scholarly journals Voronoi diagram: An adaptive spatial tessellation for processes simulation

Author(s):  
Leila Hashemi ◽  
Mir Abolfazl ◽  
Jacynthe Pouliot
Author(s):  
Raghuveer Devulapalli ◽  
Neil Peterson ◽  
John Gunnar Carlsson

A Voronoi diagram is a standard spatial tessellation that partitions a domain into sub-regions based on proximity to a fixed set of landmark points. In order to maintain control over the size and shape of these sub-regions, a weighting scheme is often used, in which each landmark has a scalar value associated with it. This suggests a natural “inverse” problem: given a fixed set of landmark points in a given planar region and a set of “desired” areas, is it possible to calculate a set of weights so that each sub-region has a particular area? In this chapter, the authors give a fast scheme for determining these weights based on theory from convex optimization, which is then applied to a variety of problems in data visualization.


2019 ◽  
Vol 86 ◽  
pp. 53-61
Author(s):  
N. G. Topolskiy ◽  
◽  
A. V. Mokshantsev ◽  
To Hoang Thanh ◽  
◽  
...  

2021 ◽  
Vol 50 ◽  
pp. 101301
Author(s):  
A.Z. Zheng ◽  
S.J. Bian ◽  
E. Chaudhry ◽  
J. Chang ◽  
H. Haron ◽  
...  

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Shengli Xu ◽  
Haitao Liu ◽  
Xiaofang Wang ◽  
Xiaomo Jiang

Surrogate models are widely used in simulation-based engineering design and optimization to save the computing cost. The choice of sampling approach has a great impact on the metamodel accuracy. This article presents a robust error-pursuing sequential sampling approach called cross-validation (CV)-Voronoi for global metamodeling. During the sampling process, CV-Voronoi uses Voronoi diagram to partition the design space into a set of Voronoi cells according to existing points. The error behavior of each cell is estimated by leave-one-out (LOO) cross-validation approach. Large prediction error indicates that the constructed metamodel in this Voronoi cell has not been fitted well and, thus, new points should be sampled in this cell. In order to rapidly improve the metamodel accuracy, the proposed approach samples a Voronoi cell with the largest error value, which is marked as a sensitive region. The sampling approach exploits locally by the identification of sensitive region and explores globally with the shift of sensitive region. Comparative results with several sequential sampling approaches have demonstrated that the proposed approach is simple, robust, and achieves the desired metamodel accuracy with fewer samples, that is needed in simulation-based engineering design problems.


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