Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
The bisector of a point and a plane parametric curve
Computer Aided Geometric Design
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
New algorithm for medial axis transform of plane domain
Graphical Models and Image Processing
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
Voronoi Diagrams of Set-Theoretic solid Models
IEEE Computer Graphics and Applications
Voronoi Diagrams for Planar Shapes
IEEE Computer Graphics and Applications
Dynamically maintaining a hierarchical planar Voronoi diagram approximation
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Technical note: Voronoi diagrams of algebraic distance fields
Computer-Aided Design
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We propose a new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams. The method supports distinct site shapes (points, line-segments, curved-arc segments, polygons, spheres, lines, polyhedra, etc.), different distance functions (Euclidean distance, convex distance functions, etc.) and is restricted to diagrams with connected Voronoi regions. The presented approach constructs a tree (a quadtree in 2D/an octree in 3D) which encodes in its nodes and in a compact way all the information required for generating an explicit representation of the boundaries of the Voronoi diagram approximation. Then, by using this hierarchical data structure a reconstruction strategy creates the diagram approximation. We also present the algorithms required for dynamically maintaining under the insertion or deletion of sites the Voronoi diagram approximation. The main features of our approach are its generality, efficiency, robustness and easy implementation.