Camera matrix from basic principles.

Derivation of a camera matrix general enough to be used for stereo rendering, and it's inverse. This problem is used to motivate and discuss projective geometry.

Derivation of a camera matrix general enough to be used for stereo rendering, and it's inverse. This problem is used to motivate and discuss projective geometry.

Published: 1570556832

A neat vector expression for the direction of refraction

Derivation of an economical vector expression for the direction of refraction.

Derivation of an economical vector expression for the direction of refraction.

Published: 1528633747

Fast quaternion math in shaders

I derive a few of the handiest quaternion functions in a way suited for implementation in shader languages.

I derive a few of the handiest quaternion functions in a way suited for implementation in shader languages.

Published: 1476037299

Round-off error propagation.

I prove some simple rules of thumb for how many decimals to keep when multiplying and dividing numbers.

I prove some simple rules of thumb for how many decimals to keep when multiplying and dividing numbers.

Published: 1475344156

Published: 1472838268, last updated: 1473618828