User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Point Placement and Associated Zeroth, First, and Second Moment Determination

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Description

The theory, numerical algorithm, and user documentation are provided for a new ''Centroidal Voronoi Tessellation (CVT)'' method of filling a region of space (2D or 3D) with particles at any desired particle density. ''Clumping'' is entirely avoided and the boundary is optimally resolved. This particle placement capability is needed for any so-called ''mesh-free'' method in which physical fields are discretized via arbitrary-connectivity discrete points. CVT exploits efficient statistical methods to avoid expensive generation of Voronoi diagrams. Nevertheless, if a CVT particle's Voronoi cell were to be explicitly computed, then it would have a centroid that coincides with the particle itself ... continued below

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65 pages

Creation Information

BURKARDT, JOHN; GUNZBURGER, MAX; PETERSON, JANET & BRANNON, REBECCA M. February 1, 2002.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 11 times . More information about this report can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

The theory, numerical algorithm, and user documentation are provided for a new ''Centroidal Voronoi Tessellation (CVT)'' method of filling a region of space (2D or 3D) with particles at any desired particle density. ''Clumping'' is entirely avoided and the boundary is optimally resolved. This particle placement capability is needed for any so-called ''mesh-free'' method in which physical fields are discretized via arbitrary-connectivity discrete points. CVT exploits efficient statistical methods to avoid expensive generation of Voronoi diagrams. Nevertheless, if a CVT particle's Voronoi cell were to be explicitly computed, then it would have a centroid that coincides with the particle itself and a minimized rotational moment. The CVT code provides each particle's volume and centroid, and also the rotational moment matrix needed to approximate a particle by an ellipsoid (instead of a simple sphere). DIATOM region specification is supported.

Physical Description

65 pages

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  • Other Information: PBD: 1 Feb 2002

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  • Report No.: SAND2002-0099
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/793224 | External Link
  • Office of Scientific & Technical Information Report Number: 793224
  • Archival Resource Key: ark:/67531/metadc735017

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  • February 1, 2002

Added to The UNT Digital Library

  • Oct. 19, 2015, 7:39 p.m.

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  • April 12, 2016, 6:56 p.m.

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BURKARDT, JOHN; GUNZBURGER, MAX; PETERSON, JANET & BRANNON, REBECCA M. User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Point Placement and Associated Zeroth, First, and Second Moment Determination, report, February 1, 2002; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc735017/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.