def _icosahedron_mapping( ):
def _make_rot_matrix( pole_angle, long_angle ):
ret_matrix = rot_x( -axis_skew )
ret_matrix = ret_matrix.multiply( rot_y( pole_angle ) ).multiply( rot_x( axis_skew ) )
ret_matrix = ret_matrix.multiply( rot_x( long_angle ) )
return ret_matrix.evalf()
# some magic constants
axis_skew = (s.pi/2 - s.atan2( s.GoldenRatio-1, s.GoldenRatio ) - s.atan2( 1, s.GoldenRatio )).evalf()
th = (s.sqrt(3)/2).evalf()
face_angle = s.atan( s.sqrt( 5 )/2 ).evalf()
ret_dict = dict()
ret_dict['a'] = ( _make_rot_matrix( 0, -s.pi/2 ), 0.5, (th*7)/3 )
ret_dict['e'] = ( _make_rot_matrix( 0, -face_angle ), 0.5, (th*5)/3 )
ret_dict['f'] = ( _make_rot_matrix( 2*s.pi/5, -s.pi/2 ), 1.5, (th*7)/3 )
ret_dict['o'] = ( _make_rot_matrix( 2*s.pi/5, -face_angle ), 1.5, (th*5)/3 )
ret_dict['k'] = ( _make_rot_matrix( 4*s.pi/5, -s.pi/2 ), 2.5, (th*7)/3 )
ret_dict['p'] = ( _make_rot_matrix( 4*s.pi/5, -face_angle ), 2.5, (th*5)/3 )
ret_dict['g'] = ( _make_rot_matrix( 6*s.pi/5, -s.pi/2 ), 3.5, (th*7)/3 )
ret_dict['l'] = ( _make_rot_matrix( 6*s.pi/5, -face_angle ), 3.5, (th*5)/3 )
ret_dict['b'] = ( _make_rot_matrix( 8*s.pi/5, -s.pi/2 ), 4.5, (th*7)/3 )
ret_dict['c'] = ( _make_rot_matrix( 8*s.pi/5, -face_angle ), 4.5, (th*5)/3 )
flip_y = rot_y( s.pi )
ret_dict['j'] = ( ret_dict['l'][0].multiply( flip_y ), 1, (th*4)/3 )
ret_dict['n'] = ( ret_dict['g'][0].multiply( flip_y ), 1, (th*2)/3 )
ret_dict['t'] = ( ret_dict['c'][0].multiply( flip_y ), 2, (th*4)/3 )
ret_dict['s'] = ( ret_dict['b'][0].multiply( flip_y ), 2, (th*2)/3 )
ret_dict['q'] = ( ret_dict['e'][0].multiply( flip_y ), 3, (th*4)/3 )
ret_dict['r'] = ( ret_dict['a'][0].multiply( flip_y ), 3, (th*2)/3 )
ret_dict['h'] = ( ret_dict['o'][0].multiply( flip_y ), 4, (th*4)/3 )
ret_dict['m'] = ( ret_dict['f'][0].multiply( flip_y ), 4, (th*2)/3 )
ret_dict['d'] = ( ret_dict['p'][0].multiply( flip_y ), 5, (th*4)/3 )
ret_dict['i'] = ( ret_dict['k'][0].multiply( flip_y ), 5, (th*2)/3 )
return ret_dict
def _make_rot_matrix( pole_angle, long_angle ):
ret_matrix = rot_x( -axis_skew )
ret_matrix = ret_matrix.multiply( rot_y( pole_angle ) ).multiply( rot_x( axis_skew ) )
ret_matrix = ret_matrix.multiply( rot_x( long_angle ) )
return ret_matrix.evalf()
