Boolean operations, local topology theory and example applications

See also Overlaying maps, planar graphs, polyhedra.

2021

  • Marcelo de Matos Menezes, Salles Viana Gomes Magalhães, Matheus Aguilar de Oliveira, W. Randolph Franklin, and Rodrigo Eduardo de Oliveira Bauer Chichorro. Fast parallel evaluation of exact geometric predicates on GPUs. submitted, January 2021.
    [abstract▼] [details] [full text] [BibTeX▼]

2020

  • Marcelo de Matos Menezes, Salles Viana Gomes de Magalhães, Matheus Aguilar, W. Randolph Franklin, and Bruno Coelho. Employing GPUs to accelerate exact geometric predicates for 3D geospatial processing. In John Krumm, editor, 2nd ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2020). ACM, nov 2020. URL: https://www.spatialgems.net/.
    [abstract▼] [details] [full text] [BibTeX▼]
  • Marcelo de Matos Menezes, Salles Viana Gomes de Magalhães, Matheus Aguilar, W. Randolph Franklin, and Bruno Coelho. Employing GPUs to accelerate exact geometric predicates for 3D geospatial processing. In John Krumm, editor, 2nd ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2020). ACM, nov 2020. URL: https://www.spatialgems.net/.
    [abstract▼] [details] [full text] [BibTeX▼]

2019

  • W. Randolph Franklin and Salles Viana Gomes de Magalhães. Minimal representations of polygons and polyhedra. In John Krumm, editor, 1st ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2019). ACM, Nov 2019. URL: https://www.spatialgems.net/.
    [abstract▼] [details] [full text] [BibTeX▼]

2018

  • W. Randolph Franklin, Salles V. G. de Magalhães, and Marcus V. A. Andrade. Data structures for parallel spatial algorithms on large datasets (vision paper). In Proceedings of BigSpatial’18: 7th ACM SIGSPATIAL Workshop on Analytics for Big Geospatial Data. Seattle, USA, 6 Nov 2018.
    [abstract▼] [details] [full text] [slides] [BibTeX▼]
  • W. Randolph Franklin, Salles V. G. de Magalhães, and Marcus V. A. Andrade. Exact fast parallel intersection of large 3-D triangular meshes (extended abstract). In 28th Annual Fall Workshop on Computational Geometry. Queens College, CUNY, New York City, 26–27 Oct 2018.
    [abstract▼] [details] [full text] [BibTeX▼]

2016

  • W. Randolph Franklin and Salles Viana Gomes de Magalhães. Local topology and parallel overlaying large planar graphs. 15 Feb 2016. Talk at Georgia Tech, School of Interactive Computing. Also given at IBM Haifa, Microsoft Haifa, Ben Gurion U, and Tel Aviv U in Dec 2015.
    [details] [slides] [BibTeX▼]

2015

  • W. Randolph Franklin and Salles Viana Gomes de Magalhães. Global properties from local topology. 10 Nov 2015. Talk at UC Santa Barbara, Center for Spatial Studies.
    [details] [slides] [BibTeX▼]

2013

  • W. Randolph Franklin. Parallel volume computation of massive polyhedron union. In 23rd Fall Workshop on Computational Geometry. City College, New York City, USA, 25–26 Oct 2013. (extended abstract).
    [abstract▼] [details] [full text] [slides] [BibTeX▼]

2005

  • Wm. Randolph Franklin. Mass properties of the union of millions of identical cubes. In Ravi Janardan, Debashish Dutta, and Michiel Smid, editors, Geometric and Algorithmic Aspects of Computer Aided Design and Manufacturing, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, volume 67, pages 329–345. American Mathematical Society, 2005.
    [details] [full text] [slides] [BibTeX▼]

2004

  • W. Randolph Franklin. Analysis of mass properties of the union of millions of polyhedra. In M. L. Lucian and M. Neamtu, editors, Geometric Modeling and Computing: Seattle 2003, pages 189–202. Nashboro Press, Brentwood TN, 2004.
    [details] [full text] [BibTeX▼]

1995

  • Mohan Kankanhalli and Wm Randolph Franklin. Area and perimeter computation of the union of a set of iso-rectangles in parallel. J. Parallel Distrib. Comput., 27(2):107–117, June 1995. doi:https://doi.org/10.1006/jpdc.1995.1076.
    [abstract▼] [details] [full text] [BibTeX▼]

1992

  • WR Franklin. Local topological properties of polyhedra. (unpublished talk), Sept 1992. URL: https://wrf.ecse.rpi.edu/wiki/Research/unpub/localtopo.pdf.
    [abstract▼] [details] [BibTeX▼]

1990

  • Wm Randolph Franklin, Narayanaswami Chandrasekhar, Mohan Kankanhalli, Varol Akman, and Peter YF Wu. Efficient geometric operations for CAD. In Michael J. Wozny, Joshua U. Turner, and K. Preiss, editors, Geometric Modeling for Product Engineering, pages 485–498. Elsevier Science Publishers B.V. (North-Holland), 1990.
    [details] [full text] [BibTeX▼]

1987

  • Wm Randolph Franklin. Polygon properties calculated from the vertex neighborhoods. In Proc. 3rd Annu. ACM Sympos. Comput. Geom., 110–118. 1987.
    [details] [full text] [BibTeX▼]

1982

  • Wm Randolph Franklin. Efficient polyhedron intersection and union. In Proc. Graphics Interface, 73–80. Toronto, 1982.
    [details] [full text] [BibTeX▼]

Contact: WRF