Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Analytic properties of plane offset curves
Computer Aided Geometric Design
Algebraic properties of plane offset curves
Computer Aided Geometric Design
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
Shelling and offsetting bodies
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The algorithm design manual
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Invertible Minkowski Sum of Polygons
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Partitions of a Simplex Leading to Accurate Spectral (Finite) Volume Reconstruction
SIAM Journal on Scientific Computing
Medial Axis Transformation of a Planar Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variable-radius offset curves and surfaces
Mathematical and Computer Modelling: An International Journal
Three dimensional extension of Bresenham's Algorithm with Voronoi diagram
Computer-Aided Design
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An ordinary Voronoi diagram partitions the space into cells with the assumption that all the sites are of the same characteristics. A kinetic site, in addition to its position and hence distance to other sites, is equipped with two more characteristics: an additive constant (such as the time delay to respond to a stimulus) and a multiplicative constant (such as the growth rate or velocity to ''catch up''). Under disparate site characteristics, the resulting competition for space becomes unfair: the notion of dominance and conquest ensue. This article reports on the geometry and the topology of kinetic Voronoi regions as pivoted by simple expressions involving dimensionless numbers derived from the site characteristics.