An efficient algorithm for construction of the power diagram from the voronoi diagram in the plane

1996 ◽  
Vol 61 (1-2) ◽  
pp. 49-61 ◽  
Author(s):  
Marina Gavrilova ◽  
Jon Rokne
Keyword(s):  
Voronoi Diagram ◽  
Efficient Algorithm ◽  
Power Diagram

CENTROID TRIANGULATIONS FROM k-SETS

2011 ◽  
Vol 21 (06) ◽  
pp. 635-659 ◽  
Author(s):  
WAEL EL ORAIBY ◽  
DOMINIQUE SCHMITT ◽  
JEAN-CLAUDE SPEHNER
Keyword(s):  
Convex Hull ◽  
Voronoi Diagram ◽  
Efficient Algorithm ◽  
Worst Case ◽  
Point Set

Given a set V of n points in the plane, no three of them being collinear, a convex inclusion chain of V is an ordering of the points of V such that no point belongs to the convex hull of the points preceding it in the ordering. We call k-set of the convex inclusion chain, every k-set of an initial subsequence of at least k points of the ordering. We show that the number of such k-sets (without multiplicity) is an invariant of V, that is, it does not depend on the choice of the convex inclusion chain. Moreover, this number is equal to the number of regions of the order-k Voronoi diagram of V (when no four points are cocircular). The dual of the order-k Voronoi diagram belongs to the set of so-called centroid triangulations that have been originally introduced to generate bivariate simplex spline spaces. We show that the centroids of the k-sets of a convex inclusion chain are the vertices of such a centroid triangulation. This leads to the currently most efficient algorithm to construct particular centroid triangulations of any given point set; it runs in O(n log n + k(n - k) log k) worst case time.

Layered Manufacturing of Thin-Walled Parts

2000 ◽  
Author(s):  
Sara McMains ◽  
Jordan Smith ◽  
Jianlin Wang ◽  
Carlo Séquin
Keyword(s):  
Voronoi Diagram ◽  
Efficient Algorithm ◽  
Fused Deposition Modeling ◽  
Layered Manufacturing ◽  
Exterior Wall ◽  
Uniform Thickness ◽  
Fused Deposition ◽  
Material Usage ◽  
Deposition Modeling ◽  
Thin Walled

Abstract We describe a new algorithm we have developed for making partially hollow layered parts with thin, dense walls of approximately uniform thickness, for faster build times and reduced material usage. We have implemented our algorithm on a fused deposition modeling (FDM) machine, using separate build volumes for a loosely filled interior and a thin, solid, exterior wall. The build volumes are derived as simple boolean combinations of slice contours and their offsets. We make use of an efficient algorithm for computing the Voronoi diagram of a general polygon as part of the process of creating offset contours. Our algorithm guarantees that the surface of the final part will be dense while still allowing an efficient build.

THREE-DIMENSIONAL SHAPES OF A FINITE SET OF POINTS

2003 ◽  
Vol 17 (02) ◽  
pp. 301-318 ◽  
Author(s):  
MAHMOUD MELKEMI
Keyword(s):  
Voronoi Diagram ◽  
Delaunay Triangulation ◽  
Efficient Algorithm ◽  
Point Cloud ◽  
Three Dimensional ◽  
Levels Of Detail ◽  
Finite Set ◽  
Set Of Points ◽  
Different Levels ◽  
Different Parts

The three-dimensional [Formula: see text]-shape is based on a mathematical formalism which determines exact relationships between points and shapes. It reconstructs surface and volume and detects 3D dot patterns for a given point cloud. [Formula: see text]-shape of a set of points is a sub-complex of Delaunay triangulation of this set. It generates a family of shapes according to the selected [Formula: see text] (a set of points). A method to compute the positions of the points of [Formula: see text] is proposed. These points are selected from the vertices of Voronoi diagram by analyzing the form of the polytopes; their elongation. This method allows the [Formula: see text]-shape to reflect different levels of detail in different parts of space. An efficient algorithm computing the three-dimensional [Formula: see text]-shape is presented, the [Formula: see text]-shape of a set of points is derived from the Delaunay triangulation of the same set. The speed of the algorithm is determined by the speed of the algorithm computing the Delaunay triangulation.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Energy efficient algorithm for lookup-tables on mobile devices

2016 ◽  
Vol 2016 (7) ◽  
pp. 1-6
Author(s):  
Sergey Makov ◽  
Vladimir Frantc ◽  
Viacheslav Voronin ◽  
Igor Shrayfel ◽  
Vadim Dubovskov ◽  
...  
Keyword(s):  
Mobile Devices ◽  
Efficient Algorithm ◽  
Energy Efficient ◽  
Lookup Tables

Model and algorithm for searching for victims in emergency situations and fires using the Voronoi diagram

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