Rida T. Farouki experiment.jpg

Professor

Department of Mechanical and Aeronautical Engineering,
University of California, Davis, CA 95616-5294.

phone: 530-752-1779    fax: 530-752-4158

e-mail: farouki@ucdavis.edu
 

education

BA, Engineering Science, Oxford University, 1978

MS, Astronomy and Space Sciences, Cornell University, 1981

MA (Honorary), Engineering Science, Oxford University, 1982

PhD, Astronomy and Space Sciences, Cornell University, 1983
 

experience

1983-1986 : Research Scientist, GE Corporate Research and Development,
                     Schenectady NY

1986-1994 : Research Staff Member, IBM Thomas J. Watson Research Center,
                     Yorktown Heights NY

1994-1998 : Professor, Department of Mechanical Engineering and Applied Mechanics,
                     University of Michigan, Ann Arbor

1998-         : Professor, Department of Mechanical and Aeronautical Engineering,
                     University of California, Davis
 


eme150b.jpgcourses taught

ENG  102     Dynamics

EME   50    
Manufacturing Processes

EME 150A
    Mechanical Design

EME 150B
    Mechanical Design

EME 172     
Automatic Control of Engineering Systems

MAE 255
       Computer Aided Design and Manufacturing

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research interests

Computer aided design and manufacturing

Geometrical algorithms and representations

Numerical methods and scientific computing


pictures from some recent trips

Florence (2005)  Barcelona (2006)  Seoul (2007)  Strobl am Wolfgangsee (2007) 

Hangzhou (2008)  Lijiang (2009) Grenoble (2009) Greece (2011)




Pythagorean-hodograph curves: algebra and geometry inseparable

Geometry and Computing Vol. 1, Springer, Berlin (728 p. + 204 illus.) ISBN 978-3-540-73397-3 (2008)


cda.jpgBy virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves
offer unique advantages for computer-aided design and manufacturing, robotics, motion
control, path planning, computer graphics, animation, and related fields. This book offers
a comprehensive and self-contained treatment of the mathematical theory of PH curves,
including algorithms for their construction and examples of their practical applications.
Special features include an emphasis on the interplay of ideas from algebra and geometry
and their historical origins, detailed algorithm descriptions, and many figures and worked
examples. The book will appeal, in whole or in part, to mathematicians, computer scientists,
and engineers.


link to Springer website  reviews on Amazon.com

click here for a list of minor corrections


journals, conferences, workshops

Various meetings and journals I have been involved with.

New Frontiers in CAGD Conference,
Bertinoro, ITALY, May 17-21, 2010

Algebraic Geometry and Geometric Modeling Conference,
Lijiang, China, July 21-26, 2009

Geometric Modeling and Processing 2008 Conference,
Hangzhou, China, April 23-25, 2008
 
Asian Symposium on Computer Mathematics,
Singapore, December 15-17, 2007
 
Workshop on Computational Methods for Algebraic Spline Surfaces,
Strobl, Austria, September 10-14, 2007
 
Zero 2007 Workshop, Korea Institute for Advanced Study,
Seoul, Korea, July 19-21, 2007

Algebraic Geometry and Geometric Modeling Conference,
Universitat de Barcelona, Spain, September 4-7, 2006

Australian Mathematical Society 49th Annual Meeting,
University of Western Australia, Perth, Australia, September 27-30, 2005

11th IMA Conference on the Mathematics of Surfaces,
University of Loughborough, England, September 5-7, 2005
 
Fifth International AFA-SMAI Conference on Curves and Surfaces,

Saint-Malo, France, June 27 - July 3, 2002

Mathematics and Visualization 2002 Workshop, Berlin, Germany,
May 22-25, 2002

Surface Approximation and Visualization II, Westport, New Zealand,
February 19-22, 2002

SIAM Conference on Geometric Design and Computing,
Sacramento, CA, Nov. 5-8, 2001

EuroConference on CAE Integration - Tools, Trends, and Technologies,
Cambridge, England, March 29 - April 1, 2001

Geometric Modeling and Processing 2000, Univerity of Hong Kong,
China, April 10-12, 2000

SIAM Conference on Geometric Design,
Albuquerque, NM, Nov. 2-5, 1999

Fourth International AFA Conference on Curves and Surfaces,
Saint-Malo, FRance, July 1-7, 1999

MSRI Workshop on Mathematical Foundations of Computer Aided Design,
Mathematical Sciences Research Institute, Berkeley, CA, June 4-5, 1999

SIAM Workshop on Integration of CAD and CFD,
University of California, Davis, April 12-13, 1999 (report)

Advances in Computational Mathematics (Springer)

Computer Aided Geometric Design (Elsevier)

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bibliography

Preprints are in the form of pdf files. For published papers, the links are to
the publisher's website (to avoid copyright infringement).

search by date of publication:

2014  2013  2012  2011  2010
2009  2008  2007  2006  2005  2004  2003  2002  2001  2000
1999  1998  1997  1996  1995  1994  1993  1992  1991  1990
1989  1988  1987  1986  1985  1984  1983  1982  1981  1980


2014

Experimental performance analysis of an inverse dynamics CNC compensation
scheme for high--speed execution of curved toolpaths
(with T. F. Schraeder),
preprint (2014)

Shape-preserving interpolation of spatial data by Pythagorean-hodograph
quintic spline curves
(with C. Manni, M. L. Sampoli, and A. Sestini),
preprint (2014)

Inverse kinematics for optimal tool orientation control in 5-axis CNC machining
(with C. Y. Han and S. Li), Computer Aided Geometric Design, to appear (2014)

Rotation-minimizing osculating frames (with C. Giannelli, M. L. Sampoli,
and A. Sestini), Computer Aided Geometric Design, to appear (2014)

C^2 interpolation of spatial data subject to arc-length constraints using
Pythagorean-hodograph quintic splines
(with L. Biard, M. Huard, and
N. Spryinski), Graphical Models 76, 40-42 (2014)


2013

Corrigendum to "Rational rotation-minimizing frames on polynomial space curves
of arbitrary degree'' [J. Symbolic Comput. 45 (2010) 844-856] (with T. Sakkalis),
Journal of Symbolic Computation
58, 99-102 (2013)

Scalar-vector algorithm for the roots of quadratic quaternion polynomials,
and the characterization of quintic rational rotation-minimizing frame curves

(with P. Dospra and T. Sakkalis), Journal of Symbolic Computation 58, 1-17 (2013)

Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants
(with P. Dospra, C. Y. Han, and T. Sakkalis), Computer Aided Geometric Design
30
, 653-671 (2013)

An interpolation scheme for designing rational rotation-minimizing camera motions
(with C. Giannelli and A. Sestini), Advances in Computational Mathematics 38,
63-82 (2013)

Optimal tool orientation control for 5-axis milling with a ball-end cutter
(with S. Li), Computer Aided Geometric Design 30, 226-239 (2013)

Experimental study of contouring accuracy for CNC machines executing
curved paths with constant and curvature-dependent feedrates

(with J. R. Conway, A. L. Darling, C. A. Ernesto, and C. A. Palomares),
Robotics and Computer Integrated Manufacturing 29, 357-369 (2013)

2012

The Bernstein polynomial basis: a centennial retrospective,
Computer Aided Geometric Design
29, 379-419 (2012)

Pythagorean-hodograph curves in Euclidean spaces of dimension greater
than 3
(with T. Sakkalis), Journal of Computational and Applied Mathematics
236, 4375-4382 (2012)

Noninvasive high resolution mechanical strain maps of the spine intervertebral
disc using nonrigid registration of magnetic resonance images
(with F. A. Fathallah,
D. A. Reiter, and J. H. Walton),  Journal of Biomechanics 45, 1534-1539 (2012)

Performance analysis of cross-coupled controllers for CNC machines
based upon precise real-time contour error measurement
(with J. R. Conway,
C. A. Ernesto, and M. Zhang), International Journal of Machine Tools and
Manufacture
52, 30-39 (2012)

A complete classification of quintic space curves with rational
rotation-minimizing frames
(with T. Sakkalis), Journal of Symbolic Computation
47, 214-226  (2012)

High-speed cornering by CNC machines under prescribed bounds on axis
accelerations and toolpath contour error
(with C. A. Ernesto), International
Journal of Advanced Manufacturing Technology
58, 327-338 (2012)

Design of C2 spatial Pythagorean-hodograph quintic splines by control polygons
(with C. Manni, F. Pelosi, and M. L. Sampoli), Lecture Notes in Computer Science
6920
, 253-269 (2012)

Design of rational rotation-minimizing rigid body motions by Hermite interpolation
(with C. Giannelli, C. Manni, and A. Sestini), Mathematics of Computation 81, 879-903
(2012)

2011

Equivalence of distinct characterizations for rational rotation-minimizing frames on
quintic space curves
(with T. Sakkalis), Computer Aided Geometric Design 28, 436-445
(2011)

Rational Pythagorean-hodograph space curves (with Z. Sir), Computer Aided Geometric
Design
28, 75-88 (2011)

2010

Quaternion and Hopf map characterizations for the existence of rational rotation-
minimizing frames on quintic space curves, Advances in Computational Mathematics
33, 331-348 (2010)

Solution of inverse dynamics problems for contour error minimization in CNC machines
(with C. A. Ernesto), International Journal of Advanced Manufacturing Technology 49,
589-604 (2010)

Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
(with T. Sakkalis), Journal of Symbolic Computation 45, 844-856 (2010)

Construction of rational surface patches bounded by lines of curvature
(with L. Biard and N. Szafran), Computer Aided Geometric Design 27, 359-371 (2010)

Construction and smoothing of triangular Coons patches with geodesic boundary curves
(with L. Biard and N. Szafran), Computer Aided Geometric Design 27, 301-312 (2010)

Geometric design using space curves with rational rotation-minimizing frames
(with C. Giannelli and A. Sestini), Lecture Notes in Computer Science Vol. 5862,
pp. 194-208, Springer (2010)


2009

Quintic space curves with rational rotation-minimizing frames (with C. Giannelli,
C. Manni, and A. Sestini), Computer Aided Geometric Design 26, 580-592 (2009)

Construction of Bezier surface patches with Bezier curves as geodesic boundaries
(with L. Biard and N. Szafran), Computer Aided Design 41, 772-781 (2009)

Spatial camera orientation control by rotation-minimizing directed frames
(with C. Giannelli), Computer Animation and Virtual Worlds 20, 457-472 (2009)

Existence conditions for Coons patches interpolating geodesic boundary curves
(with L. Biard and N. Szafran), Computer Aided Geometric Design 26, 599-614 (2009)

Non-existence of rational arc-length parameterizations for curves in R^n (with T. Sakkalis
and L. Vaserstein), Journal of Computational and Applied Mathematics 228, 494-497 (2009)

Helical polynomial curves and double Pythagorean hodographs II. Enumeration
of low-degree curves
(with C. Giannelli and A. Sestini), Journal of Symbolic
Computation
44, 307-332 (2009)

Helical polynomial curves and double Pythagorean hodographs I. Quaternion
an Hopf map representations
(with C. Giannelli and A. Sestini), Journal of
Symbolic Computation
44, 161-179 (2009)


2008


Computing the Minkowski value of the exponential function over a complex disk
(with H. I. Choi, C. Y. Han, and H. P. Moon), in Computer Mathematics (D. Kapur, ed.)
Lecture Notes in Artificial Intelligence Vol.  5081, pp. 1-21, Springer (2008)

Topological criterion for selection of quintic Pythagorean-hodograph Hermite
interpolants
(with H. I. Choi, S. H. Kwon, and H. P. Moon), Computer Aided
Geometric Design
25, 411-433 (2008)

Identification of spatial PH quintic Hermite interpolants with near-optimal
shape measures
(with C. Giannelli, C. Manni, and A. Sestini), Computer Aided
Geometric Design
25, 274-297 (2008)

2007

Evaluating the boundary and covering degree of planar Minkowski sums
and other geometrical convolutions
(with J. Hass), Journal of Computational
and Applied Mathematics
 209, 246-266 (2007)

Time-optimal feedrates along curved paths for Cartesian CNC machines with
prescribed bounds on axis velocities and accelerations
(with C. L. Boyadjieff and
S. D. Timar), International Journal of Robotics and Automation 22, 112-125 (2007)

Guaranteed consistency of surface intersections and trimmed surfaces using
a coupled topology resolution and domain decomposition scheme
(with C. Y. Han,
J. Hass, X. Song, and T. W. Sederberg),  Advances in Computational Mathematics 27,
1-26 (2007)

Time-optimal traversal of curved paths by Cartesian CNC machines under both
constant and speed-dependent axis acceleration bounds
(with S. D. Timar),
Robotics and Computer-Integrated Manufacturing 23, 563-579 (2007)

Rational space curves are not "unit speed" (with T. Sakkalis), Computer Aided
Geometric Design
24, 238-240 (2007)

A geometric product formulation for spatial Pythagorean-hodograph curves with
applications to Hermite interpolation
(with L. Noakes and C. Perwass), Computer
Aided Geometric Design
24, 220-237 (2007)

Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems
(with C. Y. Han), Applicable Algebra in Engineering, Communication, and Computing
18
, 169-189 (2007)

A control polygon scheme for design of planar C2 PH quintic spline curves
(with C. Manni, F. Pelosi, and M. L. Sampoli), Computer Aided Geometric
Design
24, 28-52  (2007)


2006

Algorithms for spatial Pythagorean-hodograph curves (with C. Y. Han),
Geometric Properties for Incomplete Data (R. Klette, R. Kozera, L. Noakes,
and J. Weickert, eds.), Springer, pp. 43-58 (2006)

2005

Smoothing of time-optimal feedrates for Cartesian CNC machines
(with C. L. Boyadjieff and S. D. Timar), Mathematics of Surfaces XI (R. Martin,
H. Bez, and M. Sabin, eds.), Springer, pp. 84-101 (2005)

Boundary evaluation algorithms for Minkowski combinations of complex sets
using topological analysis of implicit curves
(with C. Y. Han and J. Hass),
Numerical Algorithms 40, 251-283 (2005)

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics
(with F. Pelosi, C. Manni, and A. Sestini),  Advances in Computational Mathematics
22, 325-352 (2005)

Solution of elementary equations in the Minkowski geometric algebra of
complex sets
(with C. Y. Han),  Advances in Computational Mathematics,
22, 301-323 (2005)

Algorithms for time-optimal control of CNC machines along curved tool paths
(with S. D. Timar, T. S. Smith, and C. L. Boyadjieff), Robotics and Computer 
Integrated Manufacturing
21, 37-53 (2005)

2004

Topologically consistent trimmed surface approximations based on triangular patches
(with C. Y. Han, J. Hass, and T. W. Sederberg), Computer Aided Geometric Design
21, 459-478 (2004)

Robust plotting of generalized lemniscates (with C. Y. Han), Applied Numerical
Mathematics
51, 257-272 (2004)

Computation of Minkowski values of polynomials over complex sets
(with C. Y. Han),  Numerical Algorithms 36, 13-29 (2004)

Linear perturbation methods for topologically consistent representations of
free-form surface intersections (with X. W. Song, T. W. Sederberg, J. Zheng, and
J. Hass),  Computer Aided Geometric Design 21, 303-319 (2004)

Characterization and construction of helical polynomial space curves
(with C. Y. Han, C. Manni, and A. Sestini), Journal of Computational and
Applied Mathematics 162, 365-392 (2004)


2003

Rational approximation schemes for rotation-minimizing frames on Pythagorean-
hodograph curves (with C. Y. Han), Computer Aided Geometric Design 20, 435-454 (2003)

Construction of orthogonal bases for polynomials in Bernstein form on triangular and
simplex domains (with T. N. T. Goodman and T. Sauer), Computer Aided Geometric
Design 20, 209-230 (2003)

Minkowski combinations of complex sets - geometry, algorithms, and applications,
Curve and Surface Design: Saint Malo 2002 (T. Lyche, M.-L. Mazure, and L. L. Schumaker,
eds.), Nashboro Press, pp. 123-146 (2003)

Spatial C^2 PH quintic splines (with C. Manni and A. Sestini), Curve and Surface
Design:
Saint Malo 2002 (T. Lyche, M.-L. Mazure, and L. L. Schumaker, eds.),
Nashboro Press, pp. 147-156 (2003)

Shape-preserving interpolation by G^1 and G^2 PH quintic splines (with C. Manni
and A. Sestini), IMA Journal of Numerical Analysis 23, 175-195 (2003)

Minkowski geometric algebra and the stability of characteristic polynomials
(with H. P. Moon), Visualization and Mathematics III (H-C. Hege and K. Polthier, eds),
Springer, pp. 163-188 (2003)
 

2002

Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves
Graphical Models 64, 382-395 (2002)

Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves
(with M. al-Kandari and T. Sakkalis), Advances in Computational Mathematics 17,
369-383 (2002)

Structural invariance of spatial Pythagorean hodographs (with M. al-Kandari
and T. Sakkalis), Computer Aided Geometric Design 19, 395-407 (2002)

Pythagorean-hodograph curves, Handbook of Computer Aided Geometric Design
(G. Farin, J. Hoschek, and M-S. Kim, eds.), North Holland, 405-427 (2002)

Exact Minkowski products of N complex disks  (with H. Pottmann),
Reliable Computing  8, 43-66 (2002)

Optimal slicing of free-form surfaces (with M. al-Kandari, H. Pottmann, and T. S. Smith),
Computer Aided Geometric Design 19, 43-64 (2002)
 

2001

Computation of optimal composite parameterizations (with P. Costantini,
C. Manni, and A. Sestini), Computer Aided Geometric Design 18, 875-897 (2001)

Gauss map computation for free-form surfaces (with T. S. Smith),
Computer Aided Geometric Design 18, 831-850 (2001)

Efficient solution of the complex quadratic tridiagonal system for C2 PH quintic splines
(with B. K. Kuspa, C. Manni, and A. Sestini), Numerical Algorithms 27, 35-60 (2001)

ALGORITHM 812: BPOLY: An object-oriented software library of algorithms for
polynomials in Bernstein form (with Y-F. Tsai), ACM Transactions on Mathematical
Software 27, 267-296 (2001)

Real-time CNC interpolators for Bezier conics (with C. Manni and A. Sestini),
Computer Aided Geometric Design 18, 639-655 (2001)

Minkowski geometric algebra of complex sets (with H. P. Moon and B. Ravani),
Geometriae Dedicata 85, 283-315 (2001)

Sliding mode control of two arms manipulating a flexible beam (with A. S. al-Yahmadi
and T. C. Hsia), Proceedings, 32nd International Symposium on Robotics, April 19-21, 2001,
Seoul, Korea (2001)

Performance analysis of CNC interpolators for time-dependent feedrates along PH curves
(with Y-F. Tsai and B. Feldman), Computer Aided Geometric Design 18, 245-265 (2001)

Construction and shape analysis of PH quintic Hermite interpolants (with H. P. Moon
and H. I. Choi), Computer Aided Geometric Design 18, 93-115 (2001)

Exact Taylor series coefficients for variable-feedrate CNC curve interpolators
(with Y-F. Tsai), Computer Aided Design 33, 155-165 (2001)
 

2000

Bipolar and multipolar coordinates (with H. P. Moon), The Mathematics of Surfaces IX
(R. Cippola and R. Martin eds.), Springer, 348-371 (2000)

Minkowski roots of complex sets (with W. Gu and H. P. Moon), Geometric Modeling
and Processing 2000, IEEE Computer Society Press, 287-300 (2000)

Algorithms for Minkowski products and implicitly-defined complex sets
(with H. P. Moon and B. Ravani), Advances in Computational Mathematics
13, 199-229 (2000)

Curves from motion, motion from curves, Curve and Surface Design: Saint-Malo 1999
(P-J. Laurent, P. Sablonniere, and L. L. Schumaker, eds.), Vanderbilt Univ. Press,
63-90 (2000)

Physical constraints on feedrates and feed accelerations along curved tool paths
(with Y-F. Tsai and C. Wilson), Computer Aided Geometric Design 17, 337-359 (2000)

Legendre-Bernstein basis transformations,
Journal of Computational and Applied Mathematics 119, 145-160 (2000)

Convergent inversion approximations for polynomials in Bernstein form,
Computer Aided Geometric Design 17, 179-196 (2000)
 

1999

Voronoi diagram and medial axis algorithm for planar domains with curved boundaries
II. Detailed algorithm description (with R. Ramamurthy), Journal of Computational and
Applied Mathematics 102, 253-277 (1999)

Voronoi diagram and medial axis algorithm for planar domains with curved boundaries
I. Theoretical foundations (with R. Ramamurthy), Journal of Computational and Applied
Mathematics 102, 119-141 (1999)

Contour machining of free-form surfaces with real-time PH curve CNC interpolators
(with Y-F. Tsai  and G-F. Yuan), Computer Aided Geometric Design 16, 61-76 (1999)

G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate
functions on open-architecture CNC machines (with J. Manjunathaiah and G-F. Yuan),
International Journal of Machine Tools and Manufacture 39, 123-142 (1999)
 

1998

Least-squares tool path approximation with Pythagorean-hodograph curves for high-speed
CNC machining (with K. Saitou and Y-F. Tsai), The Mathematics of Surfaces VIII
(R. Cripps, ed.), Information Geometers, 245-264 (1998)

Topological and computational issues in Voronoi diagram and medial axis constructions
for planar domains with curved boundaries (with R. Ramamurthy), Proceedings, Workshop
on Differential/Topological Techniques in Geometric Modeling and Processing, Pohang,
KOREA, April 7-9, 1998, Bookplus Press, 1-26 (1998)

Cycles upon cycles: An anecdotal history of higher curves in science and engineering
(with J. Rampersad), Mathematical Methods for Curves and Surfaces II (M. Daehlen,
T. Lyche, and L. L. Schumaker, eds.), Vanderbilt Univ. Press, 95-116 (1998)

Degenerate point/curve and curve/curve bisectors arising in medial axis computations
for planar domains with curved boundaries (with R. Ramamurthy), Computer Aided
Geometric Design 15, 615-635 (1998)

Variable-feedrate CNC interpolators for constant material removal rates along
Pythagorean-hodograph curves (with J. Manjunathaiah, D. Nicholas, G-F. Yuan,
and S. Jee), Computer Aided Design 30, 631-640 (1998)

Design of rational cam profiles with Pythagorean-hodograph curves (with S. Jee
and J. Manjunathaiah), Mechanism and Machine Theory 33, 669-682 (1998)

On integrating lines of curvature, Computer Aided Geometric Design 15, 187-192 (1998)

Specified-precision computation of curve/curve bisectors (with R. Ramamurthy),
International Journal of Computational Geometry and Applications 8, 599-617 (1998)
 

1997

Numerical simulation of phase transitions in dense dusty plasmas (with S. Hamaguchi),
Advances in Dusty Plasmas (P. K. Shukla, D. A. Mendis, and T. Desai, eds.), Proceedings
of the International Conference on the Physics of Dusty Plasmas, October 21-25, 1996,
Goa, INDIA, World Scientific Press, Singapore, 87-95 (1997)

Triple point of Yukawa systems (with S. Hamaguchi and D. H. E. Dubin),
Physical Review E 56, 4671-4682 (1997)

Pythagorean-hodograph quintic transition curves of monotone curvature,
Computer Aided Design 29, 601-606 (1997)

Optimal parameterizations, Computer Aided Geometric Design 14, 153-168 (1997)

Conic approximation of conic offsets, Journal of Symbolic Computation 23, 301-313 (1997)
 

1996

Phase diagram of Yukawa systems near the one-component-plasma limit revisited (with
S. Hamaguchi and D. H. E. Dubin), Journal of Chemical Physics 105, 7641-7647 (1996)

Construction of C2 Pythagorean-hodograph interpolating splines by the homotopy method
(with G. Albrecht), Advances in Computational Mathematics 5, 417-442 (1996)

On the optimal stability of the Bernstein basis (with T. N. T. Goodman),
Mathematics of Computation 65, 1553-1566 (1996)

Real-time CNC interpolators for Pythagorean-hodograph curves (with S. Shah),
Computer Aided Geometric Design 13, 583-600 (1996)

Approximation of rolling-ball blends for free-form parametric surfaces
(with R. Sverrisson), Computer Aided Design 28, 871-878 (1996)

Computational methods for rapid prototyping of analytic solid models (with T. Koenig),
Rapid Prototyping Journal 2 (3), 41-48 (1996)

Smooth curve design with double-Tschirnhausen cubics (with J. Peters),
Annals of Numerical Mathematics 3, 63-82 (1996)

Polynomial and rational Pythagorean-hodograph curves reconciled (with H. Pottmann),
The Mathematics of Surfaces VI (G. Mullineux, ed.), Oxford Univ. Press, 355-378 (1996)

The elastic bending energy of Pythagorean-hodograph curves,
Computer Aided Geometric Design 13, 227-241 (1996)
 

1995

Computing Minkowski sums of plane curves (with A. Kaul), International Journal
of Computational Geometry and Applications 5, 413-432 (1995)

Hermite interpolation by Pythagorean-hodograph quintics (with C. A. Neff),
Mathematics of Computation 64, 1589-1609 (1995)

Path planning with offset curves for layered fabrication processes (with T. Koenig,
K. Tarabanis, J. U. Korein, and J. S. Batchelder), Journal of Manufacturing Systems 14,
355-368 (1995)

Analysis of the offset to a parabola (with T. W. Sederberg),
Computer Aided Geometric Design 12, 639-645 (1995)
 

1994

Thermodynamics of strongly-coupled Yukawa systems near the one-component-plasma
limit II. Molecular dynamics simulations (with S. Hamaguchi), Journal of Chemical Physics
101, 9885-9893 (1994)

Thermodynamics of strongly-coupled Yukawa systems near the one-component-plasma
limit I. Derivation of the excess energy (with S. Hamaguchi), Journal of Chemical Physics
101, 9876-9884 (1994)

Spline approximation of "effective" potentials under periodic boundary conditions
(with S. Hamaguchi), Journal of Computational Physics 115, 276-287 (1994)

Offset curves in layered manufacturing (with K. Tarabanis, J. U. Korein, J. S. Batchelder,
and S. R. Abrams), in Manufacturing Science and Engineering 1994, PED-Vol. 68-2
(Proceedings of the 1994 International Mechanical Engineering Congress and Exposition),
557-568, ASME, New York (1994)

Computing point/curve and curve/curve bisectors (with J. K. Johnstone), Design and
Application of Curves and Surfaces (The Mathematics of Surfaces V) (R. B. Fisher, ed.),
Oxford Univ. Press, 327-354 (1994)

The conformal map z to z^2 of the hodograph plane, Computer Aided Geometric Design 11,
363-390 (1994)

Plasma-particulate interactions in non-uniform plasmas with finite flows (with S. Hamaguchi),
Physics of Plasmas 1, 2110-2118 (1994)

The Boltzmann-Poisson system in weakly collisional sheaths (with M. Dalvie and S. Hamaguchi),
Semiconductors, Part I (W. M. Coughran, Jr., J. Cole, P. Lloyd, and J. K. White, eds.), IMA
Volumes in Mathematics and its Applications, Vol. 58, 17-31, Springer (1994)

Polarization force on a charged particulate in a non-uniform plasma (with S. Hamaguchi),
Physical Review E 49, 4430-4441 (1994)

Mass segregation, relaxation, and the Coulomb logarithm in N-body systems (again)
(with E. E. Salpeter), Astrophysical Journal 427, 676-683 (1994)

The bisector of a point and a plane parametric curve (with J. K. Johnstone),
Computer Aided Geometric Design 11, 117-151 (1994)

Pythagorean-hodograph space curves (with T. Sakkalis),
Advances in Computational Mathematics 2, 41-66 (1994)

Watch your (parametric) speed!, Computer-Aided Surface Geometry and Design
(The Mathematics of Surfaces IV) (A. Bowyer, ed.), Oxford Univ. Press, 69-95 (1994)
 

1993

Algebraically rectifiable parametric curves (with T. Sakkalis),
Computer Aided Geometric Design 10, 551-569 (1993)

A shock-tracking algorithm for surface evolution under reactive-ion etching (with M. Dalvie,
S. Hamaguchi, and S. Sethuraman), Journal of Applied Physics 74, 5172-5184 (1993)

Thermal energy of the crystalline one-component plasma from dynamical simulations
(with S. Hamaguchi), Physical Review E 47, 4330-4336 (1993)
 

1992

Phase transitions of dense systems of charged "dust" grains in plasmas (with S. Hamaguchi),
Applied Physics Letters 61, 2973-2975 (1992)

Dynamical N-body simulations of Coulomb scattering in plasma sheaths (with M. Dalvie,
S. Hamaguchi, and M. Surendra), Physical Review A 46, 7815-7829 (1992)

Hydrodynamic analysis of electron motion in the cathode fall using a Monte Carlo simulation
(with M. Dalvie,  S. Hamaguchi, and M. Surendra), Journal of Applied Physics 72, 2620-2631
(1992)

Exact equations of "simple" wavefronts (with J.-C. Chastang), Optik 91, 109-121 (1992)

Approximation by interval Bezier curves (with T. W. Sederberg),
IEEE Computer Graphics and Applications 12 (5), 87-95 (1992)

Self-consistent Monte Carlo simulation of the cathode fall including treatment of negative
glow electrons (with M. Dalvie and S. Hamaguchi), Physical Review A 46, 1066-1077 (1992)

Ion energetics in collisionless sheaths of rf process plasmas (with M. Dalvie and S. Hamaguchi),
Physics of Fluids B 4, 2362-2367 (1992)

Curves and surfaces in geometrical optics (with J.-C. Chastang), Mathematical Methods in
Computer Aided Geometric Design II, (T. Lyche & L. L. Schumaker, eds.), Academic Press,
239-260 (1992)

Analysis of a kinematic model for ion transport in rf plasma sheaths (with M. Dalvie
and S. Hamaguchi), Physical Review A 45, 5913-5928 (1992)

Flux considerations in the coupling of Monte Carlo plasma sheath simulations with feature
evolution models (with M. Dalvie and S. Hamaguchi), IEEE Transactions on Electron Devices
39, 1090-1099 (1992)

Pythagorean-hodograph curves in practical use, Geometry Processing for Design and Manufacturing
(R. E. Barnhill, ed.), SIAM, Philadelphia, 3-33 (1992)

Ponderomotive force and ion energy distributions in an rf sheath (with M. Dalvie and S. Hamaguchi),
Physical Review Letters 68, 44-47 (1992)

The mathematical evolution of wavefronts (with J.-C. Chastang),
Optics and Photonics News 3, 20-23 (1992)
 

1991

Computing with barycentric polynomials, The Mathematical Intelligencer 13, 61-69 (1991)

Ion distribution function in a weakly collisional sheath (with M. Dalvie and S. Hamaguchi),
Physical Review A 44, 3804-3821 (1991)

Monte Carlo simulations of space-charge-limited ion transport through collisional plasma
sheaths (with M. Dalvie and S. Hamaguchi), Physical Review A 44, 2664-2681 (1991)

Real rational curves are not "unit speed" (with T. Sakkalis),
Computer Aided Geometric Design 8, 151-157 (1991)

On the stability of transformations between power and Bernstein polynomial forms,
Computer Aided Geometric Design 8, 29-36 (1991)
 

1990

Boundary-condition refinement of the Child-Langmuir law for collisionless dc plasma sheaths
(with M. Dalvie and L. F. Pavarino), Journal of Applied Physics 68, 6106-6116 (1990)

Pythagorean hodographs (with T. Sakkalis),
IBM Journal of Research and Development 34, 736-752 (1990)

On the numerical condition of Bernstein-Bezier subdivision processes (with C. A. Neff),
Mathematics of Computation 55, 637-647 (1990)

Algebraic properties of plane offset curves (with C. A. Neff),
Computer Aided Geometric Design 7, 101-127 (1990)

Analytic properties of plane offset curves (with C. A. Neff),
Computer Aided Geometric Design 7, 83-99 (1990)

Singular points of algebraic curves (with T. Sakkalis),
Journal of Symbolic Computation 9, 405-421 (1990)
 

1989

Numerical stability in geometric algorithms and representations, The Mathematics of Surfaces III
(D. C. Handscomb, ed.), Oxford Univ. Press, 83-113 (1989)

Automatic parsing of degenerate quadric surface intersections (with C. A. Neff
and M. A. O'Connor), ACM Transactions on Graphics 8, 174-203 (1989)

Hierarchical segmentations of algebraic curves and some applications, Mathematical Methods
in Computer Aided Geometric Design, (T. Lyche & L. L. Schumaker, eds.), Academic Press,
239-248 (1989)
 

1988

On the numerical condition of algebraic curves and surfaces 1. Implicit equations
(with V. T. Rajan), Computer Aided Geometric Design 5, 215-252 (1988)

Algorithms for polynomials in Bernstein form (with V. T. Rajan),
Computer Aided Geometric Design 5, 1-26 (1988)

Computational issues in solid boundary evaluation, Information Sciences 44, 87-171 (1988)
 

1987

Graphical methods for surface differential geometry, The Mathematics of Surfaces II
(R. R. Martin, ed.), Oxford Univ. Press, 363-385 (1987)

On the numerical condition of polynomials in Bernstein form (with V. T. Rajan),
Computer Aided Geometric Design 4, 191-216 (1987)

Direct surface section evaluation, Geometric Modeling: Algorithms and New Trends
(G. Farin, ed.), SIAM, 319-334 (1987)

Trimmed surface algorithms for the evaluation and interrogation of solid boundary
representations, IBM Journal of Research and Development 31, 314-334 (1987)
 

1986

Surface analysis methods (with J. M. Beck and J. K. Hinds),
IEEE Computer Graphics and Applications 6 (12), 18-36 (1986)

The characterization of parametric surface sections,
Computer Vision, Graphics, and Image Processing 33, 209-236 (1986)

The approximation of non-degenerate offset surfaces,
Computer Aided Geometric Design 3, 15-43 (1986)
 

1985

Exact offset procedures for simple solids,
Computer Aided Geometric Design 2, 257-279 (1985)

A hierarchy of geometric forms (with J. K. Hinds),
IEEE Computer Graphics and Applications 5 (5), 51-78 (1985)

Do cosmic magnetic monopoles cause rapid decay of the galactic magnetic field?
(with S. L. Shapiro and I. Wasserman), Comments on Astrophysics 10, 257-265 (1985)
 

1984

Numerical simulation of the plasma and gravitational dynamics of a galactic magnetic monopole
halo (with S. L. Shapiro and I. Wasserman), Astrophysical Journal 284, 282-298 (1984)
 

1983

The collapse and violent relaxation of N-body systems: mass segregation and the secondary
maximum (with G. L. Hoffman and E. E. Salpeter), Astrophysical Journal 271, 11-21 (1983)

Simulations of galaxy mergers: cannibalism and dynamical friction
(with M. J. Duncan and S. L. Shapiro), Astrophysical Journal 271, 22-31 (1983)

Computational astrophysics on the array processor (with S. L. Shapiro and S. A. Teukolsky),
IEEE Computer 16 (6), 73-83 (1983)

Hierarchical merging and the structure of elliptical galaxies (with M. J. Duncan
and S. L. Shapiro), Astrophysical Journal 265, 597-605 (1983)
 

1982

Simulations of merging disk galaxies (with S. L. Shapiro),
Astrophysical Journal 259, 103-115 (1982)

Mass segregation, relaxation, and the Coulomb logarithm in N-body systems
(with E. E. Salpeter), Astrophysical Journal 253, 512-519 (1982)
 

1981

Computer simulations of environmental influences on galaxy evolution in dense clusters
II. Rapid tidal encounters (with S. L. Shapiro), Astrophysical Journal 243, 32-41 (1981)
 

1980

Computer simulations of environmental influences on galaxy evolution in dense clusters
I. Ram-pressure stripping (with S. L. Shapiro), Astrophysical Journal 241, 928-945 (1980)
 

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