// Angle returns the angle between two vectors.
func Angle(a, b *T) float32 {
v := Dot(a, b) / (a.Length() * b.Length())
// prevent NaN
if v > 1. {
v = v - 2
} else if v < -1. {
v = v + 2
}
return math.Acos(v)
}
// Slerp returns the spherical linear interpolation quaternion between a and b at t (0,1).
// See http://en.wikipedia.org/wiki/Slerp
func Slerp(a, b *T, t float32) T {
d := math.Acos(a[0]*b[0] + a[1]*b[1] + a[2]*b[2] + a[3]*b[3])
ooSinD := 1 / math.Sin(d)
t1 := math.Sin(d*(1-t)) * ooSinD
t2 := math.Sin(d*t) * ooSinD
q := T{
a[0]*t1 + b[0]*t2,
a[1]*t1 + b[1]*t2,
a[2]*t1 + b[2]*t2,
a[3]*t1 + b[3]*t2,
}
return q.Normalized()
}
// AxisAngle extracts the rotation in form of an axis and a rotation angle.
func (quat *T) AxisAngle() (axis vec3.T, angle float32) {
cos := quat[3]
sin := math.Sqrt(1 - cos*cos)
angle = math.Acos(cos)
var ooSin float32
if math.Abs(sin) < 0.0005 {
ooSin = 1
} else {
ooSin = 1 / sin
}
axis[0] = quat[0] * ooSin
axis[1] = quat[1] * ooSin
axis[2] = quat[2] * ooSin
return axis, angle
}