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.