from __future__ import print_function, division

from pyglet.gl import *
from math import sqrt as _sqrt, acos as _acos


def cross(a, b):
    return (a[1] * b[2] - a[2] * b[1],
            a[2] * b[0] - a[0] * b[2],
            a[0] * b[1] - a[1] * b[0])


def dot(a, b):
    return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]


def mag(a):
    return _sqrt(a[0]**2 + a[1]**2 + a[2]**2)


def norm(a):
    m = mag(a)
    return (a[0] / m, a[1] / m, a[2] / m)


def get_sphere_mapping(x, y, width, height):
    x = min([max([x, 0]), width])
    y = min([max([y, 0]), height])

    sr = _sqrt((width/2)**2 + (height/2)**2)
    #sr *= 1.5
    sx = ((x - width / 2) / sr)
    sy = ((y - height / 2) / sr)

    sz = 1.0 - sx**2 - sy**2

    if sz > 0.0:
        sz = _sqrt(sz)
        return (sx, sy, sz)
    else:
        sz = 0
        return norm((sx, sy, sz))

rad2deg = 180.0 / 3.141592


def get_spherical_rotatation(p1, p2, width, height, theta_multiplier):
    v1 = get_sphere_mapping(p1[0], p1[1], width, height)
    v2 = get_sphere_mapping(p2[0], p2[1], width, height)

    d = min(max([dot(v1, v2), -1]), 1)

    if abs(d - 1.0) < 0.000001:
        return None

    raxis = norm( cross(v1, v2) )
    rtheta = theta_multiplier * rad2deg * _acos(d)
    #rtheta = 2.0 * rad2deg * _acos(d)

    glPushMatrix()
    glLoadIdentity()
    glRotatef(rtheta, *raxis)
    mat = (c_float*16)()
    glGetFloatv(GL_MODELVIEW_MATRIX, mat)
    glPopMatrix()

    return mat
