Simple Shapes for Localization and Mapping

Abstract

Inspired by a procedural scene modelling technique in computer graphics, we investigate the use of continuous signed distance functions to model objects as geometric primitives, transformed and combined with set operations from constructive solid geometry, and deformations, such as scaling, rotation and translation. Unlike their discretized counterpart, which have become an important tool in various fields, the continuous distance function is stored as a mathematical expression, formed by analytic expressions.

We show through experiments and surveys that this representation has several benefits: such as being nearly compatible with highly sophisticated CAD tools; being fit for modelling many indoor and outdoor objects with a few primitives; requiring orders of magnitude less memory than their discrete counterpart, without compression or loss of precision; and being able to describe an infinite variety of objects through controlling the parameters of the constituent operations and primitives. Being a signed distance function, it also inherits their compelling benefits: such as defining, at each point in space, the direction and distance to the nearest surface, and whether this point is inside or outside the surface.