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1 Coordinates

The best URL for this page is https://wrfranklin.org/ aka httpsCOLONSLASHSLASHwrfranklinDOTorg. Some mail systems rewrite URLs in the body of messages, so my email signature block can be made wrong.

Email is the best way to contact me; e.g., at web23ATwrfranklinDOTorg. I have many addresses; a surprising failure mode is a correspondent combining the user and hostname from two different addresses. Even that works when I own the domain.

2 News

I am President and Managing Director of Quantum Geometry LLC. We design and implement parallel algorithms for computational geometry, CAD, and computational cartography executing on multicore and many core (NVIDIA GPU) processors.

After 45 years on the faculty of RPI, I retired in June 2023. I am still associated with RPI as an (unpaid undutied) Emeritus Professor. See the 2023 ECSE Newsletter .

The accomplishments of my former students are my proudest achievement.

3 Sponsoring conferences and contests

Since 2022 I've been a private sponsor of several GIS and geometry related conferences that I've enjoyed attending, and benefited from, over the decades. These include-

  1. ACM SIGSPATIAL 2024 29 October - 1 November, 2024, Atlanta GA USA: GIS Cup awards and travel grants.

  2. SIAM International Meshing Roundtable Workshop 2024 (SIAM IMR24) 5-8 March, 2024, Baltimore, MD, USA: student travel support.

  3. ACM SIGSPATIAL 2023 13-16 November 2023, Hamburg Germany: GIS Cup awards and travel grants.

  4. The International Geometry Summit 2023 (IGS’23) 3-7 July 2023, Genova Italy: Silver sponsor.

  5. ACM SIGSPATIAL Nov 2022 Seattle: Sponsored the travel of ten GIS Cup winners and international students. The reasons were to raise interest in the contest, in which my students and I came first in 2018 second in 2015 and 2016, and hence raise interest in this field, and to encourage international students to continue in this field.

I might like to directly sponsor a contest that would draw attention to the field but haven't figured out the details. Here is a note on that. Suggestions are welcome.

4 Research Summary

I develop and implement fast parallel algorithms on very large geometric datasets in CAD and GIS. I've also modeled and processed large terrain databases, e.g., to compress, to compute hydrography and visibility, and to site observers, and compressed 5D environmental data sets. The algorithms are the fastest in their class; awards are listed below.

3D-EPUG-OVERLAY nicely illustrates our methods. It is a fast, exact, parallel, memory-efficient, algorithm for computing the intersection between two large 3-D triangular meshes with geometric degeneracies. Applications include CAD/CAM, CFD, GIS, and additive manufacturing. 3D-EPUG-OVERLAY combines 5 techniques: multiple precision rational numbers to eliminate roundoff errors during the computations; Simulation of Simplicity to properly handle geometric degeneracies; simple data representations and only local topological information to simplify the correct processing of the data and make the algorithm more parallelizable; a uniform grid to efficiently index the data, and accelerate testing pairs of triangles for intersection or locating points in the mesh; and parallel programming to exploit current hardware. 3D-EPUG-OVERLAY is up to 101 times faster than LibiGL, and comparable to QuickCSG, a parallel inexact algorithm. 3D-EPUG-OVERLAY is also more memory efficient. In all test cases, 3D-EPUG-OVERLAY's result matched the reference solution. It is freely available, albeit research-quality code, for nonprofit research and education at https://github.com/sallesviana/MeshIntersection .

Recent papers and talks:

2022

  • W. Randolph Franklin and Salles Viana Gomes de Magalhães. Implementing simulation of simplicity for geometric degeneracies. In 4th ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2022). 1 Nov 2022.
    [abstract▼] [details] [full text] [BibTeX▼]
  • 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

  • W. Randolph Franklin, Salles Viana Gomes de Magalhães, and Wenli Li. Siting thousands of radio transmitter towers on terrains with billions of points. 2020. arXiv 2006.16783. arXiv:2006.16783.
    [abstract▼] [details] [full text] [BibTeX▼]
  • Salles V. G. de Magalhães, W. Randolph Franklin, and Marcus V. A. Andrade. An efficient and exact parallel algorithm for intersecting large 3-d triangular meshes using arithmetic filters. J. Computer Aided Design, March 2020. online 2019-12-19. doi:https://doi.org/10.1016/j.cad.2019.102801.
    [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▼]
  • Marcelo de Matos Menezes, Salles Viana Gomes Magalhães, W. Randolph Franklin, Matheus Aguilar de Oliveira, and Rodrigo E. O. Bauer Chichorro. Accelerating the exact evaluation of geometric predicates with GPUs. In Suzanne Shontz, Joaquim Peiró, and Ryan Viertel, editors, 28th International Meshing Roundtable. Buffalo, NY, USA, 16 Oct 2019. doi:10.5281/zenodo.3653101.
    [abstract▼] [details] [full text] [slides] [BibTeX▼]
  • W. Randolph Franklin and Salles V. G. de Magalhães. Computing intersection areas of overlaid 2d meshes. In IGS2019 International Geometry Summit Posters' proceedings. Vancouver, Canada, 17–21 June 2019. Solid Modeling Association.
    [abstract▼] [details] [full text] [poster] [fastforward] [BibTeX▼]

2018

  • Salles Viana Gomes de Magalhães, W. Randolph Franklin, and Ricardo dos Santos Ferreira. Fast analysis of upstream features on spatial networks (GIS Cup). In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, SIGSPATIAL '18, 622–625. New York, NY, USA, 2018. ACM. Winner (1st place). doi:https://doi.org/10.1145/3274895.3276474.
    [abstract▼] [details] [full text] [slides] [BibTeX▼]
  • 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▼]
  • W. Randolph Franklin, Salles V. G. de Magalhães, and Marcus V. A. Andrade. Exact fast parallel intersection of large 3-D triangular meshes. In 27th International Meshing Roundtable. Alberqueque, New Mexico, 2 Oct 2018.
    [abstract▼] [details] [full text] [slides] [BibTeX▼]

2017

  • W. Randolph Franklin. Applications of geometry. In Kenneth H Rosen, editor, Handbook of Discrete and Combinatorial Mathematics, Discrete Mathematics and Its Applications, chapter 13.8, pages 998–1022. CRC Press, 2nd edition, 1 Dec 2017.
    [abstract▼] [details] [full text] [BibTeX▼]

5 Professional summary

  1. In 8 lines:

    1. Emeritus Professor, ECSE Dept, RPI

    2. BSc (Toronto)

    3. AM, PhD, Applied Math (Harvard)

    4. Program Director, Numeric, Symbolic, and Geometric Computation Program, CISE, National Science Foundation, 2000—2002

    5. Visiting Professor, UC Berkeley, 1985—1986

    6. Visiting positions at Genoa, Laval, CSIRO Canberra, National University of Singapore, 1992—1993.

    7. Visitor at Georgia Tech, 2016.

  2. Brief Bio

  3. Long resume(Education - Professional Career - Publications - Presentations - Synergistic Activities and Service - Grad Students - Teaching or Course Development - Hardware Used - Professional Memberships - Major Research Grants), including postal address, email (GPG welcomed), phone

  4. Google scholar profile.

  5. Recent grants.

  6. Research

  7. Software

  8. Publications

  9. Awards

  10. RPI Articles

  11. Past students

  12. Advice

  13. Misc

  14. In favor of spatial computing contests

6 ECSE-4964/6964 Quantum Computer Programming

Poster, Syllabus, Course site.

I created this fun course based on my interests and skills, and taught it up to Fall 2022. My material is freely available for nonprofit research and education; I welcome a note if you find it useful.

7 Fun Travel

In Sept 2023 we drove my Tesla Y across the USA from Albany NY to San Diego CA on an sightseeing route: 17 days, 4183 mi, 55 charges. The literal highlight was driving up Pike's Peak. Figurative highlights included Mt Sunflower, Kansas's high point, and other fun stuff. In 2021, we'd driven this Tesla from San Diego to Albany.

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