This page provides links to papers and related material on my work on geometric algorithms for Layered Manufacturing and its applications. Portions of this work have been/are being supported by grants from NSF, NIST, and ARL (via the AHPCRC), and have also benefited significantly from a collaboration with Stratasys, Inc.. (Acknowledgements.)

Here's a summary of work done during this project.

This is joint work with various subsets of the following group
of individuals:

{P. Castillo, P. Gupta, M. Hon, I. Ilinkin,
E. Johnson, R. Miyaoka, M. Monga, J. Majhi, V. Rajagopal, R. Sriram, J. Schwerdt, M. Smid, R. Sweet}.

(Note: All papers are copyrighted by their respective publishers.)

- Research poster highlighting results of the project. [PDF]
- Slides highlighting results of the project (more detail). [HTML]

- V. Rajagopal, R. Janardan, R. Miyaoka, M. Monga, R. Sweet.
``Modeling and simulation in flexible ureteroscopy''. Proceedings of
the 24th Annual Meeting of the Engineering and Urology Society, Chicago, IL, 2009. Outstanding Paper Award (``Top-10'' submission from among 127 peer-reviewed abstracts; 18 to 20 reviews per submission.) Abstract [PDF]; Poster [PDF]; Video [WMV]

- I. Ilinkin, R. Janardan, M. Smid, E. Johnson, P. Castillo,
and J. Schwerdt.
``Heuristics for estimating contact-area of supports in
layered manufacturing''.
*ACM Journal of Experimental Algorithmics*, 11(1.6):1-19, 2007. [PDF] (Abbreviated preliminary version in*Proc. 16th CCCG, 2004,*pp. 91-94.) - R. Janardan and M. Smid. ``Geometric algorithms for
Layered Manufacturing''.
Chapter 7 in
*Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing*, (eds.: R. Janardan, M. Smid, and D. Dutta). Volume 67 of the DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, Providence, RI, 2005 [PDF] - R. Janardan and T. Woo. ``Manufacturing processes''.
Chapter 55 in
*Handbook of Discrete and Computational Geometry*, (eds.: J.E. Goodman and J. O'Rourke). 2nd edition, CRC Press, Boca Raton, FL, 2004. [PDF] (Includes a survey section on geometric methods in layered manufacturing.) - J. Schwerdt, M. Smid, R. Janardan, and E. Johnson.
``Protecting critical facets in layered manufacturing:
implementation and experimental results''.
*Computer-Aided Design*, 35(7):647-657, 2003. (Also*Proc. 2nd ALENEX*, 2000.) [PDF] - M. Hon, R. Janardan, J. Schwerdt, and M. Smid.
``Minimizing the total projection of a set of vectors, with
applications to layered manufacturing''.
*Computer-Aided Design*, 35(1):57-68, 2003. (Also.*Proc. 1st Intl. Workshop on Computational Geometry*, 2001.) [PDF] - J. Schwerdt, M. Smid, M. Hon, and R. Janardan
``Computing an optimal hatching direction in layered manufacturing''.
*International Journal of Computer Mathematics*. 79(10):1067-1081, 2002. (Also.*Proc. 1st Intl. Workshop on Computational Geometry*, 2001. (In same conf. paper as #2).) [PDF] - I. Ilinkin, R. Janardan, and M. Smid.
``Terrain polygon decomposition, with application to
layered manufacturing ''
*Proc. 8th Intl. Conference on Computing and Combinatorics, (COCOON)*, LNCS 2387, pp. 381-390, 2002. [PDF] - I. Ilinkin, R. Janardan, J. Majhi, J. Schwerdt, M. Smid, and R. Sriram.
``A decomposition-based approach to layered manufacturing''.
*Computational Geometry: Theory and Applications*, 23:117-151, 2002. (Also*Proc. 7th WADS*, 2001.) [PDF] - J. Majhi, R. Janardan, M. Smid, and J. Schwerdt.
``Multi-criteria geometric optimization problems in layered
manufacturing''
*International Journal of Mathematical Algorithms*, 2:201-225, 2001. (Also*Proc. 14th ACM SoCG*, 1998.) [PDF] - J. Schwerdt, M. Smid, R. Janardan, E. Johnson, and J. Majhi.
``Protecting critical facets in layered manufacturing''.
*Computational Geometry: Theory and Applications*, 16:187-210, 2000. (Also*Proc. 19th FSTTCS*, 1999.) [PDF] - J. Majhi, R. Janardan, M. Smid, and P. Gupta.
``On some geometric optimization problems in layered manufacturing''.
*Computational Geometry: Theory and Applications*, 12:219-239, 1999. (Also*Proc. 5th WADS*, 1997.) [PDF] - J. Schwerdt, M. Smid, J. Majhi, and R. Janardan.
``Computing the width of a three-dimensional point-set:
an experimental study''.
*ACM Journal of Experimental Algorithmics*, 4:(8) 1999. Invited paper. (Also*Proc. 2nd WAE*, 1998.) [PDF] - J. Majhi, R. Janardan, J. Schwerdt, M. Smid, and P. Gupta.
``Minimizing support structures and trapped area in
two-dimensional layered manufacturing''.
*Computational Geometry: Theory and Applications*, 12:241-267, 1999. (Also*Proc. 5th WADS*, 1997. (In same conf. paper as #8.)) [PDF]

- V. Rajagopal. Modeling and simulation in flexible ureteroscopy. M.S. Report (Plan B), Dept. of Computer Science and Engineering, Univ. of Minnesota, July 2009.
- I. Ilinkin.
*Geometric algorithms with applications to layered manufacturing*. Ph.D. Thesis, Dept. of Computer Science and Engineering, Univ. of Minnesota, August 2003. - J. Majhi.
*Geometric methods in computer-aided design and manufacturing*. Ph.D. Thesis, Dept. of Computer Science and Engineering, Univ. of Minnesota, June 1998. - P. Castillo.
*Computational geometry and layered manufacturing.*M.S. Report (Plan B), Dept. of Computer Science and Engineering, Univ. of Minnesota, May 2001. - M. Hon.
*Minimizing the total projection of a set of vectors, with applications to layered manufacturing*. M.S. Thesis (Plan A), Dept. of Computer Science and Engineering, Univ. of Minnesota, January 2001. - E. Johnson.
*Support generation for three-dimensional layered manufacturing*. M.S. Report (Plan B), Dept. of Computer Science and Engineering, Univ. of Minnesota, May 1999.

Here's an edited volume of refereed papers that resulted from an NSF-funded DIMACS Workshop on Computational Geometry and Computer-Aided Design and Manufacturing that I co-organized with Michiel Smid and Debasish Dutta.

This material is based upon work supported by the National Science Foundation under Grant No. CCR-9712226 and Grant No. CCF-0514950. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Research support from the National Institute of Standards and Technology under Contract No. 60NANB8D0002 and the Army Research Laboratories under Contract No. DAAD19-01-2-0014, support from the National Science Foundation for the DIMACS Workshop, and facilities support from the Minnesota Supercomputer Institute is also gratefully acknowledged.