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 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 __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 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_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)
