On the generation of spiral-like paths within planar shapes

• Published in: Journal of computational design and engineering Vol. 5; no. 3; pp. 348 - 357
• Main Authors: Held, Martin, de Lorenzo, Stefan
• Format: Journal Article
• Language: Korean
• Published: 2018
• Subjects: Spiral-like path; High-speed machining; Smoothing; Composite spiral; Medial axis; Double spiral
• ISSN: 2288-4300; 2288-5048

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.