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
MS, Astronomy and Space Sciences, Cornell University, 1981
MA (Honorary), Engineering Science, Oxford University, 1982
PhD, Astronomy and Space Sciences, Cornell University, 1983
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
Geometrical algorithms and representations
Numerical methods and scientific computing
By virtue of their special algebraic structures,
Pythagorean-hodograph
(PH) curves offer unique
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)
search by date of publication:
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
2008
Quintic space curves with rational
rotation-minimizing frames (with C. Giannelli,
C. Manni, and A. Sestini), preprint (2008)
Construction of Bezier surface patches with
Bezier curves as geodesic boundaries
(with L. Biard and N. Szafran), preprint (2008)
Spatial
camera orientation control by
rotation-minimizing directed frames
(with C. Giannelli), preprint (2008)
Existence conditions for Coons patches
interpolating geodesic boundary curves
(with L. Biard and N. Szafran), preprint (2008)
Non-existence of rational arc-length
parameterizations for curves in R^n (with T. Sakkalis
and L. Vaserstein), Journal of
Computational and Applied Mathematics, to appear (2008)
Computing the Minkowski value of the
exponential function over a complex disk
(with H. I. Choi, C. Y. Han, and H. P. Moon), Lecture Notes in Computer Science
Vol. 5081, Springer, to appear (2008)
Helical polynomial curves and double
Pythagorean hodographs II. Enumeration
of low-degree curves (with C. Giannelli and A. Sestini), Journal of Symbolic
Computation, to appear (2008)
Helical polynomial curves and double
Pythagorean hodographs I. Quaternion
an Hopf map representations (with C. Giannelli and A. Sestini), Journal of
Symbolic Computation, to appear (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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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
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