This updated version of Animation Maths is an accessible and practical guide to animation programming. It opens with arithmetic, solving systems and trigonometry fundamentals, then guides the reader through standard topics such as real functions, the relevant golden section, coordinate systems and vectors. All the subsequent topics are programming oriented and calculus-free and have been selected to add efficiency to your games and animations. In addition to programmable kinematics, Animation Maths offers collision detection, the parametric equations of lines and planes in 3D, and matrices, which are covered in great detail. On its extension to complex numbers, Animation Maths shows the abilities of quaternions as superior 3D rotators.