EliasFarhan
commented
3 years ago Thanks for the features list. Here are some little details:
- rotation matrix should requires an angle from maths/angle.h (https://github.com/SAE-Institute-Geneva/GPR5204_919/blob/main/include/maths/angle.h)
- how are you going to store the matrix? std::array of maths vectors?
- don't forget to implement the operator[] to be able to access a particular element of the matrix
- please define static identity matrices
- what is going to happen with non-inversable matrices (det(A) = 0)?
- why is the translation and scale matrix taking three floats instead of a vector3?
- don't forget the transpose method
- it would be great to add a method checking if the matrix is orthogonal to simplify the inversion using tranposition
Introduction
We have been asked to work on 2x2, 3x3 and 4x4 matrices for the GPR5204 class. For this task, we will use column-based matrices.
2x2 Matrix
Addition
This method adds 2 matrices and returns the resulting matrix: [(a11 + b11), (a21 + b21), (a12 + b12), (a22 + b22)].
Substraction
This method substract 2 matrices and returns the resulting matrix: [(a11 - b11), (a21 - b21), (a12 - b12), (a22 - b22)].
Multiplication (Mat2f * Mat2f)
This method multiplies 2 matrices and returns the resulting matrix (will use loops to calculate the matrix): [(a11 b11) + (a12 b21) , (a21 b11) + (a22 b21), (a11 b12) + (a12 b22), (a21 b12) + (a22 b22)]
Multiplication (Mat2f * Vec2f)
This method multiplies a matrix and a vector [x, y] and returns the resulting vector: [(a11 x) + (a12 y) , (a21 x) + (a22 y)]
Multiplication (Mat2f * float)
This method multiplies a matrix and a scalar (s) and returns the resulting matrix: [(a11 s) , (a21 s), (a12 s), (a22 s)]
Determinant
This method calculates the determinant of a matrix and returns its value (float): (a11 a22) - (a12 a21)
Inverse
This method calculates the inverse of a matrix and returns the inverted matrix: *(1 / det(A)) [a22, -a12, -a21, a11]**
3x3 Matrix
Addition
This method adds 2 matrices and returns the resulting matrix: [(a11 + b11), (a21 + b21), (a31 + b31), (a12 + b12), (a22 + b22), (a32 + b32), (a13 + b13), (a23 + b23), (a33 + b33)].
Substraction
This method substract 2 matrices and returns the resulting matrix: [(a11 - b11), (a21 - b21), (a31 - b31), (a12 - b12), (a22 - b22), (a32 - b32), (a13 - b13), (a23 - b23), (a33 - b33)].
Multiplication (Mat3f * Mat3f)
This method multiplies 2 matrices and returns the resulting matrix(will use loops to calculate the matrix): *[(a11 b11) + (a12 b21) + (a13 b31) , (a21 b11) + (a22 b21) + (a23 b31), (a31 b11) + (a32 b21) + (a33 b31), (a11 b12) + (a12 b22) + (a13 b32), (a21 b12) + (a22 b22) + (a23 b32), (a31 b12) + (a32 b22) + (a33 b32), (a11 b13) + (a12 b23) + (a13 b33), (a21 b13) + (a22 b23) + (a23 b33), (a31 b13) + (a32 b23) + (a33 b33)]**
Multiplication (Mat3f * Vec3f)
This method multiplies a matrix and a vector [x, y, z] and returns the resulting vector: *[(a11 x) + (a12 y) + (a13 z), (a21 x) + (a22 y) + (a23 z), (a31 x) + (a32 y) + (a33 z)]**
Multiplication (Mat3f * float)
This method multiplies a matrix and a scalar (s) and returns the resulting matrix: *[(a11 s) , (a21 s), (a31 s), (a12 s), (a22 s), (a32 s), (a13 s), (a23 s), (a33 s)]**
Determinant
This method calculates the determinant of a matrix and returns its value (float): *(a11 det(A11)) - (a21 det(A21)) + (a31 det(A31))** [det(Aij) is the 2x2 matrix determinant of matrix A minus the ith row and jth column]
Adjoint
This method will return the adjoint matrix: [det(A11), -det(A12), det(A13), -det(A21), det(A22), -det(A23), det(A31), -det(A32), det(A33)]
Inverse
This method calculates the inverse of a matrix and returns the inverted matrix: *(1 / det(A)) adj(A)**
Translation Matrix
This method returns the translation matrix for 2 given values (tx, ty): [1, 0, tx, 0, 1, ty, 0, 0, 1]
Rotation Matrix
This method returns the rotation matrix for a given angle(θ): [cos(θ), -sin(θ), 0, sin(θ), cos(θ), 0, 0, 0, 1]
Scale Matrix
This method returns the scale matrix for 2 given scaling values (float sx, sy): [sx, 0, 0, 0, sy, 0, 0, 0, 1]
4x4 Matrix
Addition
This method adds 2 matrices and returns the resulting matrix: [(a11 + b11), (a21 + b21), (a31 + b31), (a41 + b41), (a12 + b12), (a22 + b22), (a32 + b32), (a42 + b42), (a13 + b13), (a23 + b23), (a33 + b33), (a43+ b43), (a14 + b14), (a24 + b24), (a34 + b34), (a44 + b44)].
Substraction
This method substract 2 matrices and returns the resulting matrix: [(a11 - b11), (a21 - b21), (a31 - b31), (a41 - b41), (a12 - b12), (a22 - b22), (a32 - b32), (a42 - b42), (a13 - b13), (a23 - b23), (a33 - b33), (a43- b43), (a14 - b14), (a24 - b24), (a34 - b34), (a44 - b44)].
Multiplication (Mat4f * Mat4f)
This method multiplies 2 matrices and returns the resulting matrix (will use loops to calculate the matrix): [(a11 b11) + (a12 b21) + (a13 b31) + (a14 b41), (a21 b11) + (a22 b21) + (a23 b31) + (a24 b41), (a31 b11) + (a32 b21) + (a33 b31) + (a34 b41), (a41 b11) + (a42 b21) + (a43 b31) + (a44 b41), (a11 b12) + (a12 b22) + (a13 b32) + (a14 b42), (a21 b12) + (a22 b22) + (a23 b32) + (a24 b42), (a31 b12) + (a32 b22) + (a33 b32) + (a34 b42), (a41 b12) + (a42 b22) + (a43 b32) + (a44 b42), (a11 b13) + (a12 b23) + (a13 b33) + (a14 b43), (a21 b13) + (a22 b23) + (a23 b33) + (a24 b43), (a31 b13) + (a32 b23) + (a33 b33) + (a34 b43), (a41 b13) + (a42 b23) + (a43 b33) + (a44 b43), (a11 b14) + (a12 b24) + (a13 b34) + (a14 b44), (a21 b14) + (a22 b24) + (a23 b34) + (a24 b44), (a31 b14) + (a32 b24) + (a33 b34) + (a34 b44), (a41 b14) + (a42 b24) + (a43 b34) + (a44 b44)]
Multiplication (Mat4f * Vec4f)
This method multiplies a matrix and a vector [x, y, z, w] and returns the resulting vector: [(a11 x) + (a12 y) + (a13 z) + (a14 w), (a21 x) + (a22 y) + (a23 z) + (a24 w), (a31 x) + (a32 y) + (a33 z) + (a34 w), (a41 x) + (a42 y) + (a43 z) + (a44 w)]
Multiplication (Mat4f * float)
This method multiplies a matrix and a scalar (s) and returns the resulting matrix: [(a11 s) , (a21 s), (a31 s), (a41 s), (a12 s), (a22 s), (a32 s), (a42 s), (a13 s), (a23 s), (a33 s), (a43 s), (a14 s), (a24 s), (a34 s), (a44 s)]
Determinant
This method calculates the determinant of a matrix and returns its value (float): (a11 det(A11)) - (a21 det(A21)) + (a31 det(A31) - (a41 det(A41)) [det(Aij) is the 3x3 matrix determinant of matrix A minus the ith row and jth column]
Adjoint
This method will return the adjoint matrix: [det(A11), -det(A12), det(A13), -det(A14), -det(A21), det(A22), -det(A23), det(A24), det(A31), -det(A32), det(A33), -det(A34), -det(A41), det(A42), -det(A43), det(A44)]
Inverse
This method calculates the inverse of a matrix and returns the inverted matrix: *(1 / det(A)) adj(A)**
Translation Matrix
This method returns the translation matrix for 2 given values (float tx, ty, tz): [1, 0, 0, tx, 0, 1, 0, ty, 0, 0, 1, tz, 0, 0, 0, 1]
Rotation Matrix
This method returns the rotation matrix for a given angle (θ) and axis (x, y or z): Rx = [0, cos(θ),-sin(θ), 0, 0,sin(θ), cos(θ), 0, 1, 0, 0, 0, 0, 0, 0, 1] Ry = [-sin(θ), 0, cos(θ), 0, cos(θ), 0, sin(θ), 0, 0, 1, 0, 0, 0, 0, 0, 1] Rz = [cos(θ), -sin(θ), 0, 0, sin(θ), cos(θ), 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]
Scale Matrix
This method returns the scale matrix for 2 given scaling values (float sx, sy, sz): [sx, 0, 0, 0, 0, sy, 0, 0, 0, 0, sz, 0, 0, 0, 0, 1]