Randomized incremental construction of abstract Voronoi diagrams
Computational Geometry: Theory and Applications
Approximating smooth planar curves by arc splines
Journal of Computational and Applied Mathematics
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Spiral arc spline approximation to a planar spiral
Journal of Computational and Applied Mathematics
Computational Geometry: Theory and Applications
Motion Planning in the CL-Environment (Extended Abstract)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
The Voronoi Diagram of Curved Objects
Discrete & Computational Geometry
The predicates for the Voronoi diagram of ellipses
Proceedings of the twenty-second annual symposium on Computational geometry
Computation of medial axis and offset curves of curved boundaries in planar domain
Computer-Aided Design
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Efficient computation of continuous skeletons
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Medial axis computation for planar free-form shapes
Computer-Aided Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Computational and structural advantages of circular boundary representation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
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We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an (augmented) planar domain. Division into base cases is then possible, which, in the bottom-up phase, can be merged by trivial concatenation. The resulting construction algorithm--similar to Delaunay triangulation methods--is not bisector-based and merely computes dual links between the sites, its atomic steps being inclusion tests for sites in circles. This guarantees computational simplicity and numerical stability. Moreover, no part of the Voronoi diagram, once constructed, has to be discarded again. The algorithm works for polygonal and curved objects as sites and, in particular, for circular arcs which allows its extension to general free-form objects by Voronoi diagram preserving and data saving biarc approximations. The algorithm is randomized, with expected runtime O(n log n) under certain assumptions on the input data. Experiments substantiate an efficient behavior even when these assumptions are not met. Applications to offset computations and motion planning for general objects are described.