def test_transform1(self):
pfrom = Point(0, 0, 0)
pto = Point(0, 0, -1)
vup = Vector(0, 1, 0)
t = view_transform(pfrom, pto, vup)
I = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
self.assertTrue(matrix.equals(I, t))
def test_transform2(self):
pfrom = Point(0, 0, 0)
pto = Point(0, 0, 1)
vup = Vector(0, 1, 0)
t = view_transform(pfrom, pto, vup)
s = scale(-1, 1, -1)
self.assertTrue(matrix.equals(s, t))
def test_camera7(self):
w = World()
c = Camera(11, 11, pi / 2)
pfrom = Point(0, 0, -5)
pto = Point(0, 0, 0)
vup = Vector(0, 1, 0)
c.transform = view_transform(pfrom, pto, vup)
image = c.render(w)
self.assertTrue(
Color(0.38066, 0.47583, 0.2855).equals(image.pixel_at(5, 5)))
def update(self):
self.frame_origin = get_cam_frame(self.position, self.look_at, self.up)
self.view_transform = view_transform(self.position, self.look_at,
self.up)
if hasattr(self, 'world_view'):
del self.world_view
if hasattr(self, 'eye_view'):
del self.eye_view
if hasattr(self, 'clip_view'):
del self.clip_view
def test_transform4(self):
pfrom = Point(1, 3, 2)
pto = Point(4, -2, 8)
vup = Vector(1, 1, 0)
t = view_transform(pfrom, pto, vup)
m = Matrix([[-0.50709, 0.50709, 0.67612, -2.36643],
[0.76772, 0.60609, 0.12122, -2.82843],
[-0.35857, 0.59761, -0.71714, 0.00000],
[0.00000, 0.00000, 0.00000, 1.00000]])
self.assertTrue(matrix.equals(m, t))
def world_to_device(point, forward=True, **kwargs):
# target to look at
t = kwargs.get('look_at')
# camera position
p = kwargs.get('eye_pos')
# up pointing vector
u = kwargs.get('up')
# vertical field of view
fov_y = kwargs.get('fov_y')
# aspect ratio widht/height
a = kwargs.get('aspect')
# near clipping plane
n = kwargs.get('near')
# far clipping plane
f = kwargs.get('far')
# device pixel width
w = kwargs.get('width')
# device pixel height
h = kwargs.get('height')
# Model-View-Transform-Matrix
M = transform.view_transform(p, t, u)
# Projection Matrix
P = transform.pers_projection_transform(fov_y, a, n, f)
# Viewport/Device Transform
V = transform.viewport_transform((w, h))
if forward:
# world coordinate
w_point = point
if len(w_point) == 3:
w_point = np.append(w_point, [1])
# eye coordinate from world coordinate
e = M @ w_point
# un-normalized clip coordinate
cn = P @ e
# normalized clip coordinate (divide-by-w)
c = cn / cn[-1]
# device coordinates
d = V @ c
return d
else:
# if not forward, it becomes device_to_world func. (backward)
d = point
# clip coordinate
c = np.linalg.inv(V) @ d
# un-normalized eye coordinate
en = np.linalg.inv(P) @ c
# eye coordinate
e = en / en[-1]
# world coordinate
w_point = np.linalg.inv(M) @ e
return w_point
def test_transform3(self):
pfrom = Point(0, 0, 8)
pto = Point(0, 0, 0)
vup = Vector(0, 1, 0)
t = view_transform(pfrom, pto, vup)
self.assertTrue(matrix.equals(translate(0, 0, -8), t))
floor,
left_wall,
right_wall,
# middle,
# right,
# left
]
for i in range(10):
ball = Sphere()
ball.transform = translate(0, 1, 1.) * rotate_z(
pi * 2 / 10 * i) * translate(1, 0, 0) * scale(0.2, 0.2, 0.2)
ball.material.color = Color(i * 0.1, 1 - i * 0.1, 1 - i * 0.1)
objs.append(ball)
world = World()
world.light = Light(Point(-10, 10, -10), Color(1, 1, 1))
world.objs = objs
camera = Camera(100, 50, pi / 3)
camera.transform = view_transform(Point(0, 1.5, -5), Point(0, 1, 0),
Vector(0, 1, 0))
canvas = camera.render(world)
with open('test_034.ppm', 'w') as fout:
canvas.to_ppm(fout)
t2 = time()
print("Time spent: {:.2f}s".format(t2 - t1))