def update(self):
"""
called on every frame
apply transformation matrix and project every polygon to 2d
for color avg_z function is used
polygons are sorted on avg_z value
finally painting on surface is called
"""
# Clock vector
vector = Matrix3D.get_rot_z_matrix(self.angle).v_dot(self.vector)
# projected = self.__project(self.vector, self.center)
projected = self.__projectm(vector, self.center)
pygame.draw.polygon(self.surface, pygame.Color(255,255,255,0), (self.center, projected), 1)
# Cube
mesh = self.model.transform(Matrix3D.get_rot_z_matrix(self.angle))
#mesh = mesh.transform(Matrix3D.get_rot_x_matrix(self.angle))
mesh = mesh.transform(Matrix3D.get_scale_matrix(SCALE, SCALE, SCALE))
mesh = mesh.transform(Matrix3D.get_shift_matrix(X_SHIFT, Y_SHIFT, Z_SHIFT))
for face in mesh:
vertices = [self.__projectm(vertice, self.center) for vertice in face]
pygame.draw.polygon(self.surface, pygame.Color(255,255,255,0), vertices, 1)
self.angle += self.angle_step
# axis vectors
pygame.draw.polygon(self.surface, pygame.Color(255,0,0,0), (self.center, self.__projectm(self.x_axis, self.center)), 1)
pygame.draw.polygon(self.surface, pygame.Color(0,255,0,0), (self.center, self.__projectm(self.y_axis, self.center)), 1)
pygame.draw.polygon(self.surface, pygame.Color(0,0,255,0), (self.center, self.__projectm(self.z_axis, self.center)), 1)
def __projectm(vector, center):
"""
apply
clipping matrix
camera transformation matrix
camera rotation matrix
TODO: finally sort out vertices out of clipping area
and return tuple on 2D Coordinates
taken from : http://stackoverflow.com/questions/724219/how-to-convert-a-3d-point-into-2d-perspective-projection
"""
clipping_m = Matrix3D([
[FOV * ASPECT_RATIO, 0.0, 0.0 , 0.0],
[0.0 , FOV, 0.0 , 0.0],
[0.0 , 0.0, (far + near) / (far-near) , (2.0 * near * far) / (near-far)],
[0.0 , 0.0, 1.0 , 0.0]
])
cam_translation_m = Matrix3D.get_shift_matrix(0, 0, -10)
cam_rot_m = Matrix3D.get_rot_y_matrix(Y_ANGLE).dot(Matrix3D.get_rot_x_matrix(X_ANGLE))
# mind the order !!
new_vector = clipping_m.dot(cam_translation_m.dot(cam_rot_m)).v_dot(vector)
new_x = center[0] + new_vector.x * 16.0 / ( 2.0 * new_vector.z) + 8.0
new_y = center[1] + new_vector.y * 9.0 / ( 2.0 * new_vector.z) + 4.5
return new_x, new_y
def __projectm(vector, center):
"""
apply
clipping matrix
camera transformation matrix
camera rotation matrix
TODO: finally sort out vertices out of clipping area
and return tuple on 2D Coordinates
taken from : http://stackoverflow.com/questions/724219/how-to-convert-a-3d-point-into-2d-perspective-projection
"""
clipping_m = Matrix3D([[FOV * ASPECT_RATIO, 0.0, 0.0, 0.0],
[0.0, FOV, 0.0, 0.0],
[
0.0, 0.0, (far + near) / (far - near),
(2.0 * near * far) / (near - far)
], [0.0, 0.0, 1.0, 0.0]])
cam_translation_m = Matrix3D.get_shift_matrix(0, 0, -10)
cam_rot_m = Matrix3D.get_rot_y_matrix(Y_ANGLE).dot(
Matrix3D.get_rot_x_matrix(X_ANGLE))
# mind the order !!
new_vector = clipping_m.dot(
cam_translation_m.dot(cam_rot_m)).v_dot(vector)
new_x = center[0] + new_vector.x * 16.0 / (2.0 * new_vector.z) + 8.0
new_y = center[1] + new_vector.y * 9.0 / (2.0 * new_vector.z) + 4.5
return new_x, new_y
def test_m_transforms(self):
v = Vector3D(1, 1, 0, 1)
m = Matrix3D.get_shift_matrix(5, 5, 0)
print "shift matrix:\n", m
print "shifted vector:", m.v_dot(v)
m = Matrix3D.get_scale_matrix(2, 2, 0)
print "scale matrix:\n", m
print "scaled vector:", m.v_dot(v)
def test_m_transforms(self):
v = Vector3D(1, 1, 0, 1)
m = Matrix3D.get_shift_matrix(5, 5, 0)
print "shift matrix:\n", m
print "shifted vector:", m.v_dot(v)
m = Matrix3D.get_scale_matrix(2, 2, 0)
print "scale matrix:\n", m
print "scaled vector:", m.v_dot(v)
def get_cube_mesh():
# a cube Mesh consist of six Faces
# left
faces = []
rec = Face3D(get_rectangle_points())
t = Matrix3D.get_shift_matrix(-1, 0, 0).dot(
Matrix3D.get_rot_y_matrix(math.pi / 2))
faces.append(rec.transform(t))
# right
t = Matrix3D.get_shift_matrix(1, 0, 0).dot(
Matrix3D.get_rot_y_matrix(math.pi / 2))
faces.append(rec.transform(t))
# bottom
t = Matrix3D.get_shift_matrix(0, -1, 0).dot(
Matrix3D.get_rot_x_matrix(math.pi / 2))
faces.append(rec.transform(t))
# top
t = Matrix3D.get_shift_matrix(0, 1, 0).dot(
Matrix3D.get_rot_x_matrix(math.pi / 2))
faces.append(rec.transform(t))
# front
t = Matrix3D.get_shift_matrix(0, 0, -1)
faces.append(rec.transform(t))
# back
t = Matrix3D.get_shift_matrix(0, 0, 1)
faces.append(rec.transform(t))
return Mesh3D(faces)
def get_pyramid_mesh():
faces = []
# front
tri = Face3D(get_triangle_points())
#t = Matrix3D.get_shift_matrix(0, 0, 1).dot(Matrix3D.get_rot_x_matrix(-math.pi/4))
face = tri.transform(Matrix3D.get_rot_x_matrix(-math.pi / 4))
face = face.transform(Matrix3D.get_shift_matrix(0, 0, 1))
faces.append(face)
# back
face = tri.transform(Matrix3D.get_rot_x_matrix(math.pi / 4))
face = face.transform(Matrix3D.get_shift_matrix(0, 0, -1))
faces.append(face)
# left
face = tri.transform(Matrix3D.get_rot_x_matrix(-math.pi / 4))
face = face.transform(Matrix3D.get_rot_y_matrix(-math.pi / 2))
face = face.transform(Matrix3D.get_shift_matrix(1, 0, 0))
faces.append(face)
# right
face = tri.transform(Matrix3D.get_rot_x_matrix(-math.pi / 4))
face = face.transform(Matrix3D.get_rot_y_matrix(math.pi / 2))
face = face.transform(Matrix3D.get_shift_matrix(-1, 0, 0))
faces.append(face)
return Mesh3D(faces)
def get_pyramid_mesh():
faces = []
# front
tri = Face3D(get_triangle_points())
#t = Matrix3D.get_shift_matrix(0, 0, 1).dot(Matrix3D.get_rot_x_matrix(-math.pi/4))
face = tri.transform(Matrix3D.get_rot_x_matrix(-math.pi/4))
face = face.transform(Matrix3D.get_shift_matrix(0, 0, 1))
faces.append(face)
# back
face = tri.transform(Matrix3D.get_rot_x_matrix(math.pi/4))
face = face.transform(Matrix3D.get_shift_matrix(0, 0, -1))
faces.append(face)
# left
face = tri.transform(Matrix3D.get_rot_x_matrix(-math.pi/4))
face = face.transform(Matrix3D.get_rot_y_matrix(-math.pi/2))
face = face.transform(Matrix3D.get_shift_matrix(1, 0, 0))
faces.append(face)
# right
face = tri.transform(Matrix3D.get_rot_x_matrix(-math.pi/4))
face = face.transform(Matrix3D.get_rot_y_matrix(math.pi/2))
face = face.transform(Matrix3D.get_shift_matrix(-1, 0, 0))
faces.append(face)
return Mesh3D(faces)
def update(self):
"""
called on every frame
apply transformation matrix and project every polygon to 2d
for color avg_z function is used
polygons are sorted on avg_z value
finally painting on surface is called
"""
# Clock vector
vector = Matrix3D.get_rot_z_matrix(self.angle).v_dot(self.vector)
# projected = self.__project(self.vector, self.center)
projected = self.__projectm(vector, self.center)
pygame.draw.polygon(self.surface, pygame.Color(255, 255, 255, 0),
(self.center, projected), 1)
# Cube
mesh = self.model.transform(Matrix3D.get_rot_z_matrix(self.angle))
#mesh = mesh.transform(Matrix3D.get_rot_x_matrix(self.angle))
mesh = mesh.transform(Matrix3D.get_scale_matrix(SCALE, SCALE, SCALE))
mesh = mesh.transform(
Matrix3D.get_shift_matrix(X_SHIFT, Y_SHIFT, Z_SHIFT))
for face in mesh:
vertices = [
self.__projectm(vertice, self.center) for vertice in face
]
pygame.draw.polygon(self.surface, pygame.Color(255, 255, 255, 0),
vertices, 1)
self.angle += self.angle_step
# axis vectors
pygame.draw.polygon(
self.surface, pygame.Color(255, 0, 0, 0),
(self.center, self.__projectm(self.x_axis, self.center)), 1)
pygame.draw.polygon(
self.surface, pygame.Color(0, 255, 0, 0),
(self.center, self.__projectm(self.y_axis, self.center)), 1)
pygame.draw.polygon(
self.surface, pygame.Color(0, 0, 255, 0),
(self.center, self.__projectm(self.z_axis, self.center)), 1)
def get_cube_mesh():
# a cube Mesh consist of six Faces
# left
faces = []
rec = Face3D(get_rectangle_points())
t = Matrix3D.get_shift_matrix(-1, 0, 0).dot(Matrix3D.get_rot_y_matrix(math.pi/2))
faces.append(rec.transform(t))
# right
t = Matrix3D.get_shift_matrix(1, 0, 0).dot(Matrix3D.get_rot_y_matrix(math.pi/2))
faces.append(rec.transform(t))
# bottom
t = Matrix3D.get_shift_matrix(0, -1, 0).dot(Matrix3D.get_rot_x_matrix(math.pi/2))
faces.append(rec.transform(t))
# top
t = Matrix3D.get_shift_matrix(0, 1, 0).dot(Matrix3D.get_rot_x_matrix(math.pi/2))
faces.append(rec.transform(t))
# front
t = Matrix3D.get_shift_matrix(0, 0, -1)
faces.append(rec.transform(t))
# back
t = Matrix3D.get_shift_matrix(0, 0, 1)
faces.append(rec.transform(t))
return Mesh3D(faces)
