Game Math Cheat Sheet

Point and Vector

Operation Explanation
+/- point - point = vector, point + vector = point, vector +/- vector = vector
|| Return length of vector or point's distance to origin
normalize Change length to 1
scalar multiplication Uniform scaling
component-wise product Nonuniform scaling
dot product a∙b = |a| |b| cos(𝜃)
cross product a×b = |a| |b| sin(𝜃) n, direction of n is given by the x-hand rule
LERP Linear interpolation

Matrix

Operation Explanation
* Concatenate transforms; Transform point or vector
inverse Undoes transform, only affine matrices (combinations of pure rotations, translations, scales and shears) have inverses.
transpose Convert between row- and column-major matrices; Inverse of an orthonormal (pure rotation) matrix is equal to its transpose

Quaternion

A faster, less space and interpolate-able alternative to rotation matrix.

Operation Explanation
* (There are quite a few multiplication methods) Concatenate quaternions; Part of rotate operation
conjugate Inverse of a normalized quaternion is equal to its conjugate
inverse Inverse quaternion; Part of rotate operation
rotate Rotate
LERP Linear interpolation
SLERP Another linear interpolation, SLERP is better in quality than LERP, but can be slower