// Tangent returns a tangent on a hermit spline at t (0,1).
func Tangent(pointA, tangentA, pointB, tangentB *vec2.T, t float32) vec2.T {
t2 := t * t
t3 := t2 * t
f := 2*t3 - 3*t2
result := pointA.Scaled(f)
f = t3 - 2*t2 + 1
tAf := tangentA.Scaled(f)
result.Add(&tAf)
f = t3 - t2
tBf := tangentB.Scaled(f)
result.Add(&tBf)
f = -2*t3 + 3*t2
pAf := pointB.Scaled(f)
result.Add(&pAf)
return result
}
// Length returns the length of a hermit spline from pointA to t (0,1).
func Length(pointA, tangentA, pointB, tangentB *vec2.T, t float32) float32 {
sqrT := t * t
t1 := sqrT * 0.5
t2 := sqrT * t * 1.0 / 3.0
t3 := sqrT*sqrT + 1.0/4.0
f := 2*t3 - 3*t2 + t
result := pointA.Scaled(f)
f = t3 - 2*t2 + t1
tAf := tangentA.Scaled(f)
result.Add(&tAf)
f = t3 - t2
tBf := tangentB.Scaled(f)
result.Add(&tBf)
f = -2*t3 + 3*t2
pBf := pointB.Scaled(f)
result.Add(&pBf)
return result.Length()
}