// face returns face ID from 0 to 5 containing the r. For points on the
// boundary between faces, the result is arbitrary but deterministic.
func face(r r3.Vector) int {
abs := r.Abs()
id := 0
value := r.X
if abs.Y > abs.X {
id = 1
value = r.Y
}
if abs.Z > math.Abs(value) {
id = 2
value = r.Z
}
if value < 0 {
id += 3
}
return id
}
func TrueCentroid(a, b, c Point) interface{} {
angleA := b.Angle(c.Vector).Radians()
angleB := c.Angle(a.Vector).Radians()
angleC := a.Angle(b.Vector).Radians()
ra, rb, rc := 1., 1., 1.
if angleA != 0 {
ra = angleA / math.Sin(angleA)
}
if angleB != 0 {
rb = angleB / math.Sin(angleB)
}
if angleC != 0 {
rc = angleC / math.Sin(angleC)
}
x := r3.Vector{a.X, b.X - a.X, c.X - a.X}
y := r3.Vector{a.Y, b.Y - a.Y, c.Y - a.Y}
z := r3.Vector{a.Z, b.Z - a.Z, c.Z - a.Z}
r := r3.Vector{ra, rb - ra, rc - ra}
v := r3.Vector{
y.Cross(z).Dot(r),
z.Cross(x).Dot(r),
x.Cross(y).Dot(r),
}
return Point{v.Mul(0.5)}
}