Collisions with Signed Distance Functions
Reading time: 0 minutes and 1 second. Introduction
On Signed Distance Functions
Reading time: 12 minutes and 41 seconds. Introduction Formal Definition In more rigorous terms, signed distance functions (aka SDFs) are defined as functions that satisfy a particular form of the eikonal equation1. The general eikonal equation is of the form: $$||\nabla u(x)|| = \frac{1}{f(x)},\quad x \in \Omega,$$ where \(\Omega\) is an open set in \(\mathbb{R}^n\), and \(f(x) : \mathbb{R}^n \to \mathbb{R}\) is a function with positive values. In physical terms, the solution \(u(x)\) to this nonlinear partial differential equation can be interpreted as the shortest time needed to travel from the boundary \(\partial\Omega\) to \(x \in \Omega\), with \(f(x)\) being the speed at \(x\). ...
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