Corpus ID: 29058232

Computation of Voronoi Diagrams of Circular Arcs and Straight Lines

  title={Computation of Voronoi Diagrams of Circular Arcs and Straight Lines},
  author={Stefan Huber},
Vroni is one of few existing implementations for the stable computation of Voronoi diagrams of line segments. A topology-oriented approach in combination with double-precision floating-point arithmetic makes Vroni also the fastest and most reliable implementation available. Up to now, Voronoi diagram algorithms used in industrial applications process input data consisting of points and straightline segments. Since circular arcs are important in various applications like CAD/CAM, printed circuit… Expand


VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments
  • M. Held
  • Computer Science
  • Comput. Geom.
  • 2001
Vroni is a topology-oriented algorithm for the computation of Voronoi diagrams of points and line segments in the two-dimensional Euclidean space that is completely reliable and fast in practice and has been successfully tested within and integrated into several industrial software packages. Expand
Biarc Approximation, Simplification and Smoothing of Polygonal Curves by Means of Voronoi-Based Tolerance Bands
This work presents an algorithm for approximating multiple closed polygons in a tangent-continuous manner with circular biarcs and shows that this algorithm generates approximation curves with significantly fewer approximation primitives than previously proposed algorithms. Expand
A sweepline algorithm for Euclidean Voronoi diagram of circles
This paper presents a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space and shows that the presented algorithm is optimal with O(n^2 log n) worst-case time complexity. Expand
The Voronoi Diagram of Planar Convex Objects
A dynamic algorithm for the construction of the Euclidean Voronoi diagram of a set of convex objects in the plane using a randomized dynamic algorithm that can easily be adapted to the case of pseudo-circles sets formed by piecewise smooth convex Objects. Expand
PVD: A Stable Implementation for Computing Voronoi Diagrams of Polygonal Pockets
This work reports on an implementation of a simple algorithm which does not rely on exact arithmetic to achieve robustness but achieves its robustness through carefully engineered handling of geometric predicates. Expand
The Voronoi diagram of curved objects
This paper shows how a given set of curves can be refined such that the resulting curves define a “well-behaved” Voronoi diagram, and gives a randomized incremental algorithm to compute this diagram. Expand
Voronoi diagrams—a survey of a fundamental geometric data structure
Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computerExpand
Generalization of Voronoi Diagrams in the Plane
The algorithm presented is an improvement of a previous known result which takes $O(Nc^{\sqrt {\log N} } )$ time and is shown to be applicable under a more general metric if certain conditions are satisfied. Expand
Randomized Incremental Construction of Abstract Voronoi Diagrams
This work shows how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm; the algorithm is based on Clarkson and Shor's randomized incremental construction technique. Expand
A robust and efficient implementation for the segment Voronoi diagram
In this paper we present an efficient algorithm for the computation of the segment Voronoi diagram in two dimensions. Our algorithm can handle not only disjoint segments or segments that shareExpand