The Voronoi diagram of three arbitrary lines in R3
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Summary
It is proved that the arcs of trisectors are always monotonic in some direction and it is shown how to separate the connected components and to sort points along each arc of a trisector using only rational linear semi-algebraic tests.
- Type
- article
- Published
- 2009-03-16
- Cited by
- 10
- References
- 35
- Access
- Open access
- OpenAlex
- https://openalex.org/W1671415320
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:924244
Keywords
Voronoi diagram, Power diagram, Diagram, Weighted Voronoi diagram, Polyhedron
References
- Robust Construction of the Voronoi Diagram of a Polyhedron
- Near-optimal parameterization of the intersection of quadrics
- An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
- A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
- Approximate medial axis as a voronoi subcomplex
- Voronoi diagrams—a survey of a fundamental geometric data structure
- Triangulations in CGAL
- Vertical decomposition of a single cell in a three-dimensional arrangement of surfaces and its applications
- Common Tangents to Spheres in ℝ3
- Three dimensional euclidean Voronoi diagrams of lines with a fixed number of orientations
- Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic: I - representations
- Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils
- Primal Dividing and Dual Pruning: Output-Sensitive Construction of Four-Dimensional Polytopes and Three-Dimensional Voronoi Diagrams
- Applications of random sampling in computational geometry, II
- Applications of random sampling to on-line algorithms in computational geometry
- On the computation of an arrangement of quadrics in 3D
- New applications of random sampling in computational geometry
- Computing the medial axis of a polyhedron reliably and efficiently
- Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
- An exact and efficient approach for computing a cell in an arrangement of quadrics
Cited by
- On soft predicates in subdivision motion planning
- Towards exact numerical Voronoi diagrams
- Constructing the Exact Voronoi Diagram of Arbitrary Lines in Space
- Rods and Rings: Soft Subdivision Planner for R^3 x S^2
- Computing the Topology of Voronoï Diagrams of Parallel Half-Lines
- Towards Exact Numerical Voronoi Diagrams ( Invited Talk )
- Constructing the Exact Voronoi Diagram of Arbitrary Lines in Three-Dimensional Space - with Fast Point-Location
- 27 VORONOI DIAGRAMS AND DELAUNAY TRIANGULATIONS
- Robust Geometric Computation
- Constructing the Exact Voronoi Diagram of Arbitrary Lines in Three-Dimensional Space - with Fast Poi