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Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware
, 1999
"... We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation of ..."
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Cited by 233 (26 self)
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We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation
Kinetic Voronoi/Delaunay Drawing Tools
 In Proceedings of the 3rd International Symposium on Voronoi Diagrams in Science and Engineering
, 2006
"... We describe two reversible linedrawing methods for cartographic applications based on the kinetic (movingpoint) Voronoi diagram. Our objectives were to optimize the user’s ability to draw and edit the map, rather than to produce the most efficient batchoriented algorithm for large data sets, and a ..."
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Cited by 2 (2 self)
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. There are thus three parts to our method: the maintenance of MP in the DT/VD; the use of MP to draw the constrained edges in the Delaunay triangulation; and the use of MP to draw the line segment Voronoi diagram. In all cases deletion is the inverse of the original drawing: move MP so as to “roll up
Kinetic and dynamic Delaunay tetrahedralizations in three dimensions
 Computer Physics Communications
"... Pacs: 02.40.S, 02.10.R We describe the implementation of algorithms to construct and maintain threedimensional dynamic Delaunay triangulations with kinetic vertices using a threesimplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Ini ..."
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Cited by 17 (3 self)
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Pacs: 02.40.S, 02.10.R We describe the implementation of algorithms to construct and maintain threedimensional dynamic Delaunay triangulations with kinetic vertices using a threesimplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation
DYNAMIC CARTOGRAPHY USING VORONOI/DELAUNAY METHODS
 ISPRS WORKSHOP ON UPDATING GEOSPATIAL DATABASES WITH IMAGERY & THE 5TH ISPRS WORKSHOP ON DMGISS
"... We describe two reversible linedrawing methods for cartographic applications based on the kinetic (movingpoint) Voronoi diagram. Our objectives were to optimize the user’s ability to draw and edit the map, rather than to produce the most efficient batchoriented algorithm for large data sets, and ..."
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of MP. There are thus three parts to our method: the maintenance of MP in the DT/VD; the use of MP to draw the constrained edges in the Delaunay triangulation; and the use of MP to draw the line segment Voronoi diagram. In all cases deletion is the inverse of the original drawing: move MP so as to “roll
DYNAMIC FIELD PROCESS SIMULATION WITHIN GIS: THE VORONOI APPROCHE
"... Simulation of a dynamic and continuous phenomenon (field) is a difficult task for GISs as their data structures are 2D and static and are not welladapted to manage neither the dynamic behavior of the phenomenon nor its geometrical and topological information. In this paper we present the Voronoi di ..."
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Cited by 1 (0 self)
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Simulation of a dynamic and continuous phenomenon (field) is a difficult task for GISs as their data structures are 2D and static and are not welladapted to manage neither the dynamic behavior of the phenomenon nor its geometrical and topological information. In this paper we present the Voronoi
Dynamic Voronoi/Delaunay Methods and Applications
, 2003
"... This paper presents simple point insertion and deletion operations in Voronoi diagrams and Delaunay triangulations which may be useful for a wide variety of applications, either where interactivity is important, or where local modification of the topology is preferable to global rebuilding. While in ..."
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This paper presents simple point insertion and deletion operations in Voronoi diagrams and Delaunay triangulations which may be useful for a wide variety of applications, either where interactivity is important, or where local modification of the topology is preferable to global rebuilding. While
The Kinetic 3D Voronoi Diagram: A Tool for Simulating Environmental Processes
"... Simulations of environmental processes are usually modelled by partial differential equations that are approximated with numerical methods, based on regular grids. An attractive alternative for simulating a fluid flow is the FreeLagrange Method (FLM). In this paper, I discuss the use of the FLM—bas ..."
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Cited by 2 (0 self)
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—based on the Voronoi diagram (VD)—for the modelling of fluid flow in three dimensions (e.g. the movement of underground water or of pollution plumes in the ocean). Such a technique requires the kinetic threedimensional VD, that is a VD for which the points are allowed to move freely in space. I present a new
Modelling threedimensional geoscientific fields with the voronoi diagram and its dual
 International Journal of Geographical Information Science
"... Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often threedimensional, they tend to change continuously over time, and the collection of samples to study the phenomena is problematic, which often results in highly aniso ..."
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Cited by 8 (2 self)
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on the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT), and argue that they have many advantages over other tessellations. We discuss the main properties of the 3D VD/DT, present some GIS operations that are greatly simplified when the VD/DT is used, and, to analyse two or more fields, we
The 3D Voronoi Diagram: A Tool for the Modelling of Geoscientific Datasets
"... A lot of efforts and money are being spent, both by commercial companies and by the academic world, for the development of tools to model 3D geographical information. In most cases, the ”3D GISs ” built are systems where 3D objects can be visualised (in a 3D environment), and where in some cases pri ..."
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present an alternative solution for the modelling of geoscientific datasets: the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT). We first discuss the VD/DT model and its properties, and we show that it has many advantages over already existing models/structures for analysing
Results 1  10
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1,989