The aesthetics of rapidly-exploring random trees

Abstract

Rapidly-Exploring Random Trees (RRTs) have been introduced as an algorithmic concept for the rapid exploration of configuration spaces targeting fast path planning, mainly applied in the field of robotics. Typically, such structured space organizations are only used on an algorithmic level but not for direct visual representation. In this paper, we illustrate the aesthetics of such RRTs by displaying them in a visual form that serves as a basis to generate algorithmic art. Apart from the visual encoding of such space-filling node-link diagrams, we demonstrate how these trees grow in the configuration space for RRT layouts with and without incremental distances from the initial point. Additionally, RRTs can be visually enhanced by several inherent tree metrics such as tree depth, subtree size, and branching factors to make the diagrams more aesthetically appealing and readable. We provide examples of different tree sizes and illustrate the effect of changes to several control parameters such as color coding, line segment thickness, layouts, and shape constraints.