### Ray Casting in the Function Graph object





The Function Graph object in the editor allows you to plot cartesian and polar graphs of arbitrary functions. Since the functions are authored in Javascript, it’s actually quite easy to add logic and more or less arbitrary code to them, i.e. we’re not restricted to stricly maths-like functions. One of the advantages of this is that it was quite easy to expose ray hit testing results as inputs to the functions. This has allowed for some quite interesting graphs!

### Introduction to Convolution Integrals





I recently added support for convolution integrals on the Function Graph object in the editor. I thought I’d take the opportunity to write a quick introduction on the topic and present a few interactive diagrams. As with previous posts, this is not meant to be a complete teaching resource on convolution integrals. There are many excellent resources out there already! It’s just another take on them with some, hopefully interesting, diagrams.

### Indirect Illumination using Cubemaps

Rendering engines often use cubemaps to store some form of lighting. There are a myriad of techniques that use them ranging from static to dynamic, direct and indirect, diffuse and specular lighting and so on. In this post we’ll try to illustrate some of the common steps in capturing, filtering and using cubemaps to achieve some form of lighting.

### Signed Distance Fields

A Signed Distance Field is a mathematical construct where the distance to a closed surface is computed along a set of positions, with the sign of the distance used to indicate whether the position is inside or outside the surface. The positions are typically chosen to be on a regular grid and they work well in both 2D and 3D. They were made popular in computer graphics by this SIGGRAPH 2007 paper by Valve. If you haven’t already read it, it’s definitely worth a read!

In this post we’ll investigate using a simple 2D SDF to approximate a shape. It’s by no means the only use of SDF, but it’s one that’s easy to visualize and has practical use in computer graphics.

### Floating point numbers

Let’s kick things off with an interactive diagram explaining floating point numbers! There are many ways to explain this, but I’ve always found that diagrams help. The Wikipedia page on single-precision floats has all the details on how they work, including links to external tools allowing you to convert decimal to binary and vice versa.