Matrix Class

Matrix Class features breakdown:

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Operators:

• multiplication (vector or matrix)
• division (scalar)

Special cases:

These functions are not members of the Matrix class, they return Matrix and Vector type.

• orthographic(left, right, bottom, top, zNear, zFar) (Orthographic Projection 4x4 matrix)
• perspective(fov, aspect, znear, zfar) (Perspective projection matrix 4x4. FOVY)
• perspectiveX(fov, aspect, znear, zfar) (Perspective projection matrix 4x4. FOVX)
• lookAt(eye, center, up) (returns a view matrix 4x4)
• project(obj, model, proj, viewport) (returns a 3D vector, projects to viewport)
• unproject(winx, winy, winz, modelview, projection, viewport) (Unproject a point from the screen and return the object coordinates.)

Functions:

• scale(value) (scale matrix by a vector)
• det() (returns the determinant of the matrix)
• inverse() (returns the inverse of the matrix)
• rotate(axis, theta) (rotate the matrix by axis and angle)
• translate(vecA) (translate the matrix using a vector)
• transpose() (Transpose the matrix)
• shearXY(x, y) (shear the matrix along the x, y)
• shearYZ(y, z) (shear the matrix along the z, y)
• shearXZ(x, z) (shear the matrix aling the x, z)

Identities:

These are not part of the Matrix class, so their output needs to be passed as input to the Matrix constructor.

• identity(size) (returns a matrix identity)
• zero_matrix(size) (returns a matrix filled with zeros)

Examples:

It is a NxN Matrix class. However, some functions only apply for certain dimensions only so for example a 8x8 matrix will be limited in functionality.

Declaration of a matrix:

from gem import matrix

matrixA = matrix.Matrix(4)

mdata = [[1.0, 0.0, 0.0, 0.0],
        [0.0, 1.0, 0.0, 0.0],
        [0.0, 0.0, 1.0, 0.0],
        [0.0, 0.0, 0.0, 1.0]]

matrixB = matrix.Matrix(4, data=mdata)

matrixC = matrix.Matrix(4, data=matrix.identity(4))


# Output:
# MatrixA:  0.0, 0.0, 0.0, 0.0
#           0.0, 0.0, 0.0, 0.0
#           0.0, 0.0, 0.0, 0.0
#           0.0, 0.0, 0.0, 0.0

# MatrixB:  1.0, 0.0, 0.0, 0.0
#           0.0, 1.0, 0.0, 0.0
#           0.0, 0.0, 1.0, 0.0
#           0.0, 0.0, 0.0, 1.0

# MatrixC:  1.0, 0.0, 0.0, 0.0
#           0.0, 1.0, 0.0, 0.0
#           0.0, 0.0, 1.0, 0.0
#           0.0, 0.0, 0.0, 1.0

Operators usage: They have to be the same size matrices in order for the operators to work. The vector size needs to match that of the matrix, for example a 3D vector can only be multiplied by a 3x3 matrix, a 4D vector by a 4x4 matrix and so on.

from gem import matrix
from gem import vector

# Initialize some matrices and vectors
matrixA = matrix.Matrix(4, data=matrix.indetity(4))
matrixB = matrix.Matrix(4, data=matrix.indetity(4))
vectorA = vector.Vector(4, data=[2.0, 1.0, 3.0, 5.0])

# Matrix Multiplication (NxN * NxN)
matrixC = matrixA * matrixB

# Vector Multiplication (NxN * ND)
matrixD = matrixA * vectorA

# Matrix Division (NxN / scalar)
matrixE = matrixB / 2.0

Function usage: Inside the matrix class most functions have two declartion, regular function name and with a "i_" in front of it. For example, the scale function is declared as "scale" and "i_scale", the former will return a new scaled matrix, the latter will scale the matrix in its place. So any function with "i_" in front of the function name will do the changes in place without returning a new matrix.

Example:

from gem import matrix
from gem import vector

matrixA = matrix.Matrix(3, data=matrix.indetity(4))
vectorS = vector.Vector(3, data=[2.0, 3.0, 4.0])

# This will scale the matrix by creating a new one
matrixS = matrixA.scale(vectorS)

# This will scale the matrix in-place
matrixA.i_scale(vectorS)

# Return the determinant of the matrix
matrixADet = matrixA.det()

#Output:
# matrixA:  1.0, 0.0, 0.0, 0.0
#           0.0, 1.0, 0.0, 0.0
#           0.0, 0.0, 1.0, 0.0
#           0.0, 0.0, 0.0, 1.0

# vectorS:  2.0, 3.0, 4.0

# matrixS:  2.0, 0.0, 0.0, 0.0
#           0.0, 3.0, 0.0, 0.0
#           0.0, 0.0, 4.0, 0.0
#           0.0, 0.0, 0.0, 1.0

# marixADet: 24