Module Matrix
Expand source code
# Copyright (C) 2024
# Wassim Jabi <wassim.jabi@gmail.com>
#
# This program is free software: you can redistribute it and/or modify it under
# the terms of the GNU Affero General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
#
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more
# details.
#
# You should have received a copy of the GNU Affero General Public License along with
# this program. If not, see <https://www.gnu.org/licenses/>.
import math
class Matrix:
@staticmethod
def Add(matA, matB):
"""
Description
----------
Adds the two input matrices.
Parameters
----------
matA : list
The first input matrix.
matB : list
The second input matrix.
Returns
-------
list
The matrix resulting from the addition of the two input matrices.
"""
matC = []
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
for i in range(len(matA)):
tempRow = []
for j in range(len(matB)):
tempRow.append(matA[i][j] + matB[i][j])
matC.append(tempRow)
return matC
@staticmethod
def ByRotation(angleX=0, angleY=0, angleZ=0, order="xyz"):
"""
Description
----------
Creates a 4x4 rotation matrix.
Parameters
----------
angleX : float , optional
The desired rotation angle in degrees around the X axis. The default is 0.
angleY : float , optional
The desired rotation angle in degrees around the Y axis. The default is 0.
angleZ : float , optional
The desired rotation angle in degrees around the Z axis. The default is 0.
order : string , optional
The order by which the roatations will be applied. The possible values are any permutation of "xyz". This input is case insensitive. The default is "xyz".
Returns
-------
list
The created 4X4 rotation matrix.
"""
def rotateXMatrix(radians):
""" Return matrix for rotating about the x-axis by 'radians' radians """
c = math.cos(radians)
s = math.sin(radians)
return [[1, 0, 0, 0],
[0, c,-s, 0],
[0, s, c, 0],
[0, 0, 0, 1]]
def rotateYMatrix(radians):
""" Return matrix for rotating about the y-axis by 'radians' radians """
c = math.cos(radians)
s = math.sin(radians)
return [[ c, 0, s, 0],
[ 0, 1, 0, 0],
[-s, 0, c, 0],
[ 0, 0, 0, 1]]
def rotateZMatrix(radians):
""" Return matrix for rotating about the z-axis by 'radians' radians """
c = math.cos(radians)
s = math.sin(radians)
return [[c,-s, 0, 0],
[s, c, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]
xMat = rotateXMatrix(math.radians(angleX))
yMat = rotateYMatrix(math.radians(angleY))
zMat = rotateZMatrix(math.radians(angleZ))
if order.lower() == "xyz":
return Matrix.Multiply(Matrix.Multiply(zMat,yMat),xMat)
if order.lower() == "xzy":
return Matrix.Multiply(Matrix.Multiply(yMat,zMat),xMat)
if order.lower() == "yxz":
return Matrix.Multiply(Matrix.Multiply(zMat,xMat),yMat)
if order.lower == "yzx":
return Matrix.Multiply(Matrix.Multiply(xMat,zMat),yMat)
if order.lower() == "zxy":
return Matrix.Multiply(Matrix.Multiply(yMat,xMat),zMat)
if order.lower() == "zyx":
return Matrix.Multiply(Matrix.Multiply(xMat,yMat),zMat)
@staticmethod
def ByScaling(scaleX=1.0, scaleY=1.0, scaleZ=1.0):
"""
Description
----------
Creates a 4x4 scaling matrix.
Parameters
----------
scaleX : float , optional
The desired scaling factor along the X axis. The default is 1.
scaleY : float , optional
The desired scaling factor along the X axis. The default is 1.
scaleZ : float , optional
The desired scaling factor along the X axis. The default is 1.
Returns
-------
list
The created 4X4 scaling matrix.
"""
return [[scaleX,0,0,0],
[0,scaleY,0,0],
[0,0,scaleZ,0],
[0,0,0,1]]
@staticmethod
def ByTranslation(translateX=0, translateY=0, translateZ=0):
"""
Description
----------
Creates a 4x4 translation matrix.
Parameters
----------
translateX : float , optional
The desired translation distance along the X axis. The default is 0.
translateY : float , optional
The desired translation distance along the X axis. The default is 0.
translateZ : float , optional
The desired translation distance along the X axis. The default is 0.
Returns
-------
list
The created 4X4 translation matrix.
"""
return [[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[translateX,translateY,translateZ,1]]
@staticmethod
def Multiply(matA, matB):
"""
Description
----------
Multiplies the two input matrices. When transforming an object, the first input matrix is applied first
then the second input matrix.
Parameters
----------
matA : list
The first input matrix.
matB : list
The second input matrix.
Returns
-------
list
The matrix resulting from the multiplication of the two input matrices.
"""
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
nr = len(matA)
nc = len(matA[0])
matC = []
for i in range(nr):
tempRow = []
for j in range(nc):
tempRow.append(0)
matC.append(tempRow)
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
# iterate through rows of X
for i in range(len(matA)):
# iterate through columns of Y
tempRow = []
for j in range(len(matB[0])):
# iterate through rows of Y
for k in range(len(matB)):
matC[i][j] += matA[i][k] * matB[k][j]
return matC
@staticmethod
def Subtract(matA, matB):
"""
Description
----------
Subtracts the two input matrices.
Parameters
----------
matA : list
The first input matrix.
matB : list
The second input matrix.
Returns
-------
list
The matrix resulting from the subtraction of the second input matrix from the first input matrix.
"""
if not isinstance(matA, list):
return None
if not isinstance(matB, list):
return None
matC = []
for i in range(len(matA)):
tempRow = []
for j in range(len(matB)):
tempRow.append(matA[i][j] - matB[i][j])
matC.append(tempRow)
return matC
@staticmethod
def Transpose(matrix):
"""
Description
----------
Transposes the input matrix.
Parameters
----------
matrix : list
The input matrix.
Returns
-------
list
The transposed matrix.
"""
return [list(x) for x in zip(*matrix)]Classes
class Matrix-
Expand source code
class Matrix: @staticmethod def Add(matA, matB): """ Description ---------- Adds the two input matrices. Parameters ---------- matA : list The first input matrix. matB : list The second input matrix. Returns ------- list The matrix resulting from the addition of the two input matrices. """ matC = [] if not isinstance(matA, list): return None if not isinstance(matB, list): return None for i in range(len(matA)): tempRow = [] for j in range(len(matB)): tempRow.append(matA[i][j] + matB[i][j]) matC.append(tempRow) return matC @staticmethod def ByRotation(angleX=0, angleY=0, angleZ=0, order="xyz"): """ Description ---------- Creates a 4x4 rotation matrix. Parameters ---------- angleX : float , optional The desired rotation angle in degrees around the X axis. The default is 0. angleY : float , optional The desired rotation angle in degrees around the Y axis. The default is 0. angleZ : float , optional The desired rotation angle in degrees around the Z axis. The default is 0. order : string , optional The order by which the roatations will be applied. The possible values are any permutation of "xyz". This input is case insensitive. The default is "xyz". Returns ------- list The created 4X4 rotation matrix. """ def rotateXMatrix(radians): """ Return matrix for rotating about the x-axis by 'radians' radians """ c = math.cos(radians) s = math.sin(radians) return [[1, 0, 0, 0], [0, c,-s, 0], [0, s, c, 0], [0, 0, 0, 1]] def rotateYMatrix(radians): """ Return matrix for rotating about the y-axis by 'radians' radians """ c = math.cos(radians) s = math.sin(radians) return [[ c, 0, s, 0], [ 0, 1, 0, 0], [-s, 0, c, 0], [ 0, 0, 0, 1]] def rotateZMatrix(radians): """ Return matrix for rotating about the z-axis by 'radians' radians """ c = math.cos(radians) s = math.sin(radians) return [[c,-s, 0, 0], [s, c, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]] xMat = rotateXMatrix(math.radians(angleX)) yMat = rotateYMatrix(math.radians(angleY)) zMat = rotateZMatrix(math.radians(angleZ)) if order.lower() == "xyz": return Matrix.Multiply(Matrix.Multiply(zMat,yMat),xMat) if order.lower() == "xzy": return Matrix.Multiply(Matrix.Multiply(yMat,zMat),xMat) if order.lower() == "yxz": return Matrix.Multiply(Matrix.Multiply(zMat,xMat),yMat) if order.lower == "yzx": return Matrix.Multiply(Matrix.Multiply(xMat,zMat),yMat) if order.lower() == "zxy": return Matrix.Multiply(Matrix.Multiply(yMat,xMat),zMat) if order.lower() == "zyx": return Matrix.Multiply(Matrix.Multiply(xMat,yMat),zMat) @staticmethod def ByScaling(scaleX=1.0, scaleY=1.0, scaleZ=1.0): """ Description ---------- Creates a 4x4 scaling matrix. Parameters ---------- scaleX : float , optional The desired scaling factor along the X axis. The default is 1. scaleY : float , optional The desired scaling factor along the X axis. The default is 1. scaleZ : float , optional The desired scaling factor along the X axis. The default is 1. Returns ------- list The created 4X4 scaling matrix. """ return [[scaleX,0,0,0], [0,scaleY,0,0], [0,0,scaleZ,0], [0,0,0,1]] @staticmethod def ByTranslation(translateX=0, translateY=0, translateZ=0): """ Description ---------- Creates a 4x4 translation matrix. Parameters ---------- translateX : float , optional The desired translation distance along the X axis. The default is 0. translateY : float , optional The desired translation distance along the X axis. The default is 0. translateZ : float , optional The desired translation distance along the X axis. The default is 0. Returns ------- list The created 4X4 translation matrix. """ return [[1,0,0,0], [0,1,0,0], [0,0,1,0], [translateX,translateY,translateZ,1]] @staticmethod def Multiply(matA, matB): """ Description ---------- Multiplies the two input matrices. When transforming an object, the first input matrix is applied first then the second input matrix. Parameters ---------- matA : list The first input matrix. matB : list The second input matrix. Returns ------- list The matrix resulting from the multiplication of the two input matrices. """ if not isinstance(matA, list): return None if not isinstance(matB, list): return None nr = len(matA) nc = len(matA[0]) matC = [] for i in range(nr): tempRow = [] for j in range(nc): tempRow.append(0) matC.append(tempRow) if not isinstance(matA, list): return None if not isinstance(matB, list): return None # iterate through rows of X for i in range(len(matA)): # iterate through columns of Y tempRow = [] for j in range(len(matB[0])): # iterate through rows of Y for k in range(len(matB)): matC[i][j] += matA[i][k] * matB[k][j] return matC @staticmethod def Subtract(matA, matB): """ Description ---------- Subtracts the two input matrices. Parameters ---------- matA : list The first input matrix. matB : list The second input matrix. Returns ------- list The matrix resulting from the subtraction of the second input matrix from the first input matrix. """ if not isinstance(matA, list): return None if not isinstance(matB, list): return None matC = [] for i in range(len(matA)): tempRow = [] for j in range(len(matB)): tempRow.append(matA[i][j] - matB[i][j]) matC.append(tempRow) return matC @staticmethod def Transpose(matrix): """ Description ---------- Transposes the input matrix. Parameters ---------- matrix : list The input matrix. Returns ------- list The transposed matrix. """ return [list(x) for x in zip(*matrix)]Static methods
def Add(matA, matB)-
Description
Adds the two input matrices.
Parameters
matA:list- The first input matrix.
matB:list- The second input matrix.
Returns
list- The matrix resulting from the addition of the two input matrices.
Expand source code
@staticmethod def Add(matA, matB): """ Description ---------- Adds the two input matrices. Parameters ---------- matA : list The first input matrix. matB : list The second input matrix. Returns ------- list The matrix resulting from the addition of the two input matrices. """ matC = [] if not isinstance(matA, list): return None if not isinstance(matB, list): return None for i in range(len(matA)): tempRow = [] for j in range(len(matB)): tempRow.append(matA[i][j] + matB[i][j]) matC.append(tempRow) return matC def ByRotation(angleX=0, angleY=0, angleZ=0, order='xyz')-
Description
Creates a 4x4 rotation matrix.
Parameters
angleX:float, optional- The desired rotation angle in degrees around the X axis. The default is 0.
angleY:float, optional- The desired rotation angle in degrees around the Y axis. The default is 0.
angleZ:float, optional- The desired rotation angle in degrees around the Z axis. The default is 0.
order:string, optional- The order by which the roatations will be applied. The possible values are any permutation of "xyz". This input is case insensitive. The default is "xyz".
Returns
list- The created 4X4 rotation matrix.
Expand source code
@staticmethod def ByRotation(angleX=0, angleY=0, angleZ=0, order="xyz"): """ Description ---------- Creates a 4x4 rotation matrix. Parameters ---------- angleX : float , optional The desired rotation angle in degrees around the X axis. The default is 0. angleY : float , optional The desired rotation angle in degrees around the Y axis. The default is 0. angleZ : float , optional The desired rotation angle in degrees around the Z axis. The default is 0. order : string , optional The order by which the roatations will be applied. The possible values are any permutation of "xyz". This input is case insensitive. The default is "xyz". Returns ------- list The created 4X4 rotation matrix. """ def rotateXMatrix(radians): """ Return matrix for rotating about the x-axis by 'radians' radians """ c = math.cos(radians) s = math.sin(radians) return [[1, 0, 0, 0], [0, c,-s, 0], [0, s, c, 0], [0, 0, 0, 1]] def rotateYMatrix(radians): """ Return matrix for rotating about the y-axis by 'radians' radians """ c = math.cos(radians) s = math.sin(radians) return [[ c, 0, s, 0], [ 0, 1, 0, 0], [-s, 0, c, 0], [ 0, 0, 0, 1]] def rotateZMatrix(radians): """ Return matrix for rotating about the z-axis by 'radians' radians """ c = math.cos(radians) s = math.sin(radians) return [[c,-s, 0, 0], [s, c, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]] xMat = rotateXMatrix(math.radians(angleX)) yMat = rotateYMatrix(math.radians(angleY)) zMat = rotateZMatrix(math.radians(angleZ)) if order.lower() == "xyz": return Matrix.Multiply(Matrix.Multiply(zMat,yMat),xMat) if order.lower() == "xzy": return Matrix.Multiply(Matrix.Multiply(yMat,zMat),xMat) if order.lower() == "yxz": return Matrix.Multiply(Matrix.Multiply(zMat,xMat),yMat) if order.lower == "yzx": return Matrix.Multiply(Matrix.Multiply(xMat,zMat),yMat) if order.lower() == "zxy": return Matrix.Multiply(Matrix.Multiply(yMat,xMat),zMat) if order.lower() == "zyx": return Matrix.Multiply(Matrix.Multiply(xMat,yMat),zMat) def ByScaling(scaleX=1.0, scaleY=1.0, scaleZ=1.0)-
Description
Creates a 4x4 scaling matrix.
Parameters
scaleX:float, optional- The desired scaling factor along the X axis. The default is 1.
scaleY:float, optional- The desired scaling factor along the X axis. The default is 1.
scaleZ:float, optional- The desired scaling factor along the X axis. The default is 1.
Returns
list- The created 4X4 scaling matrix.
Expand source code
@staticmethod def ByScaling(scaleX=1.0, scaleY=1.0, scaleZ=1.0): """ Description ---------- Creates a 4x4 scaling matrix. Parameters ---------- scaleX : float , optional The desired scaling factor along the X axis. The default is 1. scaleY : float , optional The desired scaling factor along the X axis. The default is 1. scaleZ : float , optional The desired scaling factor along the X axis. The default is 1. Returns ------- list The created 4X4 scaling matrix. """ return [[scaleX,0,0,0], [0,scaleY,0,0], [0,0,scaleZ,0], [0,0,0,1]] def ByTranslation(translateX=0, translateY=0, translateZ=0)-
Description
Creates a 4x4 translation matrix.
Parameters
translateX:float, optional- The desired translation distance along the X axis. The default is 0.
translateY:float, optional- The desired translation distance along the X axis. The default is 0.
translateZ:float, optional- The desired translation distance along the X axis. The default is 0.
Returns
list- The created 4X4 translation matrix.
Expand source code
@staticmethod def ByTranslation(translateX=0, translateY=0, translateZ=0): """ Description ---------- Creates a 4x4 translation matrix. Parameters ---------- translateX : float , optional The desired translation distance along the X axis. The default is 0. translateY : float , optional The desired translation distance along the X axis. The default is 0. translateZ : float , optional The desired translation distance along the X axis. The default is 0. Returns ------- list The created 4X4 translation matrix. """ return [[1,0,0,0], [0,1,0,0], [0,0,1,0], [translateX,translateY,translateZ,1]] def Multiply(matA, matB)-
Description
Multiplies the two input matrices. When transforming an object, the first input matrix is applied first then the second input matrix.
Parameters
matA:list- The first input matrix.
matB:list- The second input matrix.
Returns
list- The matrix resulting from the multiplication of the two input matrices.
Expand source code
@staticmethod def Multiply(matA, matB): """ Description ---------- Multiplies the two input matrices. When transforming an object, the first input matrix is applied first then the second input matrix. Parameters ---------- matA : list The first input matrix. matB : list The second input matrix. Returns ------- list The matrix resulting from the multiplication of the two input matrices. """ if not isinstance(matA, list): return None if not isinstance(matB, list): return None nr = len(matA) nc = len(matA[0]) matC = [] for i in range(nr): tempRow = [] for j in range(nc): tempRow.append(0) matC.append(tempRow) if not isinstance(matA, list): return None if not isinstance(matB, list): return None # iterate through rows of X for i in range(len(matA)): # iterate through columns of Y tempRow = [] for j in range(len(matB[0])): # iterate through rows of Y for k in range(len(matB)): matC[i][j] += matA[i][k] * matB[k][j] return matC def Subtract(matA, matB)-
Description
Subtracts the two input matrices.
Parameters
matA:list- The first input matrix.
matB:list- The second input matrix.
Returns
list- The matrix resulting from the subtraction of the second input matrix from the first input matrix.
Expand source code
@staticmethod def Subtract(matA, matB): """ Description ---------- Subtracts the two input matrices. Parameters ---------- matA : list The first input matrix. matB : list The second input matrix. Returns ------- list The matrix resulting from the subtraction of the second input matrix from the first input matrix. """ if not isinstance(matA, list): return None if not isinstance(matB, list): return None matC = [] for i in range(len(matA)): tempRow = [] for j in range(len(matB)): tempRow.append(matA[i][j] - matB[i][j]) matC.append(tempRow) return matC def Transpose(matrix)-
Description
Transposes the input matrix.
Parameters
matrix:list- The input matrix.
Returns
list- The transposed matrix.
Expand source code
@staticmethod def Transpose(matrix): """ Description ---------- Transposes the input matrix. Parameters ---------- matrix : list The input matrix. Returns ------- list The transposed matrix. """ return [list(x) for x in zip(*matrix)]