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

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

Distance Field Textures

A friend recently turned me onto a really cool paper (thanks James!) that Valve wrote that allows you to encode monochromatic (black & white) textures in a way that they can be incredibly low resolution, but when you scale them … Continue reading

Analytic Fog Density

There are a number of ways to implement the effect of fog with modern real time rendered graphics. This blog post will explain how to render fog that has varying density, based on a function of X,Y,Z location in space, … Continue reading

Bezier Curves Part 2 (and Bezier Surfaces)

This is a follow up post to Bezier Curves. My plan was to write a post about b-splines and nurbs next, but after looking into them deeper, I found out they aren’t going to work for my needs so I’m … Continue reading

Bezier Curves

Bezier curves are pretty cool. They were invented in the 1950s by Pierre Bezier while he was working at the car company Renault. He created them as a succinct way of describing curves mathematically that could be shared easily with … Continue reading

Soft Maximum vs Hard Maximum

The other day i stumbled on an interesting concept called a “Soft Maximum”. If you think of the normal maximum, you might have something like this: if valueA and valueB come from functions, there’s usually going to be a sharp … Continue reading

Converting RGB to Grayscale

If you were converting an RGB pixel to grayscale, you might be like me and be tempted to just add the red, green and blue components together and divide by 3 to get the grayscale equivalent of the color. That’s … Continue reading