## Dual Numbers & Automatic Differentiation

In the last post, I talked about imaginary numbers, complex numbers, and how to use them to rotate vectors in 2d. In this post, I want to share another interesting type of number called a “Dual Number” that uses the … Continue reading

## Using Imaginary Numbers To Rotate 2D Vectors

I’m a big fan of “exotic” math and programming techniques. There’s nothing I like more than seeing something common used in an uncommon way to do something that I didn’t know was possible. In this post I share a technique … Continue reading

## Four Ways to Calculate Sine Without Trig

Is it possible to sin without trig? That is a question that has plagued theologians for centuries. As evil as trigonometry is, modern science shows us that yes, it is possible to sin without trig. Here are some ways that … Continue reading

## One Dimensional Bezier Curves

I was recently looking at the formula for bezier curves: Quadratic Bezier curve: A * (1-T)^2 + B * 2 * (1-T) * T + C * T ^2 Cubic Bezier curve: A*(1-T)^3+3*B*(1-T)^2*T+3*C*(1-T)*T^2+D*T^3 (more info available at Bezier Curves Part … Continue reading

## Counting in Binary is a Fractal

I can’t remember for sure but I think I read about this first in A New Kind Of Science by Stephen Wolfram (yes, the same guy who made Wolfram Alpha!). Counting in binary is actually a fractal, check out these … Continue reading

## Wang Tiling

Wang tiling is a really cool concept… it’s a good way to use 2d tiled graphics in such a way that can look very organic, without discernable patterns. The basic idea of how they work is that each tile has … Continue reading

## Temporal supersampling, flipquads and real time raytracing

Follow me on this train of thought ðŸ˜› 1) There’s this thing called super sampling where you render an image at a larger resolution, so that you can properly downsample it to the right size (the size of your screen … Continue reading

## What if My Equation DOESN’T Equal Zero??

Take a simple equation such as y = 2x. You can transform that into the equation 2x – y = 0, and then could write it as f(x,y) = 2x – y = 0. Now we have some function of … Continue reading