr.ColorWhite},
}
irs[0].PointOfImpact = P1
irs[0].Normal = gnr.VectorDifference(P1, s.Center)
irs[0].Distance = gnr.VectorDifference(P1, r.Origin).Magnitude()
if inSqrt != 0 {
irs[1].PointOfImpact = P2
irs[1].Normal = gnr.VectorDifference(P2, s.Center)
irs[1].Distance = gnr.VectorDifference(P2, r.Origin).Magnitude()
} else {
irs = irs[0:1]
}
return irs
}
func (p *Plane) DistanceToPoint(pt *gnr.Vector3f) float64 {
n := gnr.CopyVector3f(p.Normal).Normalize()
return math.Abs(gnr.VectorProduct(n, pt) + p.Distance)
}