On the generation of spiral-like paths within planar shapes
Martin Held, Stefan de Lorenzo · Journal of Computational Design and Engineering · 2017
Abstract We simplify and extend prior work by Held and Spielberger [CAD 2009, CAD&A 2014] to obtain spiral-like paths inside of planar shapes bounded by straight-line segments and circular arcs: We use a linearization to derive a simple algorithm that computes a continuous spiral-like path which (1) consists of straight-line segments, (2) has no self-intersections, (3) respects a user-specified maximum step-over distance, and (4) starts in the interior and ends at the boundary of the shape. Then we extend this basic algorithm to double-spiral paths that start and end at the boundary, and show how these double spirals can be used to cover complicated planar shapes by composite spiral paths. We also discuss how to improve the smoothness and reduce the curvature variation of our paths, and how to boost them to higher levels of continuity. Highlights The algorithm computes a spiral path within planar shapes with and without islands. It respects a user-specified maximum step-over distance. Double spirals and composite spiral paths can be computed. Heuristics for smoothing the spirals are discussed. The algorithm is simple and easy to implement, and suitable for various applications.