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 test_matrix_dot(self):
"""test dot product identity matrix and transpose"""
mi = Matrix3D.identity()
# I dot transposed(I) = I
assert mi == mi.dot(mi.transpose())
mr = Matrix3D([
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
])
assert mr.dot(mi) == mr
test_transposed = Matrix3D([[1, 5, 9, 13], [2, 6, 10, 14],
[3, 7, 11, 15], [4, 8, 12, 16]])
assert mr.transpose() == test_transposed
test_m = Matrix3D([
[30, 70, 110, 150],
[70, 174, 278, 382],
[110, 278, 446, 614],
[150, 382, 614, 846],
])
assert mr.dot(mr.transpose()) == test_m
A = Matrix3D([[3, 0, 0, 0], [0, -1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 1]])
B = Matrix3D([[math.sqrt(3) / 2, 0, -1 / 2, 0], [0, 1, 0, 0],
[1 / 2, 0, math.sqrt(3) / 2, 0], [0, 0, 0, 1]])
C = Matrix3D([[1, 0, 0, 3], [0, 1, 0, -1], [0, 0, 1, 2], [0, 0, 0, 1]])
# testing assosiativeness (A*B)*C == A*(B*C)
assert A.dot(B).dot(C) == A.dot(B.dot(C))
def test_scale(self):
m = Matrix3D.identity()
m2 = m.scale(2.0)
print "2 * I:\n", m2
m3 = m2.scale(1.0 / 2.0)
print "1/2 * ( 2 * I):\n", m3
assert m3 == m
def test_scale(self):
m = Matrix3D.identity()
m2 = m.scale(2.0)
print "2 * I:\n", m2
m3 = m2.scale(1.0/2.0)
print "1/2 * ( 2 * I):\n", m3
assert m3 == m
def test_transformations(self):
# test zeros
m = Matrix3D.zeros()
assert isinstance(m, Matrix3D)
# test if __repr__ is able to convert to object
m1 = eval(m.__repr__())
assert m == m1
# test identity
m = Matrix3D.identity()
assert isinstance(m, Matrix3D)
# test __getitem__ interface
assert m[0, 0] == 1
assert m[1, 1] == 1
assert m[2, 2] == 1
assert m[3, 3] == 1
# get column vector
assert m.col(0) == [1, 0, 0, 0]
m1 = Matrix3D.identity()
assert m1.dot(Matrix3D.identity()) == Matrix3D.identity()
assert m1.dot(Matrix3D.zeros()) == Matrix3D.zeros()
def test_transformations(self):
# test zeros
m = Matrix3D.zeros()
assert isinstance(m, Matrix3D)
# test if __repr__ is able to convert to object
m1 = eval(m.__repr__())
assert m == m1
# test identity
m = Matrix3D.identity()
assert isinstance(m, Matrix3D)
# test __getitem__ interface
assert m[0, 0] == 1
assert m[1, 1] == 1
assert m[2, 2] == 1
assert m[3, 3] == 1
# get column vector
assert m.col(0) == [1, 0, 0, 0]
m1 = Matrix3D.identity()
assert m1.dot(Matrix3D.identity()) == Matrix3D.identity()
assert m1.dot(Matrix3D.zeros()) == Matrix3D.zeros()
def test_det(self):
m = Matrix3D.identity()
print "det(I)=", m.det()
# for next example look at
# http://matheguru.com/lineare-algebra/207-determinante.html
mr = Matrix3D([
[5, 0, 3, -1],
[3, 0, 0, 4],
[-1, 2, 4, -2],
[1, 0, 0, 5],
])
print "T(mr)=\n", mr.transpose()
print "det(mr)=", mr.det()
assert mr.det() == 66
print "det(T(mr))=", mr.transpose().det()
assert mr.det() == mr.transpose().det()
def test_det(self):
m = Matrix3D.identity()
print "det(I)=", m.det()
# for next example look at
# http://matheguru.com/lineare-algebra/207-determinante.html
mr = Matrix3D([
[ 5, 0, 3, -1 ],
[ 3, 0, 0, 4 ],
[ -1, 2, 4, -2 ],
[ 1, 0, 0, 5 ],
])
print "T(mr)=\n", mr.transpose()
print "det(mr)=", mr.det()
assert mr.det() == 66
print "det(T(mr))=", mr.transpose().det()
assert mr.det() == mr.transpose().det()
def test_matrix_dot(self):
"""test dot product identity matrix and transpose"""
mi = Matrix3D.identity()
# I dot transposed(I) = I
assert mi == mi.dot(mi.transpose())
mr = Matrix3D([
[ 1, 2, 3, 4 ],
[ 5, 6, 7, 8 ],
[ 9, 10, 11, 12 ],
[ 13, 14, 15, 16 ],
])
assert mr.dot(mi) == mr
test_transposed = Matrix3D([
[1, 5, 9, 13],
[2, 6, 10, 14],
[3, 7, 11, 15],
[4, 8, 12, 16]
])
assert mr.transpose() == test_transposed
test_m = Matrix3D([
[30, 70, 110, 150],
[70, 174, 278, 382],
[110, 278, 446, 614],
[150, 382, 614, 846],
])
assert mr.dot(mr.transpose()) == test_m
A = Matrix3D([
[ 3, 0, 0, 0 ],
[ 0, -1, 0, 0 ],
[ 0, 0, 2, 0 ],
[ 0, 0, 0, 1 ]
])
B = Matrix3D([
[ math.sqrt(3)/2, 0, -1/2, 0 ],
[ 0, 1, 0, 0 ],
[ 1/2, 0, math.sqrt(3)/2, 0 ],
[ 0, 0, 0, 1]
])
C = Matrix3D([
[1, 0, 0, 3],
[0, 1, 0, -1],
[0, 0, 1, 2],
[0, 0, 0, 1]
])
# testing assosiativeness (A*B)*C == A*(B*C)
assert A.dot(B).dot(C) == A.dot(B.dot(C))
