Publications (after 1998)
Perturbation of solid models:
Subsequent papers and book (2010):
Topological invariance of parametric objects (TR #1061,
DIRO, Université de Montréal)
Technical report #1061 consists of Parts I, II and III, below.
Parts I and II were published in shortened form as:
Self-intersection of composite curves and surfaces.
Computer Aided Geometric Design (15), No 5, 507-527, May 1998.
Part III was published in slightly modified form as:
Equivalence of topological form for curvilinear geometric
International Journal of Computational Geometry
and Applications. (10), No. 6, 609-622, 2000.
A hard copy of TR #1061 is available on request from
N. F. Stewart:
Part I: Perturbation of Bézier curves
Part II: Perturbation of triangular Bézier patches
Part III: Preservation of the topological form of objects defined by
Ferguson, D. R., Peters, T. J. and Stewart, N. F. Well-defined
toplogy for robust modelling and simultions. MSRI Workshop on
Mathematical Foundations of CAD. Mathematical Sciences Research
Institute, Berkeley, CA, June 4-5, 1999.
- Stewart, N. F. Perturbations of well-formed solids. Sixth
SIAM Conference on Geometric Design, Albuquerque, NM, November
2-5, 1999. SIAM News, July/August 1999.
- Egli, R. and Stewart, N. F. A framework for system
specification using chains on cell complexes. Computer-Aided
Design (31), 669-681, 1999. Due to a production error, the
complete paper was reprinted: Computer-Aided Design (32),
- Peters, T. J. and Stewart, N. F. Computational Topology
for CFD: theorems, criteria and issues. First MIT Conference on
Computational Fluid and Solid Mechanics, June 12-14, 2001. In
Computational Fluid and Solid Mechanics, Vol. 2 (ed. K. J. Bathe),
Cambridge MA, Elsevier, 2001, pp. 951-953.
- Egli, R. and Stewart, N. F. Chain-model shape-pattern
schemata. Planning and Design B (29), No. 5, 779-788,
- Stewart, N. F. Computation of well-defined and accurate
representations of the intersection of two sets specified by
trimmed-NURBS patches. Workshop on Geometric Modelling and
Animation, Foundations of Computational Mathematics (FOCM),
Minneapolis, MI, August 5-14, 2002. Abstract, p. 40.
- Mow, C., Peters, T. J. and Stewart, N. F. Specifying useful
error bounds for geometry tools: an intersector exemplar.
Computer Aided Geometric Design (20), No. 5, 247-251,
- Ferguson, D. R., Hoffmann, C. M., Maekawa, T., Patrikalakis,
N. M., Peters, T. J., Sakkalis, T. and Stewart, N. F. Accurate
numerical intersection of geometric objects. International
Conference on Industrial and Applied Mathematics (ICIAM03),
Sydney, Australia, July 7-11, 2003. Abstract, p. 96.
- Peters, T. J., et al
Computational topology for regular closed sets
(within the ITANGO project). Topology Atlas Contributions
(9), No. 1, 2004, 12 pp.
- Hoffmann, C. M., Park, G., Simard, J.-R. and Stewart, N. F.
Residual iteration and accurate polynomial evaluation for
shape-interrogation applications. Proceedings, ACM Symposium on
Solid Modeling and Applications SM '04, Genova, Italy,
June 9-11, 2004, pp. 9-14.
( pdf )
- Stewart, N. F. Accuracy in shape interrogation applications.
Invited talk, ACM Symposium on Solid Modeling and Applications,
SM '04, Genova, Italy, June 9-11, 2004. See Hoffmann-Stewart, 2005.
Egli, R. and Stewart, N. F. Chain models in simulation.
Mathematics and Computers in Simulation (66), No. 6,
449-468, 2004. (pdf)
- Moore, E. L. F., Peters, T. J., Ferguson, D. R. and
Stewart, N. F. Integrating topology and geometry for
macro-molecular simulations (Extended Abstract, Work in
Progress) Dagstuhl Seminar Proceedings,
Dagstuhl Seminar 04351, August 22-27, 2004.
- Hoffmann, C. M. and Stewart, N. F. Accuracy and semantics
in shape-interrogation applications.
Graphical Models (67), No. 5, 373-389, September 2005.)
- Andersson, L.-E., Stewart, N. F. and Zidani, M. Conditions for use of a
non-selfintersection conjecture. Computer Aided Geometric Design (23),
See also: Proof of a non-selfintersection conjecture,
Technical Report 1276, DIRO, April 24, 2006, containing additional proof.
- Stewart, N. F. and Zidani, M. Transfinite interpolation for well-definition in
error analysis in solid modelling.
Dagstuhl Seminar Proceedings,
Dagstuhl Seminar 06021, January 8-13, 2006.
Dagstuhl Proceedings). Lecture Notes in Computer Science LNCS 5045,
pp. 181-192, Springer, 2008.
- Qi, J., Shapiro, V. and Stewart, N. F. Single-set and class-of-sets semantics for
Computer-Aided Design (38), No. 10, 1088-1098, October 2006.
- Jiang, D. and Stewart, N. F. Backward error analysis in computational geometry.
Sixth Annual International Workshop on Computational Geometry and Applications,
Glasgow, UK, May 8-11, 2006. Lecture Notes in Computer Science LNCS3980, 50-60,
Springer-Verlag, Heidelberg, 2006
- Andersson, L.-E., Stewart, N. F. and Zidani, M. Error analysis
for operations in solid modeling in the presence of uncertainty.
SIAM J. Scientific Computing (29), No. 2, 811-826, 2007.
- Jiang, D. and Stewart, N. F. Reliable joining of surfaces for
combined mesh-surface models. Proceedings, 21st European Conference on
Modelling and Simulation (ECMS 2007), Prague, Czech Republic, June 4-6,
- Jiang, D. and Stewart, N. F.
Robustness of Boolean operations on subdivision-surface models.
Lecture Notes in Computer Science LNCS 5492-0161, pp. 161-174, Springer-Verlag, Heidelberg, 2009.
- Jiang, D. and Stewart, N. F. Floating-point arithmetic for computational-geometry problems with uncertain data. International Journal of
Computational Geometry and Applications (19), No.4, 371-385, August 2009.
- Andersson, L.-E. and Stewart, N. F. Introduction to the Mathematics of Subdivision Surfaces, Society for Industrial and Applied Mathematics
(SIAM), 356 pages, 2010.
- Nivoliers, V., Gérot, C., Ostromoukhov, V. and Stewart, N. F. L-system construction of one-dimensional subdivision schemes. Computer
Aided Geometric Design (29), No. 2, 150-161, 2012.
- Shao, P. and Stewart, N. F. Managing uncertainty and discontinuous condition numbers in finite-precision geometric computation. Soft
Computing (17), No. 8, 1425-1437, August 2013.
- Abdoli, S., Boumedien-Zidani, M. and Stewart, N. F. Uncertainty management in feature-based geometric modeling and data exchange. Second
International Conference on Vulnerability and Risk Analysis and Management (ICVRAM2014). University of Liverpool, UK, July 13-16, 2014. Proceedings,