def v_dot(self, vector):
"""
calculate dot product of Matrix3D with inverted(Vector3D)
| a1 | b1 | c1 | d1 | | x | | a1*x + b1*y + c1*z + d1*h |
| a2 | b2 | c2 | d2 | . | y | = | a2*x + b2*y + c2*z + d2*h |
| a3 | b3 | c3 | d3 | | z | | a3*x + b3*y + c3*z + d3*h |
| a4 | b4 | c4 | d4 | | h | | a4*x + b4*y + c4*z + d4*h |
"""
assert isinstance(vector, Vector3D)
ret_data = [0, 0, 0, 0]
for index in range(4):
row_vec = Vector3D.from_list(self.__data[index])
ret_data[index] = row_vec.dot(vector)
return Vector3D.from_list(ret_data)
def v_dot(self, vector):
"""
calculate dot product of Matrix3D with inverted(Vector3D)
| a1 | b1 | c1 | d1 | | x | | a1*x + b1*y + c1*z + d1*h |
| a2 | b2 | c2 | d2 | . | y | = | a2*x + b2*y + c2*z + d2*h |
| a3 | b3 | c3 | d3 | | z | | a3*x + b3*y + c3*z + d3*h |
| a4 | b4 | c4 | d4 | | h | | a4*x + b4*y + c4*z + d4*h |
"""
assert isinstance(vector, Vector3D)
ret_data = [0, 0, 0, 0]
for index in range(4):
row_vec = Vector3D.from_list(self.__data[index])
ret_data[index] = row_vec.dot(vector)
return Vector3D.from_list(ret_data)
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 dot(self, other):
"""
return dot product of these to 4x4 matrices
Matrix A : self
Matrix B : other
TODO: find a way to describe this in short terms
| a11 | a12 | a13 | a14 | | b11 | b12 | b13 | b14 | | row[1].col[1] row[1].col[2] ... ... |
| a21 | a22 | a23 | a24 | . | b21 | b22 | b23 | b24 | = | row[2].col[1] row[2].col[2] ... ... |
| a31 | a32 | a33 | a34 | | b31 | b32 | b33 | b34 | | ... ... |
| a41 | a42 | a43 | a44 | | b41 | b42 | b43 | b44 | | |
"""
assert isinstance(other, Matrix3D)
ret_matrix = self.zeros()
for rownum in range(4):
row_vec = Vector3D.from_list(self.row(rownum))
for colnum in range(4):
col_vec = Vector3D.from_list(other.col(colnum))
ret_matrix[rownum][colnum] = row_vec.dot(col_vec)
return ret_matrix
def dot(self, other):
"""
return dot product of these to 4x4 matrices
Matrix A : self
Matrix B : other
TODO: find a way to describe this in short terms
| a11 | a12 | a13 | a14 | | b11 | b12 | b13 | b14 | | row[1].col[1] row[1].col[2] ... ... |
| a21 | a22 | a23 | a24 | . | b21 | b22 | b23 | b24 | = | row[2].col[1] row[2].col[2] ... ... |
| a31 | a32 | a33 | a34 | | b31 | b32 | b33 | b34 | | ... ... |
| a41 | a42 | a43 | a44 | | b41 | b42 | b43 | b44 | | |
"""
assert isinstance(other, Matrix3D)
ret_matrix = self.zeros()
for rownum in range(4):
row_vec = Vector3D.from_list(self.row(rownum))
for colnum in range(4):
col_vec = Vector3D.from_list(other.col(colnum))
ret_matrix[rownum][colnum] = row_vec.dot(col_vec)
return ret_matrix
