Computing straight skeletons for arc polygons

Franz Aurenhammer, Bert Jüttler, B. Weiß

Research output: Contribution to conferenceAbstractResearchpeer-review

Abstract

We generalize the offsetting process that defines straight skeletons of polygons [1] 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 and tracing the paths of the vertices. These paths define the associated skeletons and the associated decomposition into patches. While the skeleton forms a tree, the patches of our decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is nontrivial; for example one has to ensure that the offsetting object stays an arc polygon. This leads us to an event-driven algorithm for oset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) will be presented to analyze the performance of our algorithm.
Original languageEnglish
Publication statusPublished - 2017

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Computing straight skeletons for arc polygons. / Aurenhammer, Franz; Jüttler, Bert; Weiß, B.

2017.

Research output: Contribution to conferenceAbstractResearchpeer-review

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N2 - We generalize the offsetting process that defines straight skeletons of polygons [1] 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 and tracing the paths of the vertices. These paths define the associated skeletons and the associated decomposition into patches. While the skeleton forms a tree, the patches of our decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is nontrivial; for example one has to ensure that the offsetting object stays an arc polygon. This leads us to an event-driven algorithm for oset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) will be presented to analyze the performance of our algorithm.

AB - We generalize the offsetting process that defines straight skeletons of polygons [1] 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 and tracing the paths of the vertices. These paths define the associated skeletons and the associated decomposition into patches. While the skeleton forms a tree, the patches of our decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is nontrivial; for example one has to ensure that the offsetting object stays an arc polygon. This leads us to an event-driven algorithm for oset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) will be presented to analyze the performance of our algorithm.

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