basic matrix math:

ken-perlin asked me to get familiar with 4x4 matrix math, matrix multiplication & using matrices to transform vectors.

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a matrix has rows & columns:

[2 3 4
 4 5 7]

therefore, 2x2 matrix (2r, 2c). this is the order of a matrix.

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addition, subtraction can be done with matrices that have the same order. it’s pretty much like an array:

$$a=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$$ $$b=\left[\begin{array}{cc}2& 2\\ 4& 5\end{array}\right]$$

so a + b:

$$A+B=\left[\begin{array}{cc}1+2& 2+2\\ 3+4& 4+5\end{array}\right]$$

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multiplication is a little more tricky.

say you have matrices:

$$a=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$$ $$b=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]$$

we have a 1x3 matrix and a 3x1 matrix.

to be able to multiply, the columns in matrix 1 needs to be the same as rows in the second. the order is determined the by the last two numbers. for example:

 
a. b is 1x3 matrix multiplied by 3x1 matrix. 
 
can be multipled; order of resulting matrix ab will be 1x1. 
 

therefore, order matters.

multiplication is row x column.

$$BA=\left[\begin{array}{c}4\\ 5\\ 6\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$$ $$(3\times 1)(1\times 3)=3\times 3$$ $$BA=\left[\begin{array}{ccc}4(1)& 4(2)& 4(3)\\ 5(1)& 5(2)& 5(3)\\ 6(1)& 6(2)& 6(3)\end{array}\right]$$ $$BA=\left[\begin{array}{ccc}4& 8& 12\\ 5& 10& 15\\ 6& 12& 18\end{array}\right]$$

you can essentially use these to transform vectors. i mean this is what p5 translate() does.

for example, rotation matrices can move a point in space. general formula:

$$r(a)=\left[\begin{array}{cc}cos(a)& -sin(a)\\ sin(a)& cos(a)\end{array}\right]$$

reflection: move a point the same distance & same angle across a plane. this is simpler to do, just multiple by 1,0 for whatever needs to stay; and 0,-1 to flip.

used organic chemistry tutor videos, and this for rotation & reflection.

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