def add_vector(matrix, vector):
if isinstance(matrix, list):
matrix = structures.Matrix([matrix])
result = structures.Matrix(matrix.no_rows(), matrix.no_cols())
for y in range(matrix.no_rows()):
for x in range(matrix.no_cols()):
result.set_index(y, x, matrix.access_index(y, x) + vector[x])
return result
def scale_matrix(kx, ky, kz):
''' Returns a matrix for scaling by (kx, ky, kz) '''
return structures.Matrix([
[kx, 0, 0, 0],
[0, ky, 0, 0],
[0, 0, kz, 0],
[0, 0, 0, 1],
])
def translation_matrix(dx = 0, dy = 0, dz = 0):
''' Returns a matrix for a translation of (dx, dy, dz) '''
return structures.Matrix([
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[dx, dy, dz, 1],
])
def orthographic_projection_matrix():
''' Returns a matrix used in projection to provide depth '''
return structures.Matrix([
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
])
def rotate_y_matrix(ry):
''' Returns a matrix for rotation about the x=y-axis by ry radians '''
cos = math.cos(ry)
sin = math.sin(ry)
return structures.Matrix([
[cos, 0, sin, 0],
[0, 1, 0, 0],
[-sin, 0, cos, 0],
[0, 0, 0, 1],
])
def rotate_x_matrix(rx):
''' Returns a matrix for rotation about the x-axis by rx radians '''
cos = math.cos(rx)
sin = math.sin(rx)
return structures.Matrix([
[1, 0, 0, 0],
[0, cos, -sin, 0],
[0, sin, cos, 0],
[0, 0, 0, 1],
])
def rotate_z_matrix(rz):
''' Returns a matrix for rotation about the z-axis by rz radians '''
cos = math.cos(rz)
sin = math.sin(rz)
return structures.Matrix([
[cos, -sin, 0, 0],
[sin, cos, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
])
def perspective_projection_matrix(dz):
''' Returns a matrix used in projection to provide depth '''
if (10 - dz) == 0:
z = 0
else:
z = 1 / (10 - dz)
return structures.Matrix([
[z, 0, 0, 0],
[0, z, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
])
def multiply(matrix_1, matrix_2):
if matrix_1.no_cols() != matrix_2.no_rows():
print("ERROR: Matrix 1's {} columns do not match Matrix 2's {} rows".format(matrix_1.no_cols(), matrix_2.no_rows()))
return None
result = structures.Matrix(matrix_1.no_rows(), matrix_2.no_cols())
# Finding the dot product of the row of matrix 1 and the column of matrix 2 for each element in the new matrix
for y in range(matrix_1.no_rows()):
for x in range(matrix_2.no_cols()):
sum = 0
for i in range(matrix_1.no_cols()):
sum += matrix_1.access_index(y, i) * matrix_2.access_index(i, x)
result.set_index(y, x, sum)
return result
def h_stack(matrix_1, matrix_2):
''' Adds matrix_2 to the right columns of matrix_1 '''
result = structures.Matrix(matrix_1.no_rows(), matrix_1.no_cols() + matrix_2.no_cols())
for y in range(matrix_1.no_rows()):
result.set_row(y, matrix_1.access_row(y) + matrix_2.access_row(y))
return result
def convert_to_int_matrix(matrix):
result = structures.Matrix(matrix.no_rows(), matrix.no_cols())
for y in range(matrix.no_rows()):
for x in range(matrix.no_cols()):
result.set_index(y, x, int(matrix.access_index(y, x)))
return result