Computational geometry: an introduction
Computational geometry: an introduction
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
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
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
SIAM Review
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Brief paper: The Zermelo-Voronoi diagram: A dynamic partition problem
Automatica (Journal of IFAC)
Approximating generalized distance functions on weighted triangulated surfaces with applications
Journal of Computational and Applied Mathematics
Optimal partitioning for multi-vehicle systems using quadratic performance criteria
Automatica (Journal of IFAC)
| Hi-index | 7.30 |
The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a ''boat-sail distance'', which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.