# Boolean operations, local topology theory and example applications

See also Overlaying maps, planar graphs, polyhedra.

#### 2022

- 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.***J. Computer Aided Design*, September 2022. Special Issue: 28th International Meshing Roundtable: Mesh Modeling for Simulations and Visualization. URL: https://www.sciencedirect.com/science/article/abs/pii/S0010448522000616, doi:https://doi.org/10.1016/j.cad.2022.103285.

[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, Andreas Züfle, and Cyrus Shahabi, editors,*Spatial Gems*, volume 1, chapter 11. ACM, 2022. URL: https://www.spatialgems.net/.

[abstract▼] [details] [full text] [BibTeX▼] - W. Randolph Franklin and Salles Viana Gomes de Magalhães.
**Minimal representations of polygons and polyhedra.**In John Krumm, Andreas Züfle, and Cyrus Shahabi, editors,*Spatial Gems*, volume 1, chapter 5. ACM, 2022. URL: https://www.spatialgems.net/.

[abstract▼] [details] [full text] [BibTeX▼]

#### 2021

- W. Randolph Franklin, Salles Viana Gomes de Magalhães, and Eric N Landis.
**Fast 3-D Euclidean connected components.**In John Krumm, editor,*3rd ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2021)*. ACM, 2 nov 2021. URL: https://www.spatialgems.net/.

[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▼]

#### 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://wrfranklin.org/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.

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#### 1982

- Wm Randolph Franklin.
**Efficient polyhedron intersection and union.**In*Proc. Graphics Interface*, 73–80. Toronto, 1982.

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*Contact:* WRF