In a previous post I showed how to use dual numbers to be able to get both the value and derivative of a function at the same time: Dual Numbers & Automatic Differentiation That post mentions that you can extend … Continue reading

# Category Archives: Graphics

This post talks about how to render images like the below in real time using ray tracing. Some realism in the images come from reflection and refraction, but the real icing on the cake comes from Fresnel, total internal reflection … Continue reading

The last post showed how to fit a equation to a set of 2d data points, using least squares fitting. It allowed you to do this getting only one data point at a time, and still come up with the … Continue reading

This Post In Short: Fit a curve of degree N to a data set, getting data points 1 at a time. Storage Required: 3*N+2 values. Update Complexity: roughly 3*N+2 additions and multiplies. Finalize Complexity: Solving Ax=b where A is an … Continue reading

This is an extension of a paper I wrote which shows how to use the linear texture sampling capabilities of the GPU to calculate points on Bezier curves. You store the control points in the texture, then sample along the … Continue reading

While it’s true that the GPU texture sampler can evaluate digital logic circuits, it turns out there’s a much better and simpler way to evaluate logic with textures. That better and simpler way isn’t even that useful unfortunately! This post … Continue reading

This is an extension of a paper I wrote which shows how to use the linear texture sampling capabilities of the GPU to calculate points on Bezier curves. You store the control points in the texture, then sample along the … Continue reading

The images below were path traced using 100,000 samples per pixel, using the sample code provided in this post. Path tracing is a specific type of ray tracing that aims to make photo realistic images by solving something called the … Continue reading

I’ve been working on getting a better understanding of the Discrete Fourier Transform. I’ve figured out some things which have really helped my intuition, and made it a lot simpler in my head, so I wanted to write these up … Continue reading

I attended SIGGRAPH this year and there were some amazing talks. There were quite a few talks dealing with the Fourier transform of images and sampling patterns, signal frequencies and bandwidth so I feel compelled to write up a blog … Continue reading