- Professional summary: Professor, ECSE Dept, RPI — BSc (Toronto) — AM, PhD, Applied Math (Harvard) — Program Director, Numeric, Symbolic, and Geometric Computation Program, CISE, National Science Foundation, 2000–2002 — Visiting Professor, UC Berkeley, 1985–1986 — Visiting positions at Genoa, Laval, CSIRO Canberra, National University of Singapore, 1992–1993.
- List of my 16 PhD and 68 masters graduates (former students).
- Brief Bio — GPG key (I welcome GPG-encrypted email.) — Vcard
- 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
- Google scholar profile
- Recent Grants
- Search my wiki: You can search my wiki by using the search box at the top right of most pages. (This does not search my pages that are not part of the wiki, such as pages over 10 years old. However, google works there.)
Paper and Talk Awards
- Winner (2nd place), GISCUP 2015: Salles V. G. Magalhães, Marcus V. A. Andrade, W. Randolph Franklin and Wenli Li. Fast path planning under polygonal obstacle constraints. In 4th GIS-focused algorithm competition, GISCUP 2015, co-located with ACM SIGSPATIAL GIS, Bellevue WA USA, 4 Nov 2015. (paper).
- Winner of the Best Paper Award (2nd place), AGILE 2012: Salles V. G. Magalhães, Marcus V. A. Andrade, W. Randolph Franklin and Guilherme C. Pena. A new method for computing the drainage network based on raising the level of an ocean surrounding the terrain. In Jérome Gensel and Didier Josselin and Danny Vandenbroucke, editor, Bridging the Geographic Information Sciences: International AGILE'2012 Conference, pages 391-407. Springer, 24-27 April 2012. (URL) (paper, talk).
- Winner of best paper award, Geoinfo 2013: Chaulio R. Ferreira, Marcus V. A. Andrade, Salles V. G. Magalhães, W. R. Franklin and Guilherme C. Pena. A Parallel Sweep Line Algorithm for Visibility Computation. In Geoinfo 2013, XIV Brazilian Symposium on GeoInformatics, Campos do Jordão, SP, Brazil, 24-27 Nov 2013. (paper).
- Winner of the best fast forward presentation award, ACM SIGSPATIAL GIS 2009: Tsz-Yam Lau, You Li, Zhongyi Xie and W. Randolph Franklin. Sea Floor Bathymetry Trackline Surface Fitting Without Visible Artifacts Using ODETLAP. In 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2009), Seattle WA USA, 4-6 Nov 2009. (paper, video, talk: pptx, pdf, poster: pptx, pdf).
Geometry has been my overriding interest since high school in the 1960s. Geometry is the "branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids" (Merriam–Webster dictionary). The Geo in geometry is from the Greek Γη meaning, ''earth, ground, land''. (The American Heritageï¿½ Book of English Usage). My major recently concluded project was Geo*, a DARPA–funded project for representing and operating on terrain, that is, elevation.
My big long-term unsolved problem is to devise a mathematics of terrain, which would respect its physical properties. To date, I've been nibbling around the edges.
One recently ended project (Cutler, Zimmie, Franklin. NSF CMMI-0835762: CDI-Type I: Fundamental Terrain Representations and Operations) attempted to predict how erosion occurs in levee failure by overtopping, and, after a failure, to reverse-simulate what happened.
A earlier major project was Geo*, funded by DARPA, studied representing and operating on terrain, that is, elevation.
I've applied the same underlying principles in Computational Geometry producing algorithms useful for large datasets, mostly in 3D, and usually implemented.
Both topics are applications of my long term theme of emphasizing small, simple, and fast data structures and algorithms. Note that efficiency in both space and time can become more important as machines get faster. This research is applicable to computational cartography, computer graphics, computational geometry, and geographic information science.
16 PhD students (7 currently employed at a college), and 68 masters students have been graduated under my advisement, (names and theses).
My research has been externally funded by the National Science Foundation under Grants ENG-7908139, ECS-8021504, ECS-8351942, CCF-9102553, CCF-0306502, DMS-0327634, CMMI-0835762 and IIS-1117277 by DARPA/DSO, via the NGA, under the GeoStar program, by the US Army Topographic Engineering Center, and by IBM, Sun Microsystems, and Schlumberger-Doll Research.
Many of the algorithms have been implemented. The code is available for nonprofit research and education. RPI Computer graphics group
- A 2-slide summary of my research is here.
- A good summary talk is this:
Research on Terrain Visibility, Viewshed, Observer Siting
Given a large DEM terrain, we have efficient parallel (using both OpenMP and CUDA) algorithms to compute
- the viewshed of an observer,
- the visibility index, i.e., the viewshed's area, of every point,
- how to site multiple observers to jointly cover the most terrain, perhaps while requiring the observers to be intervisible.
Here is some of our published work. There are links to papers and talks.
- Chaulio R. Ferreira, Marcus V. A. Andrade, Salles V. G. Magalhães and W. Randolph Franklin. An efficient external memory algorithm for terrain viewshed computation. , 2015. submitted. (paper).
- Guilherme C. Pena, Marcus V.A. Andrade, Salles V.G. Magalhães, W. R. Franklin and Chaulio R. Ferreira. An Improved Parallel Algorithm using GPU for Siting Observers on Terrain. In 16th International Conference on Enterprise Information Systems (ICEIS 2014), pages 367-375, Lisbon, 27-30 April 2014. (paper, talk).
- Chaulio R. Ferreira, Marcus V. A. Andrade, Salles V. G. Magalhães, W. R. Franklin and Guilherme C. Pena. A parallel algorithm for viewshed computation on grid terrains. Journal of information and data management, 5(1), 2014. invited. (paper).
- Guilherme Pena, Salles Magalhães, Marcus Andrade, Randolph Franklin, Chaulio Ferreira, Wenli Li and Daniel Benedetti. An efficient GPU multiple-observer siting method based on sparse-matrix multiplication. In 3rd ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data (BigSpatial) 2014, Dallas TX USA, 4 Nov 2014. (paper, talk).
- Wenli Li, W. Randolph Franklin, Daniel N. Benedetti and Salles V. G. Magalhães. Parallel Multiple Observer Siting on Terrain. In 22nd ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL 2014), Dallas, Texas, USA, 4-7 Nov 2014. (paper, poster).
- Chaulio R. Ferreira, Marcus V. A. Andrade, Salles V. G. Magalhães, W. R. Franklin and Guilherme C. Pena. A Parallel Sweep Line Algorithm for Visibility Computation. In Geoinfo 2013, XIV Brazilian Symposium on GeoInformatics, Campos do Jordão, SP, Brazil, 24-27 Nov 2013. Winner of best paper award, http://www.geoinfo.info/geoinfo2013/index.php. (paper).
- Wenli Li, W. Randolph Franklin and Daniel Benedetti. Parallel Multiple Observer Siting on Terrain. In 23rd Fall Workshop on Computational Geometry, City College, New York City, USA, 25-26 Oct 2013. (extended abstract). (paper, talk).
- Salles V. G. Magalhães, Marcus V. A. Andrade and W. Randolph Franklin. Multiple Observer Siting in Huge Terrains Stored in External Memory. International Journal of Computer Information Systems and Industrial Management (IJCISIM), 3, 2011. (URL) (paper).
- Marcus V. A. Andrade, Salles V. G. Magalhães, Mirella A. Magalhães, W. Randolph Franklin and Barbara M. Cutler. Efficient viewshed computation on terrain in external memory. Geoinformatica, 2010. (online 26 Nov 2009). (URL) (paper).
- Daniel M. Tracy, W. Randolph Franklin, Barbara Cutler , Marcus A Andrade, Franklin T Luk, Metin Inanc and Zhongyi Xie. Multiple observer siting and path planning on lossily compressed terrain. In Proceedings of SPIE Vol. 6697 Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, San Diego CA. International Society for Optical Engineering, 27 August 2007. paper 6697-16. (paper).
- Daniel M. Tracy, W Randolph Franklin and Franklin Luk. Multiple Observer Siting on a Compressed Terrain (extended abstract). In 16th Fall Workshop on Computational Geometry, Smith College, Northampton MA, 10-11 Nov 2006. (abstract, poster).
- W. Randolph Franklin and Christian Vogt. Tradeoffs when multiple observer siting on large terrain cells. In Andreas Riedl and Wolfgang Kainz and Gregory Elmes, editor, Progress in Spatial Data Handling: 12th International Symposium on Spatial Data Handling, pages 845-861. Springer, 2006. ISBN 978-3-540-35588-5. (paper, talk).
- W. Randolph Franklin and Christian Vogt. Efficient observer siting on large terrain cells (extended abstract). In GIScience 2004: Third International Conference on Geographic Information Science, U Maryland College Park, 20-23 Oct 2004. (paper, talk).
- W. Randolph Franklin. Siting observers on terrain. In Dianne Richardson and Peter van Oosterom, editor, Advances in Spatial Data Handling: 10th International Symposium on Spatial Data Handling, pages 109-120, 2002. (paper).
- W. Randolph Franklin. Approximating visibility. In GIScience 2000, Savannah, Georgia, USA, 30 Oct 2000. (paper).
- Wm Randolph Franklin and Clark Ray. Higher isn't Necessarily Better: Visibility Algorithms and Experiments. In Thomas C. Waugh and Richard G. Healey, editor, Advances in GIS Research: Sixth International Symposium on Spatial Data Handling, pages 751-770, Edinburgh. The International Geographical Union's Commission on Geographical Information Systems and The Association for Geographic Information, 5-9 Sept 1994. (paper).
Here are some related papers, to 3D object visibility
- Wm Randolph Franklin and Mohan Kankanhalli. Parallel Object-Space Hidden Surface Removal. In Proceedings of SIGGRAPH'90, pages 87-94, Aug 1990. (paper).
- Wm Randolph Franklin and Varol Akman. Adaptive Grid for polyhedral visibility in object space, an implementation. Computer Journal, 31(1):56-60, Feb 1988. (paper).
- Wm Randolph Franklin. A linear time exact hidden surface algorithm. In Kenneth I. Joy and others, editor, Tutorial: Computer Graphics: Image Synthesis, pages 218-224. , 1988.
- Wm Randolph Franklin and Varol Akman. A simple and efficient haloed line algorithm for hidden line elimination. Computer Graphics Forum, 6(2):103-109, May 1987. (paper).
- Wm Randolph Franklin. An exact hidden sphere algorithm that operates in linear time. Comput. Graph. Image Process., 15:364-379, 1981. (paper).
- Wm Randolph Franklin. A linear time exact hidden surface algorithm. Comput. Graph., 14(3):117-123, 1980. (paper).
- Wm Randolph Franklin. Combinatorics of hidden surface algorithms. . PhD thesis, Center for Research in Computing Technology, Harvard Univ., Jun 1978. (parts: 1, 2, 3, 4).
- W. Randolph Franklin. Prism — A Prism Plotting Program. In Allan H. Schmidt, editor, Mapping Software and Cartographic Data Bases, pages 75-79. , 1979.
- Wm Randolph Franklin and Harry R. Lewis. 3-D Graphic Display of Discrete Spatial Data By Prism Maps. In Proc. SIGGRAPH'78, pages 70-75, Aug 1978. (paper).
More Research Details
These are on a separate page, whose table of contents follows.
- 1. Computational cartography research
- 1.1 Alternate Terrain Reps
- 1.2 Parallel and distributed cartography computation
- 1.3 Hydrography, bathymetry
- 1.4 Erosion modeling
- 1.5 GeoStar
- 1.6 Visibility, Multi-observer siting, Path planning
- 1.7 Gridding contours
- 1.8 Overlaying two maps (aka Planar graphs)
- 1.9 Logic programming for map overlay
- 1.10 Triangulated irregular network
- 1.11 Prism
- 1.12 General cartography
- 2. Computational geometry research
- 2.1 Fundamentals
- 2.2 Local data structures for polyhedra
- 2.3 Parallel and distributed geometry algorithms
- 2.4 Connected components in $E^3$
- 2.5 Linear time object space hidden surfaces
- 2.6 Nearest points in E2 and E3
- 2.7 All near point pairs in E3
- 2.8 Overlaying 3D triangulations
- 2.9 UNION2, UNION3, and Boolean operations and their mass properties
- 2.10 Perimeter and area of the union of circles
- 2.11 Octree creation
- 2.12 Edge intersection
- 2.13 Misc papers
- 3. Other research topics
- 4. Open topics
- 5. Old program solicitations
- 6. Short notes
- 7. Advice
- 8. Proposal writers cheat sheet
- 9. Workshop organizers cheat sheet
- 10. Software notes and reviews
- Advice to: Grad Student Applicants Apparently only ONE person a year reads this — DQE Examineesknow your material — Doctoral Candidacy Examineeshave a plan — Job Seekers particularly for older professionals
- Textbook Reviewing CriteriaMake it easy to teach a good course
- Famous RPI graphics–related grads It is possible to survive RPI and prosper
- RPI pages: Academic calendarWhen do classes start and end; holidays — Class scheduleTimes, rooms, profs
- Travel Photos