October 2025

# Calculating the Bounding Rectangle of a Circular Sector

Sun
19
Oct 2025

This article will be short and straight to the point. While working with geometry in 2D, I was recently looking for an algorithm to calculate the bounding box of a specific shape that I initially called a "cone". Actually, as I'm talking about 2D, I should rather say I needed the bounding rectangle of a circular sector - a part of a circle with a limited angle around an axis pointing in a specific direction.

When developing a 2D game, this shape can represent, for example, the area of effect of an attack, such as punching nearby enemies, firing a shotgun, spraying some substance ahead, or casting a magical spell. Calculating its bounding rectangle can be useful for querying a space-partitioning data structure (like a grid, a quadtree, etc.) for potentially affected objects.

I prototyped my solution in ShaderToy, which you can see here: shadertoy.com/view/w3jcRw.

Comments | #math Share