Mitered Offsets and Skeletons for Circular Arc Polygons
| Autor: | Franz Aurenhammer, Bert Jüttler, Bastian Weiß |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Process (computing) Geometry Theoretical Computer Science Arc (geometry) Computational Mathematics Planar Biarc Computational Theory and Mathematics Medial axis Piecewise Geometry and Topology MathematicsofComputing_DISCRETEMATHEMATICS ComputingMethodologies_COMPUTERGRAPHICS Mathematics |
| Zdroj: | International Journal of Computational Geometry & Applications. 30:235-256 |
| ISSN: | 1793-6357 0218-1959 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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