Multiplicatively weighted crystal growth Voronoi diagrams (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
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
A fast algorithm for Euclidean distance maps of a 2-D binary image
Information Processing Letters
A unified linear-time algorithm for computing distance maps
Information Processing Letters
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
SIAM Review
Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space
Computer Aided Geometric Design
Dynamically maintaining a hierarchical planar Voronoi diagram approximation
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
| Hi-index | 0.00 |
This paper studies the multiplicatively weighted crystal-growth Voronoi diagram, which describes the partition of the plane into crystals with different growth speeds. This type of the Voronoi diagram is defined, and its basic properties are investigated. An approximation algorithm is proposed. This algorithm is based on a finite difference method, called a fast marching method, for solving a special type of a partial differential equation. The proposed algorithm is applied to the planning of a collision-free path for a robot avoiding enemy attacks.