Matrices for Tech Artists, a Cheat Sheet

Think of Matrices as Spaces

Figure -1- Basic Matrix
Figure -2- Columns of a matrix

Identity Matrix

Figure -3- Identity Matrix
Figure -4- Identity Matrix

Uniform Scaled Matrix

Figure -5- Uniform Scale
Figure -6- Mesh at half scale

Axis Scaled Matrix

Figure -7- Axis scaled
Figure -8- Mesh scaled 3 times along an axis

Mirror Matrix

Figure -9- axis mirror matrix
Figure -10- flip in x
Figure -11- mesh flipped in x

Matrix with Normalized Basis

Figure -12- normal basis Vector
Figure -13- Example of normal basis
Figure -14- mesh transforemed with normalized basis

Matrix with Orthogonal Basis

Figure -15- matrix with orthogonal basis
Figure -16- matrix with orthogonal basis example
Figure -17- mesh transformed with matrix with orthogonal basis

Orthogonal Matrices

Figure -18- Orthogonal matrix example
Figure -19- mesh transformed by an orthogonal matrix

Rotation Matrices

Figure -20- rotation matrices
Figure -21- rotation around x 45 degrees

What about Translation

Figure -22- Affine transformation
Figure -23- MVP matrix

Homogeneous Coordinates

Figure -24- Homogeneous matrix coordinate
Figure -25- Translation along x axis
Figure -26- Translation in X axis with 6 units

Projection Matrices

Figure -27- Projection Matrix. n=near, f=far, t=top, r=right, l=left, b=bottom

Some Extra Details

Further Reading

  1. Link to my favourit Linear Algebera book; http://math.mit.edu/~gs/linearalgebra/
  2. A fantastic series on YouTube which explains the matrix transformations: https://youtu.be/XkY2DOUCWMU
  3. Affine Transformations: https://en.wikipedia.org/wiki/Affine_transformation
  4. An amazing article on projection matrices from Scratch Pixel: https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix

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Technical Artist

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Shahriar Shahrabi

Shahriar Shahrabi

Technical Artist

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