Author Archives: Allen Chou

This post is part of my Game Math Series. A quaternion is a very useful mathematical object devised by Sir William Rowan Hamilton as an extension to complex numbers. It is often used to compactly represent 3D orientations with just … Continue reading →

This post is part of my Game Math Series. I first saw this technique in an article, Hacking Quaternions, written by Jonathan Blow (author of Braid). To normalize a vector, you divide its individual components by its length. The bottle … Continue reading →

This post is part of my Game Math Series. We have seen how to approximate a function using polynomials in this post. A good candidate for polynomial approximation would be the sine function, for it is used a lot in … Continue reading →

This post is part of my Game Math Series. Polynomials A polynomial is an expression consisting of linear combination of products of variables raised to non-negative integer powers. In this post, I will specifically focus on polynomials of a single … Continue reading →

This post is part of my Game Math Series. Splitting Matrices into Blocks When performing matrix multiplication, we can split matrices into “blocks”. The matrix multiplication can then be performed as if each block is a single matrix element, given … Continue reading →

This post is part of my Game Math Series. Definition of Matrix Multiplication Let and be a -by- matrix and an -by- matrix, respectively. Let denote the element in the matrix on row and column (zero-based indexing), “element (, )” … Continue reading →