Visiting Scientist, IBM T.J. Watson Research Center,
NY 1987 - 1988
Assistant Professor, New Mexico State University,
Las Cruces, NM 1986 - 1987
Part-time Instructor, University of Rochester,
Rochester, NY 1983 - 1986.
PUBLICATIONS
In Journals and Books
T. Sakkalis, The computation of the index of a Morse function at
a critical point, Intern. J. Math. & Math. Sci. Vol. II,
No. 4 (1988), 721-726. MR 90a:58026.
T. Sakkalis, Signs of algebraic numbers,
Computers and Mathematics, Springer Verlag, (1989), 131-134. MR 90m:12004.
T. Sakkalis and R.T. Farouki, Singular points of algebraic curves,
J. Symbolic Computation, 9 (1990), 405-421. MR 91f:14056.
T. Sakkalis, The Euclidean algorithm and the degree of the Gauss map,
SIAM J. of Computing, Vol. 19, No. 3 (1990), 538-543. MR 91m:68092.
R.T. Farouki and T. Sakkalis,
Pythagorean Hodographs, IBM J. of Research
and Development, Vol. 34. No. 5 (1990), 736-752. MR 92a:65063.
T. Sakkalis, On a theorem of H. Hopf, Intern. J. Math. &
Math. Sci., Vol. 13, No. 4 (1990), 813-816. MR 91k:57038.
T. Sakkalis,
The topological configuration of a real algebraic curve, Bulletin
Austr. Math. Soc., Vol. 43, No. 1 (1991), 37-50. MR 92e:14056.
R.T. Farouki and T. Sakkalis, Real rational curves are not "unit speed" ,
Computer Aided Geometric Design, 8 (1991) 151-157.
MR 92d:65034.
T. Sakkalis, On relations between Jacobians and
resultants of polynomials in two variables,
Bulletin Austr. Math. Soc., 47 (1993), 473-481. MR 94e:12001.
T. Sakkalis and R.T. Farouki,
Algebraically rectifiable parametric curves,
Computer
Aided Geometric Design, 10 (1993) 551-569. MR 95c:65028.
C. Cheng, T. Sakkalis and S. Wang,
A case of the Jacobian conjectrure,
Journal
of Pure and Applied Algebra, Vol. 96 (1994), 15-18. MR 95i:14018a.
D. Polemi and T. Sakkalis, Singular algebraic curves over finite
fields, Lecture Notes of Computer Science, Springer Verlag
Vol. 793 (1993), 24-37. MR 95i:14053.
R.T. Farouki and T. Sakkalis,
Pythagorean-hodograph space curves, Advances
in Computational Mathematics 2 (1994), 41-66. MR 95b:50003.
T. Sakkalis and Z. Ligatsikas,
Computing the topological degree of polynomial maps,
Bulletin Austr. Math. Soc., 56 (1997), 87-94. MR 98g:55002.
T. Maekawa, N.M. Patrikalakis, T. Sakkalis and G. Yu, Analysis and
applications of pipe surfaces, Computer Aided Geometric Design,
15 5 (1998), 437-458. MR 99c:68254.
T. Sakkalis, Some applications of the resultant, Bulletin of the
Greek Mathematical Society, Vol. 42, (1999), 89-95. MR 2002d:14097.
T. Sakkalis and Ch. Charitos, Approximating curves via alpha shapes,
Graphical Models and Image Processing, Vol. 61,
No. 3 (1999), 165-176.
T. Sakkalis, G. Shen and N.M. Patrikalakis, Representational validity of
boundary representation models, Computer Aided Design,
32 (2000) 719-726.
T. Sakkalis, G. Shen and N.M. Patrikalakis, Topological and geometric
properties of interval solid models, Graphical Models, 63,
163-175 (2001).
G. Shen, T. Sakkalis and N.M. Patrikalakis, Boundary representation
model rectification, Graphical Models, 63, 177-195 (2001).
J. Wallner, T. Sakkalis, T. Maekawa, H. Pottmann and G. Yu,
Self-intesection of offset curves and surfaces, International
Journal of Shape Modeling, Vol. 7, No. 1, 1-21 (2001).
G. Shen, T. Sakkalis and N.M. Patrikalakis, A Rectification algorithm
for manifold boundary representation models. Idmme'2002-Selected
papers book. P. Chedmail, G. Cognet, C. Fortin, C. Mascle and
J. Pegna, Editors. Kluwer Publishing Company, (129-138) 2002.
R.T. Farouki, M. al-Kandari and T. Sakkalis,
Hermite interpolation by rotation-invariant spatial
Pythagorean-hodograph curves, Advances in Computational
Mathematics, 17: 369-383 (2002). MR 2003e:65011.
R.T. Farouki, M. al-Kandari and T. Sakkalis,
Structural invariance of spatial
Pythagorean hodographs, Computer Aided Geometric Design,
19 (2002) 395-407. MR 2003g:65019.
T. Sakkalis, Polynomial remainders and plane automorphisms,
Bulletin Austr. Math. Soc, 68 (2003), No. 1, 73-79.
MR 2005a:14085.
C. Cheng and T. Sakkalis, Power linear maps of nilpotency index two,
Communications in Algebra, Vol. 32, No. 7 (2004), 2635-2637.
MR 2005f:14116.
T. Sakkalis, T. J. Peters and J. Bisceglio
Isotopic Approximations and Interval Solids,
Computer Aided Design, 36 (11), (2004), 1089-1100.
T. Sakkalis,
A note on proper polynomial maps,
Communications in Algebra, Vol. 33, No. 9 (2005), 3359-3365. MR 2006g:14096.
T. J. Peters, J. Bisceglio, D.R. Ferguson, C.M. Hoffmann, T. Maekawa,
N.M. Patrikalakis, T. Sakkalis and N.F. Stewart
Computational Topology for Regular Closed Sets
(within the I-TANGO project),
On-line Journal Topology Atlas Invited Contributions,
Vol. 9, No. 1, pp. 12 (2004).
K.H. Ko, T. Sakkalis and N.M. Patrikalakis,
Resolution of multiple roots of nonlinear polynomial systems,
International J. of Shape Modeling, Vol 11, No. 1 (2005) 121-147.
K. Abe, J. Bisceglio, D.R. Ferguson, T. J. Peters, A.C. Russell and T. Sakkalis,
Computational topology for isotopic surface reconstruction,
Theoretical Computer Science., 365 (2006) 184-198.
R.T. Farouki and T. Sakkalis,
Rational space curves are not "unit speed", Computer Aided Geometric Design,
24 (2007) 238-240.
T. Sakkalis, The fundamental theorem of algebra: An elementary proof,
Bulletin of the Greek Mathematical Society
, Vol. 53, (2007), 131-134.
K.H. Ko, T. Sakkalis and N.M. Patrikalakis,
A reliable algorithm for computing the topological degree of a mapping in R^2,
Applied Mathematics and Computation, 196 (2008) 666-678.
T. Sakkalis, R.T. Farouki and L. Vaserstein,
Non-existence of rational arc length parameterizations for curves in R^n,
J. Computational and Applied Mathematics, 228(2009) 494-497.
L. Vaserstein, T. Sakkalis and S. Frisch,
Polynomial parametrization of Pythagorean tuples
, Int. J. Number Theory, Vol. 6 (6) (2010), 1261-1272.
R.T. Farouki and T. Sakkalis,
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
, J. Symbolic Computation, Vol. 45 (8) (2010), 844-856.
R.T. Farouki and T. Sakkalis,
Equivalence of distinct characterizations for rational rotation-minimizing frames
on quintic space curves,
Computer Aided Geometric Design, 28 (2011) 436-445.
R.T. Farouki and T. Sakkalis,
A complete classification of quintic space curves
with rational rotation--minimizing frames,
J. Symbolic Computation, Vol. 47 (2) (2012), 214-226.
T. Sakkalis and R.T. Farouki,
Pythagorean-hodograph curves in
Euclidean spaces of dimension greater than 3,
J. Computational and Applied Mathematics, 236 (2012) 4375-4382.
R.T. Farouki, C.Y. Han, P. Dospra and T. Sakkalis,
Rotation-minimizing Euler-Rodrigues
rigid-body motion interpolants,
Computer Aided Geometric Design, 30 (2013) 653-671.
R.T. Farouki, P. Dospra and T. Sakkalis,
Scalar-vector algorithm for the roots of quadratic quaternion polynomials,
and the characterization of quintic rational rotation-minimizing frame curves,
J. Symbolic Computation, Vol. 58 (2013), 1-17.
R.T. Farouki and T. Sakkalis,
Corrigendum to "Rational rotation-minimizing frames on polynomial space curves
of arbitrary degree'' [J. Symbolic Comput. 45 (2010) 844-856],
J. Symbolic Computation, Vol. 58 (2013), 99-102.
Kwanghee Ko and T. Sakkalis,
Orthogonal projection of points in CAD/CAM applications: an overview,
J. of Computational Design and Engineering, Vol. 1, No. 2 (2014), 116-127.
C. Cheng and T. Sakkalis,
On new types of rational rotation-minimizing frame space curves,
J. Symbolic Computation, Vol. 74 (2016), 400-407.
T. Sakkalis,
Jacobians of quaternion polynomials,
Bulletin of the Greek Mathematical Society , Vol. 61, (2017), 31-40.
T. Sakkalis, Kwanghee Ko and Galam Song,
Roots of quaternion polynomials; theory and computation.Theoretical Computer Science, to appear.
T. Sakkalis,
Polynomials and degrees of maps in real normed algebras, Communications in Mathematics, to appear.
R. T. Farouki and T. Sakkalis,
Construction of rational curves with rational arc lenghts by direct integration.Computer Aided Geometric Design, to appear.
In Proceedings of Conferences
T. Sakkalis and R.T. Farouki, Rectification of parametric curves,
Computer Aided Geometric Design: From Theory to Practice, NTUA,
Athens, Greece, (1995), 97-102.
G. Shen, T. Sakkalis and N.M. Patrikalakis, Manifold boundary
representation model rectification, Proceedings of the 3rd
International Conference on Integrated Design and Manufacturing in
Mechanical Engineering, C. Mascle, C. Fortin, J. Pegna, editors.
Page 199 and CDROM. Montreal, QC, Canada. May 2000. Presse internationale
Polytechnique, Montreal, Canada, May 2000.
http://www.congresbcu.com/idmme-csme2000.htm
N.M. Patrikalakis, T. Sakkalis and G. Shen, Boundary representation
models: validity and rectification, invited paper in Proceedings of
The 9th IMA Conference on the Mathematics of Surfaces, University of
Cambridge, September 2000. R. Cipolla and R. Martin, editors. pp. 389-409.
London, UK, Springer Verlag, 2000.
G. Shen, T. Sakkalis and N.M. Partikalakis, Interval
methods for B-rep model verification and rectification, Proceedings of
the ASME 26th Design Automation Conference, Baltimore, MD,
September 2000. P. 140 and CDROM. NY, ASME 2000.
G. Shen, T. Sakkalis and N.M. Partikalakis, Analysis of
boundary representation model rectification, Proceedings of
the Sixth ACM Solid Modeling Symposium, D.C. Anderson and K. Lee,
editors. Ann Arbor, Michigan, June 2001. pp. 149-158. NY: ACM, 2001.
T. Sakkalis and T.J. Peters, Ambient isotopic approximations for
surface reconstruction and interval solids, 8th ACM Symposium on
Solid Modeling and Applications. G. Elber and V. Shapiro, Editors.
Seattle Washington, June 16-20, (2003) 176-184.
D. Ferguson, C. Hoffmann, T. Maekawa, N. Patrikalakis, T. Peters, T.
Sakkalis and N. F. Stewart, Accurate Numerical Intersection
of Geometric Objects, 5th International Congress on
Industrial and Applied Mathematics (ICIAM 2003). Sydney,
Australia, July 2003.
K.H. Ko,T. Sakkalis and N.M. Patrikalakis,
Nonlinear Polynomial Systems: Multiple Roots and
their Multiplicities, Shape Modeling International Conference, SMI
2004. F. Giannini and A. Pasko, Editors. Genoa, Italy, June 2004. Los
Alamitos, CA: IEEE Computer Society Press, (2004), 87-98.
H. Mukundan, K.H. Ko, T. Maekawa, T. Sakkalis and
N.M. Patrikalakis, Tracing Surface Intersections with a
Validated ODE System Solver, Proceedings of the Ninth EG/ACM
Symposium on Solid Modeling and Applications. G. Elber,
N.M. Patrikalakis and P. Brunnet, Editors. Genoa, Italy, June 2004.
Eurographics Press (2004), 249-254.
K. Abe, J. Bisceglio, T.J. Peters, A.C. Russell, D.R. Ferguson and T.
Sakkalis, Computational Topology for Reconstruction
of Surfaces with Boundary: Integrating Experiments and Theory,
International Conference on Shape Modeling and Applications (SMI'05)
. MIT, June 15-17, 2005. IEEE Computer Society Press, (2005) 288-297.
Technical Reports
T. Sakkalis, On the zeros of a polynomial vector field,
IBM RC-13303, (1987).