Publications (after 1998)
Perturbation of solid models:

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:

Selfintersection of composite curves and surfaces.
Computer Aided Geometric Design (15), No 5, 507527, May 1998.

Part III was published in slightly modified form as:

Equivalence of topological form for curvilinear geometric
objects.
International Journal of Computational Geometry
and Applications. (10), No. 6, 609622, 2000.

A hard copy of TR #1061 is available on request from
N. F. Stewart:
stewart@iro.umontreal.ca

Part I: Perturbation of Bézier curves

Part II: Perturbation of triangular Bézier patches

Part III: Preservation of the topological form of objects defined by
parametric patches
Subsequent papers and book (2010):

Ferguson, D. R., Peters, T. J. and Stewart, N. F. Welldefined
toplogy for robust modelling and simultions. MSRI Workshop on
Mathematical Foundations of CAD. Mathematical Sciences Research
Institute, Berkeley, CA, June 45, 1999.
 Stewart, N. F. Perturbations of wellformed solids. Sixth
SIAM Conference on Geometric Design, Albuquerque, NM, November
25, 1999. SIAM News, July/August 1999.
 Egli, R. and Stewart, N. F. A framework for system
specification using chains on cell complexes. ComputerAided
Design (31), 669681, 1999. Due to a production error, the
complete paper was reprinted: ComputerAided Design (32),
447459, 2000.
 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 1214, 2001. In
Computational Fluid and Solid Mechanics, Vol. 2 (ed. K. J. Bathe),
Cambridge MA, Elsevier, 2001, pp. 951953.
 Egli, R. and Stewart, N. F. Chainmodel shapepattern
schemata. Planning and Design B (29), No. 5, 779788,
2002.
 Stewart, N. F. Computation of welldefined and accurate
representations of the intersection of two sets specified by
trimmedNURBS patches. Workshop on Geometric Modelling and
Animation, Foundations of Computational Mathematics (FOCM),
Minneapolis, MI, August 514, 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, 247251,
2003.
 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 711, 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.
(
Online journal)
 Hoffmann, C. M., Park, G., Simard, J.R. and Stewart, N. F.
Residual iteration and accurate polynomial evaluation for
shapeinterrogation applications. Proceedings, ACM Symposium on
Solid Modeling and Applications SM '04, Genova, Italy,
June 911, 2004, pp. 914.
( pdf )
 Stewart, N. F. Accuracy in shape interrogation applications.
Invited talk, ACM Symposium on Solid Modeling and Applications,
SM '04, Genova, Italy, June 911, 2004. See HoffmannStewart, 2005.

Egli, R. and Stewart, N. F. Chain models in simulation.
Mathematics and Computers in Simulation (66), No. 6,
449468, 2004. (pdf)
 Moore, E. L. F., Peters, T. J., Ferguson, D. R. and
Stewart, N. F. Integrating topology and geometry for
macromolecular simulations (Extended Abstract, Work in
Progress) Dagstuhl Seminar Proceedings,
Dagstuhl Seminar 04351, August 2227, 2004.
Manuscript:
(pdf)
(
Dagstuhl Proceedings)
 Hoffmann, C. M. and Stewart, N. F. Accuracy and semantics
in shapeinterrogation applications.
Graphical Models (67), No. 5, 373389, September 2005.)
(
pdf ).
 Andersson, L.E., Stewart, N. F. and Zidani, M. Conditions for use of a
nonselfintersection conjecture. Computer Aided Geometric Design (23),
599611, 2006.
(pdf)
See also: Proof of a nonselfintersection conjecture,
Technical Report 1276, DIRO, April 24, 2006, containing additional proof.
(pdf).
 Stewart, N. F. and Zidani, M. Transfinite interpolation for welldefinition in
error analysis in solid modelling.
Dagstuhl Seminar Proceedings,
Dagstuhl Seminar 06021, January 813, 2006.
Manuscript:
(pdf)
(
Dagstuhl Proceedings). Lecture Notes in Computer Science LNCS 5045,
pp. 181192, Springer, 2008.
 Qi, J., Shapiro, V. and Stewart, N. F. Singleset and classofsets semantics for
geometric models.
ComputerAided Design (38), No. 10, 10881098, 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 811, 2006. Lecture Notes in Computer Science LNCS3980, 5060,
SpringerVerlag, Heidelberg, 2006
(pdf).
 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, 811826, 2007.
(pdf)
 Jiang, D. and Stewart, N. F. Reliable joining of surfaces for
combined meshsurface models. Proceedings, 21st European Conference on
Modelling and Simulation (ECMS 2007), Prague, Czech Republic, June 46,
2007. (pdf)
 Jiang, D. and Stewart, N. F.
Robustness of Boolean operations on subdivisionsurface models.
Lecture Notes in Computer Science LNCS 54920161, pp. 161174, SpringerVerlag, Heidelberg, 2009.
 Jiang, D. and Stewart, N. F. Floatingpoint arithmetic for computationalgeometry problems with uncertain data. International Journal of
Computational Geometry and Applications (19), No.4, 371385, 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. Lsystem construction of onedimensional subdivision schemes. Computer
Aided Geometric Design (29), No. 2, 150161, 2012.
 Shao, P. and Stewart, N. F. Managing uncertainty and discontinuous condition numbers in finiteprecision geometric computation. Soft
Computing (17), No. 8, 14251437, August 2013.
 Abdoli, S., BoumedienZidani, M. and Stewart, N. F. Uncertainty management in featurebased geometric modeling and data exchange. Second
International Conference on Vulnerability and Risk Analysis and Management (ICVRAM2014). University of Liverpool, UK, July 1316, 2014. Proceedings,
pp. 330339.