QuaternionRotatePoint.scala

// quick and dirty from
// https://math.stackexchange.com/questions/40164/how-do-you-rotate-a-vector-by-a-unit-quaternion

def quaternion_mult(q: Vector[Double],r: Vector[Double]) =
  Vector(r(0)*q(0)-r(1)*q(1)-r(2)*q(2)-r(3)*q(3),
         r(0)*q(1)+r(1)*q(0)-r(2)*q(3)+r(3)*q(2),
         r(0)*q(2)+r(1)*q(3)+r(2)*q(0)-r(3)*q(1),
         r(0)*q(3)-r(1)*q(2)+r(2)*q(1)+r(3)*q(0))
          
def point_rotation_by_quaternion(point: Vector[Double],q: Vector[Double]) = {
  val r = 0.0 +: point
  val q_conj = Vector(q(0),-q(1),-q(2),-q(3))
  quaternion_mult(quaternion_mult(q,r),q_conj).tail
}

println(point_rotation_by_quaternion(Vector(1, 0, 0),Vector(0.5.sqrt, 0.0, 0.5.sqrt, 0.0)))