The offsetting process that defines straight skeletons of polygons is generalized to arc polygons, i.e., to planar shapes with piecewise circular boundaries. The offsets are obtained by shrinking or expanding the circular arcs on the boundary in a co-circular manner, and tracing the paths of their endpoints. These paths define the associated shape-preserving skeleton, which decomposes the input object into patches. While the skeleton forms a forest of trees, the patches of the decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is non-trivial; the boundary of the offsetting object may get into self-contact and may even splice. This leads us to an event-driven algorithm for offset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) are analyzed to study the practical performance of our algorithm.
|Seiten (von - bis)
|International Journal of Computational Geometry and Applications
|Veröffentlicht - 2020