# Transposed Matrix Properties

Today I derived, geometrically, the following: $$(A * B)^{T} = C \\ C = B^{T} * A^{T} \label{eq1}$$ Listed on the wikipedia page without much a description (property number 3), this property hid from me for a good 24 hours and confused me. I had been working on creating

# GJK: Common Implementation Mistake

Thanks to some cool discussions with my friend Nathan Carlson I’ve learned a bit about GJK. There are two versions floating around in the computer science community, and one of them is much easier to implement than the other. I will assume readers have a basic understanding of the theory

# Transformations: Change of Basis Matrix

When dealing with tensors and having to transform them from one basis to another the formula to do so isn’t all that intuitive, especially when 3D programmers are used to transformation concatenations. I’m sure any reader familiar with 3D would understand that two transformation matrices can be combined to make

# Geometric Duality Transformation

One topic I’ve found to be extremely interesting is the idea of dual space in terms of a polyhedron. After recently being introduced to Fourier transforms (thanks Professor Morhmann!) and image processing I’ve been thinking about dual space in the same sort of light: as a mathematical transformation. I’d like to

# thatgamecompany Internship!

Recently inspired by my colleague Allen’s interesting blog post about his hiring experience I’ve decided to follow suit and share my own experience on acquiring an internship the year before graduation! I’m sure most anyone reading my blog knows of a company called thatgamecompany. I have recently been offered a summer

# Buoyancy, Rigid Bodies and Water Surface

I’ve spent the last couple weeks researching eigenvalue decomposition and solving cubic polynomials in order to simulate a liquid surface and polyhedral buoyancy! I gave a lecture about this topic at my university and hope the slides can be of interest or help to someone. I’ve attached a couple demo

# Code Sample: Gaussian Elimination

In my current portfolio project I came across the need for an implementation of Gaussian Elimination to solve a system of equations in C++. I’ve decided to open source the code and use it for a code sample as a portfolio piece. Here is an entire working program:

# Dynamically Slicing Shapes

Just this morning I finished up a small open source project, along with a huge article at gamedev.tutsplus. The open source project is an implementation of Sutherland-Hodgman clipping which can be used in many advanced shape and mesh manipulation techniques. Gif of the open source project in action. Slicing a

# Sprite Batching and Texture Atlases

Recently I gave a small lecture on sprite batching and texture atlases. Hopefully these resources here can help somebody in the future!