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 (t *Triangle) ToPlane() *Plane {
v1 := gnr.VectorDifference(t.Points[1], t.Points[0])
v2 := gnr.VectorDifference(t.Points[2], t.Points[0])
normal := gnr.VectorCross(v1, v2)
return &Plane{
Normal: normal,
Distance: -gnr.VectorProduct(normal, t.Points[0]),
}
}
func (t *Triangle) Contains(p *gnr.Vector3f) bool {
tp := t.ToPlane()
na := (&Triangle{
Points: [3]*gnr.Vector3f{t.Points[0], t.Points[1], p},
}).ToPlane().Normal
nb := (&Triangle{
Points: [3]*gnr.Vector3f{t.Points[1], t.Points[2], p},
}).ToPlane().Normal
nc := (&Triangle{
Points: [3]*gnr.Vector3f{t.Points[2], t.Points[0], p},
}).ToPlane().Normal
denom := math.Pow(tp.Normal.Magnitude(), 2)
ba := gnr.VectorProduct(tp.Normal, na) / denom
bb := gnr.VectorProduct(tp.Normal, nb) / denom
bc := gnr.VectorProduct(tp.Normal, nc) / denom
return ba >= 0 && ba <= 1 && bb >= 0 && bb <= 1 && bc >= 0 && bc <= 1
}
func (aab *AxisAlignedBox) RayInteraction(r *gnr.Ray) []*gnr.InteractionResult {
planes := []gnr.Object{
&Plane{
Normal: &gnr.Vector3f{-1, 0, 0},
Distance: -gnr.VectorProduct(&gnr.Vector3f{-1, 0, 0}, aab.Min),
},
&Plane{
Normal: &gnr.Vector3f{1, 0, 0},
Distance: -gnr.VectorProduct(&gnr.Vector3f{1, 0, 0}, aab.Max),
},
&Plane{
Normal: &gnr.Vector3f{0, -1, 0},
Distance: -gnr.VectorProduct(&gnr.Vector3f{0, -1, 0}, aab.Min),
},
&Plane{
Normal: &gnr.Vector3f{0, 1, 0},
Distance: -gnr.VectorProduct(&gnr.Vector3f{0, 1, 0}, aab.Max),
},
&Plane{
Normal: &gnr.Vector3f{0, 0, -1},
Distance: -gnr.VectorProduct(&gnr.Vector3f{0, 0, -1}, aab.Min),
},
&Plane{
Normal: &gnr.Vector3f{0, 0, 1},
Distance: -gnr.VectorProduct(&gnr.Vector3f{0, 0, 1}, aab.Max),
},
}
irs := gnr.ObjectSlice(planes).AggregateSliceInteractionResult(func(irs []*gnr.InteractionResult, o gnr.Object) []*gnr.InteractionResult {
newIrs := o.RayInteraction(r)
p := o.(*Plane)
newIrs = gnr.InteractionResultSlice(newIrs).SelectInteractionResult(func(ir *gnr.InteractionResult) *gnr.InteractionResult {
// Correct for IEEE754 errors by aligning PoIs with sides of box
if math.Abs(p.Normal.X) == 1 {
ir.PointOfImpact.X = -p.Distance * p.Normal.X
}
if math.Abs(p.Normal.Y) == 1 {
ir.PointOfImpact.Y = -p.Distance * p.Normal.Y
}
if math.Abs(p.Normal.Z) == 1 {
ir.PointOfImpact.Z = -p.Distance * p.Normal.Z
}
return ir
})
return append(irs, newIrs...)
})
irs = gnr.InteractionResultSlice(irs).Where(func(ir *gnr.InteractionResult) bool {
return aab.Contains(ir.PointOfImpact)
})
return irs
}
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)
}