#!/usr/bin/env python3
"""Checks the relative frame used by Sable's OBB collision.

Sable gives a ship block OBB the SubLevel pose q_ship and gives the custom player
OBB q_entity. For an upright player relative to the logical deck, q_entity must be
q_ship, so inverse(q_ship) * q_entity is identity.
"""
import math


def qx(deg):
    a = math.radians(deg) / 2.0
    return (math.cos(a), math.sin(a), 0.0, 0.0)  # w,x,y,z


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


def close(a,b,eps=1e-9):
    return all(abs(x-y)<eps for x,y in zip(a,b))

for deg in (0,20,90,180):
    ship=qx(deg)
    entity=ship
    relative=mul(conj(ship),entity)
    world_up=rotate(entity,(0.0,1.0,0.0))
    world_gravity=rotate(ship,(0.0,-1.0,0.0))
    assert close(relative,(1.0,0.0,0.0,0.0)) or close(relative,(-1.0,0.0,0.0,0.0))
    assert abs(sum(a*b for a,b in zip(world_up,world_gravity))+1.0)<1e-9
    print(f"X {deg:3d}: relative={relative}, up={world_up}, gravity={world_gravity}")

print("OK: player OBB stays upright relative to the logical deck at 0/20/90/180 degrees")