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 test_rot_matrices(self):
m = Matrix3D.get_rot_x_matrix(100)
assert m.dot(Matrix3D.identity()) == m
m = Matrix3D.get_rot_y_matrix(100)
assert m.dot(Matrix3D.identity()) == m
m = Matrix3D.get_rot_z_matrix(100)
assert m.dot(Matrix3D.identity()) == m
# rotate vector only in x-axis around x - nothing should happen
v1 = Vector3D(1, 0, 0, 1)
assert Matrix3D.get_rot_x_matrix(100).v_dot(v1) == v1
v1 = Vector3D(0, 1, 0, 1)
assert Matrix3D.get_rot_y_matrix(100).v_dot(v1) == v1
v1 = Vector3D(0, 0, 1, 1)
assert Matrix3D.get_rot_z_matrix(100).v_dot(v1) == v1
# rotate vectors really
v1 = Vector3D(1.0, 0.0, 0.0, 1.0)
# 90 degrees or pi/2
real_v = Matrix3D.get_rot_z_matrix(math.pi / 2).v_dot(v1)
test_v = Vector3D.from_list([0.000000, 1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# 180 degrees
real_v = Matrix3D.get_rot_z_matrix(math.pi).v_dot(v1)
test_v = Vector3D.from_list([-1.000000, 0.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# 270 degrees
real_v = Matrix3D.get_rot_z_matrix(math.pi + math.pi / 2).v_dot(v1)
test_v = Vector3D.from_list([0.000000, -1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# 360 degrees
real_v = Matrix3D.get_rot_z_matrix(2 * math.pi).v_dot(v1)
test_v = Vector3D.from_list([1.000000, 0.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# rotate around Y-Axis about 180 degrees
real_v = Matrix3D.get_rot_y_matrix(math.pi).v_dot(v1)
test_v = Vector3D.from_list([-1.000000, 0.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# rotate y:90 and x:90 -> (0, 1, 0, 1)
real_v = Matrix3D.get_rot_y_matrix(math.pi / 2).v_dot(v1)
test_v = Vector3D.from_list([0.000000, 0.000000, -1.000000, 1.000000])
assert real_v.nearly_equal(test_v)
real_v = Matrix3D.get_rot_x_matrix(math.pi / 2).v_dot(real_v)
test_v = Vector3D.from_list([0.000000, 1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# and this is the combined version
rot_y = Matrix3D.get_rot_y_matrix(math.pi / 2)
print "rotation around y:\n", rot_y
rot_x = Matrix3D.get_rot_x_matrix(math.pi / 2)
print "rotation around x:\n", rot_x
rot_z = Matrix3D.get_rot_z_matrix(math.pi / 2)
print "rotation around z:\n", rot_z
rot_m = rot_x.dot(rot_y.dot(rot_z))
print "combined rotation matrix:\n", rot_m
real_v = rot_m.v_dot(v1)
print "resulting vector:", real_v
test_v = Vector3D.from_list([0.000000, 1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
def test_rot_matrices(self):
m = Matrix3D.get_rot_x_matrix(100)
assert m.dot(Matrix3D.identity()) == m
m = Matrix3D.get_rot_y_matrix(100)
assert m.dot(Matrix3D.identity()) == m
m = Matrix3D.get_rot_z_matrix(100)
assert m.dot(Matrix3D.identity()) == m
# rotate vector only in x-axis around x - nothing should happen
v1 = Vector3D(1, 0, 0, 1)
assert Matrix3D.get_rot_x_matrix(100).v_dot(v1) == v1
v1 = Vector3D(0, 1, 0, 1)
assert Matrix3D.get_rot_y_matrix(100).v_dot(v1) == v1
v1 = Vector3D(0, 0, 1, 1)
assert Matrix3D.get_rot_z_matrix(100).v_dot(v1) == v1
# rotate vectors really
v1 = Vector3D(1.0, 0.0, 0.0, 1.0)
# 90 degrees or pi/2
real_v = Matrix3D.get_rot_z_matrix(math.pi/2).v_dot(v1)
test_v = Vector3D.from_list([0.000000, 1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# 180 degrees
real_v = Matrix3D.get_rot_z_matrix(math.pi).v_dot(v1)
test_v = Vector3D.from_list([-1.000000, 0.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# 270 degrees
real_v = Matrix3D.get_rot_z_matrix(math.pi + math.pi/2).v_dot(v1)
test_v = Vector3D.from_list([0.000000, -1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# 360 degrees
real_v = Matrix3D.get_rot_z_matrix(2 * math.pi).v_dot(v1)
test_v = Vector3D.from_list([1.000000, 0.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# rotate around Y-Axis about 180 degrees
real_v = Matrix3D.get_rot_y_matrix(math.pi).v_dot(v1)
test_v = Vector3D.from_list([-1.000000, 0.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# rotate y:90 and x:90 -> (0, 1, 0, 1)
real_v = Matrix3D.get_rot_y_matrix(math.pi/2).v_dot(v1)
test_v = Vector3D.from_list([0.000000, 0.000000, -1.000000, 1.000000])
assert real_v.nearly_equal(test_v)
real_v = Matrix3D.get_rot_x_matrix(math.pi/2).v_dot(real_v)
test_v = Vector3D.from_list([0.000000, 1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
# and this is the combined version
rot_y = Matrix3D.get_rot_y_matrix(math.pi/2)
print "rotation around y:\n", rot_y
rot_x = Matrix3D.get_rot_x_matrix(math.pi/2)
print "rotation around x:\n", rot_x
rot_z = Matrix3D.get_rot_z_matrix(math.pi/2)
print "rotation around z:\n", rot_z
rot_m = rot_x.dot(rot_y.dot(rot_z))
print "combined rotation matrix:\n", rot_m
real_v = rot_m.v_dot(v1)
print "resulting vector:", real_v
test_v = Vector3D.from_list([0.000000, 1.000000, 0.000000, 1.000000])
assert real_v.nearly_equal(test_v)
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)
