class M3:
z = M(((0, 0, 0), (0, 0, 0), (0, 0, 0)))
z._det = 0
e = M(((1, 0, 0), (0, 1, 0), (0, 0, 1)))
e._det = 1
@staticmethod
def x_rot(a): # right hand rule rotation!
m = M((
(1, 0, 0),
(0, cos(a), -sin(a)),
(0, sin(a), cos(a)),
))
m._det = 1
return m
@staticmethod
def y_rot(a):
if a == 1:
return M3.e
m = M((
(cos(a), 0, -sin(a)),
(0, 1, 0),
(sin(a), 0, cos(a)),
))
m._det = 1
return m
@staticmethod
def z_rot(a):
if a == 1:
return M3.e
m = M((
(cos(a), -sin(a), 0),
(sin(a), cos(a), 0),
(0, 0, 1),
))
m._det = 1
return m
@staticmethod
def grow(s):
if s == 0:
return M3.z
if s == 1:
return M3.e
m = M((
(s, 0, 0),
(0, s, 0),
(0, 0, s),
))
m._det = s**3
return m
def x_rot(a): # right hand rule rotation!
m = M((
(1, 0, 0),
(0, cos(a), -sin(a)),
(0, sin(a), cos(a)),
))
m._det = 1
return m
def z_rot(a):
if a == 1:
return M3.e
m = M((
(cos(a), -sin(a), 0),
(sin(a), cos(a), 0),
(0, 0, 1),
))
m._det = 1
return m
def y_rot(a):
if a == 1:
return M3.e
m = M((
(cos(a), 0, -sin(a)),
(0, 1, 0),
(sin(a), 0, cos(a)),
))
m._det = 1
return m
class M2:
z = M(((0, 0), (0, 0)))
z._det = 0
e = M(((1, 0), (0, 1)))
e._det = 1
@staticmethod
def grower2(s):
if s == 0:
return M2.z
if s == 1:
return M2.e
m = M((
(s, 0),
(0, s),
))
m._det = s**2
return m
def grower2(s):
if s == 0:
return M2.z
if s == 1:
return M2.e
m = M((
(s, 0),
(0, s),
))
m._det = s**2
return m
def grow(s):
if s == 0:
return M3.z
if s == 1:
return M3.e
m = M((
(s, 0, 0),
(0, s, 0),
(0, 0, s),
))
m._det = s**3
return m
def projection(v, camera, centre):
"""
Project 3D vector onto 2D screen.
:param v: 3D Vector
:param camera: Camera object
:param centre: 2D Vector, centre of screen
:return: 2D Vector, position on screen
"""
v -= camera.pos # camera is basically the origin after this
v = M3.z_rot(-camera.z_angle) @ v # rotate points on z-axis around camera
v = M3.x_rot(-camera.x_angle) @ v # in the opposite direction
sx = 1 / v._value[1] # more distance => point closer to middle (?)
sy = 1 / v._value[1]
sx *= 800 # zoom way in (original pyramid is tiny)
sy *= -800 # tk has y pointing down
res = M(((sx, 0, 0), (0, 0, sy))) @ v # Apply transform from Q3 to Q2
res += centre # move to the middle
return res