# Computing straight skeletons for arc polygons

Franz Aurenhammer, Bert Jüttler, B. Weiß

Publikation: KonferenzbeitragAbstractForschungBegutachtung

### 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.
Originalsprache englisch Veröffentlicht - 2017

Decomposition
Splines

### Dies zitieren

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

2017.

Publikation: KonferenzbeitragAbstractForschungBegutachtung

title = "Computing straight skeletons for arc polygons",
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.",
author = "Franz Aurenhammer and Bert J{\"u}ttler and B. Wei{\ss}",
year = "2017",
language = "English",

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TY - CONF

T1 - Computing straight skeletons for arc polygons

AU - Aurenhammer, Franz

AU - Jüttler, Bert

AU - Weiß, B.

PY - 2017

Y1 - 2017

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.

M3 - Abstract

ER -