#!/usr/bin/env python3
"""Regression check for the test9/test10 fake-impulse bug."""
import math


def qx(deg):
    a=math.radians(deg)/2
    return (math.cos(a),math.sin(a),0.0,0.0)

def conj(q):
    w,x,y,z=q; return (w,-x,-y,-z)

def mul(a,b):
    aw,ax,ay,az=a; bw,bx,by,bz=b
    return (aw*bw-ax*bx-ay*by-az*bz,
            aw*bx+ax*bw+ay*bz-az*by,
            aw*by-ax*bz+ay*bw+az*bx,
            aw*bz+ax*by-ay*bx+az*bw)

def rotate(q,v):
    r=mul(mul(q,(0.0,*v)),conj(q)); return r[1:]

def invrotate(q,v): return rotate(conj(q),v)
def close(a,b,e=1e-9): return all(abs(x-y)<e for x,y in zip(a,b))

local=(0.17,0.42,-0.08)
for deg in (0,20,45,90,180):
    world=rotate(qx(deg),local)
    recovered=invrotate(qx(deg),world)
    assert close(recovered,local)
    print(f"X {deg:3d}: local={local} -> world={world} -> local={recovered}")
print('OK: changing ship orientation changes world representation without changing local velocity')