Department of Mechanical and Aeronautical Engineering,
University of California, Davis, CA 956165294.
phone: 5307521779 fax: 5307524158
email: 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
19861994 : Research Staff Member, IBM Thomas J. Watson Research Center,
Yorktown
Heights
NY
19941998 : 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
Mathematics and
Visualization 2002 Workshop, Berlin, Germany,
May 2225, 2002
Surface
Approximation
and
Visualization
II, Westport, New Zealand,
February 1922, 2002
SIAM Conference on
Geometric Design and Computing,
Sacramento, CA, Nov. 58, 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 1012, 2000
SIAM Conference on
Geometric Design,
Albuquerque, NM, Nov. 25, 1999
Fourth International
AFA Conference on Curves and Surfaces,
SaintMalo, FRance, July 17, 1999
MSRI
Workshop on Mathematical Foundations of Computer Aided Design,
Mathematical Sciences Research Institute, Berkeley, CA, June 45, 1999
SIAM Workshop on
Integration of CAD and CFD,
University of California, Davis, April 1213,
1999 (report)
Advances in Computational Mathematics (Springer)
Computer Aided Geometric Design (Elsevier)
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2009 2008
2007 2006 2005 2004 2003 2002
2001
2000
1999 1998 1997 1996 1995 1994 1993 1992 1991 1990
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Experimental performance analysis of an
inverse dynamics CNC compensation
scheme for highspeed execution of curved toolpaths (with T. F.
Schraeder),
preprint (2014)
Shapepreserving interpolation of spatial
data by Pythagoreanhodograph
quintic spline curves (with C. Manni, M. L. Sampoli, and A.
Sestini),
preprint (2014)
Inverse kinematics for optimal tool orientation
control in 5axis CNC machining
(with C. Y. Han and S. Li), Computer
Aided Geometric Design, to appear (2014)
Rotationminimizing 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
arclength constraints using
Pythagoreanhodograph quintic splines (with L. Biard, M. Huard, and
N. Spryinski), Graphical Models
76, 4042 (2014)
Scalarvector
algorithm
for
the
roots of
quadratic quaternion polynomials,
and the characterization of quintic rational rotationminimizing frame
curves
(with P. Dospra and T. Sakkalis), Journal
of
Symbolic
Computation 58,
117 (2013)
Rotationminimizing
EulerRodrigues
rigidbody
motion
interpolants
(with P. Dospra, C. Y. Han, and T. Sakkalis), Computer Aided Geometric Design
30, 653671 (2013)
An
interpolation
scheme
for
designing
rational
rotationminimizing
camera
motions
(with C. Giannelli and A. Sestini), Advances
in
Computational
Mathematics 38,
6382 (2013)
Optimal
tool
orientation
control
for
5axis
milling
with
a
ballend
cutter
(with S. Li), Computer Aided
Geometric Design 30,
226239 (2013)
Experimental
study
of
contouring
accuracy
for
CNC
machines
executing
curved paths with constant and curvaturedependent feedrates
(with J. R. Conway, A. L. Darling, C. A. Ernesto, and C. A. Palomares),
Robotics and Computer Integrated
Manufacturing 29,
357369 (2013)
2012
The
Bernstein
polynomial
basis:
a
centennial
retrospective,
Computer Aided Geometric
Design 29, 379419
(2012)
Pythagoreanhodograph
curves
in
Euclidean
spaces
of
dimension
greater
than 3 (with T. Sakkalis), Journal
of
Computational
and
Applied
Mathematics
236, 43754382 (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, 15341539 (2012)
Performance
analysis
of
crosscoupled
controllers
for
CNC
machines
based upon precise realtime contour error measurement (with J. R.
Conway,
C. A. Ernesto, and M. Zhang), International
Journal
of
Machine
Tools
and
Manufacture 52, 3039
(2012)
A
complete
classification
of
quintic
space
curves
with
rational
rotationminimizing frames (with T. Sakkalis), Journal of Symbolic Computation
47, 214226 (2012)
Highspeed
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, 327338 (2012)
Design
of
C2
spatial
Pythagoreanhodograph
quintic
splines
by
control
polygons
(with C. Manni, F. Pelosi, and M. L. Sampoli), Lecture Notes in Computer Science
6920, 253269 (2012)
Equivalence
of
distinct
characterizations
for
rational
rotationminimizing
frames
on
quintic space curves (with T. Sakkalis), Computer Aided Geometric Design 28, 436445
(2011)
Rational
Pythagoreanhodograph
space
curves
(with Z. Sir), Computer Aided
Geometric
Design 28, 7588 (2011)
2010
Quaternion
and
Hopf
map
characterizations
for
the
existence
of
rational
rotation
minimizing
frames
on
quintic
space
curves, Advances
in
Computational Mathematics
33, 331348 (2010)
Solution
of
inverse
dynamics
problems
for
contour
error
minimization
in
CNC
machines
(with C. A. Ernesto), International
Journal of Advanced Manufacturing Technology 49,
589604 (2010)
Rational
rotationminimizing
frames
on
polynomial
space
curves
of
arbitrary
degree
(with T. Sakkalis), Journal of
Symbolic Computation 45,
844856
(2010)
Construction
of
rational
surface
patches
bounded
by
lines
of
curvature
(with L. Biard and N. Szafran), Computer
Aided
Geometric
Design
27,
359371 (2010)
Construction
and
smoothing
of
triangular
Coons
patches
with
geodesic
boundary
curves
(with L. Biard and N. Szafran), Computer Aided Geometric Design 27,
301312
(2010)
Geometric
design
using
space
curves
with
rational
rotationminimizing
frames
(with C. Giannelli and A. Sestini), Lecture
Notes
in
Computer
Science Vol. 5862,
pp. 194208, Springer (2010)
Construction
of
Bezier
surface
patches
with
Bezier
curves
as
geodesic
boundaries
(with L. Biard and N. Szafran), Computer
Aided
Design
41,
772781
(2009)
Spatial
camera
orientation
control
by
rotationminimizing
directed
frames
(with C. Giannelli), Computer
Animation and Virtual Worlds 20,
457472
(2009)
Existence
conditions
for
Coons
patches
interpolating
geodesic
boundary
curves
(with L. Biard and N. Szafran), Computer
Aided
Geometric
Design
26,
599614 (2009)
Nonexistence
of
rational
arclength
parameterizations
for
curves
in
R^n (with T. Sakkalis
and L. Vaserstein), Journal of
Computational and Applied Mathematics 228, 494497 (2009)
Helical
polynomial
curves
and
double
Pythagorean
hodographs
II.
Enumeration
of lowdegree curves (with C. Giannelli and A. Sestini), Journal of Symbolic
Computation 44,
307332 (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,
161179
(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. 121, Springer (2008)
Topological
criterion
for
selection
of
quintic
Pythagoreanhodograph
Hermite
interpolants (with H. I. Choi, S. H. Kwon, and H. P. Moon), Computer Aided
Geometric Design 25,
411433 (2008)
Identification
of
spatial
PH
quintic
Hermite
interpolants
with
nearoptimal
shape measures (with C. Giannelli, C. Manni, and A. Sestini), Computer Aided
Geometric Design 25,
274297 (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, 246266 (2007)
Timeoptimal
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, 112125 (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,
126 (2007)
Timeoptimal
traversal
of
curved
paths
by
Cartesian
CNC
machines
under
both
constant and speeddependent axis acceleration bounds (with S. D.
Timar),
Robotics and ComputerIntegrated
Manufacturing 23,
563579 (2007)
Rational
space
curves
are
not
"unit
speed" (with T. Sakkalis), Computer
Aided
Geometric Design 24,
238240 (2007)
A
geometric
product
formulation
for
spatial
Pythagoreanhodograph
curves
with
applications to Hermite interpolation (with L. Noakes and C.
Perwass), Computer
Aided Geometric Design 24,
220237
(2007)
Root
neighborhoods,
generalized
lemniscates,
and
robust
stability
of
dynamic
systems
(with C. Y. Han), Applicable Algebra
in Engineering, Communication, and Computing
18, 169189 (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, 2852
(2007)
Algorithms for spatial Pythagoreanhodograph
curves (with C. Y. Han),
Geometric Properties for Incomplete
Data (R. Klette, R. Kozera, L. Noakes,
and J. Weickert, eds.), Springer, pp. 4358 (2006)
Smoothing of timeoptimal 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. 84101 (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, 251283 (2005)
Geometric
Hermite
interpolation
by
spatial
Pythagoreanhodograph
cubics
(with F. Pelosi, C. Manni, and A. Sestini), Advances in
Computational Mathematics
22, 325352 (2005)
Solution
of
elementary
equations
in
the
Minkowski
geometric
algebra
of
complex sets
(with
C. Y. Han), Advances in Computational Mathematics,
22, 301323 (2005)
Algorithms
for
timeoptimal
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,
3753
(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, 459478 (2004)
Robust
plotting
of
generalized
lemniscates
(with C. Y. Han), Applied Numerical
Mathematics 51, 257272
(2004)
Computation
of
Minkowski
values
of
polynomials
over
complex
sets
(with C. Y. Han), Numerical Algorithms 36, 1329
(2004)
Linear
perturbation
methods
for
topologically
consistent
representations
of
freeform
surface
intersections (with X. W.
Song, T. W. Sederberg, J. Zheng, and
J. Hass), Computer Aided Geometric Design 21,
303319 (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, 365392 (2004)
Rational
approximation
schemes
for
rotationminimizing
frames
on
Pythagorean
hodograph
curves
(with C. Y. Han), Computer Aided Geometric Design 20,
435454 (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, 209230 (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. 123146 (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. 147156 (2003)
Shapepreserving
interpolation
by
G^1
and
G^2
PH
quintic
splines (with C. Manni
and A. Sestini), IMA Journal of Numerical Analysis 23,
175195 (2003)
Minkowski geometric algebra and the stability
of characteristic polynomials
(with H. P. Moon), Visualization and Mathematics III (HC.
Hege and K. Polthier, eds),
Springer, pp. 163188 (2003)
Exact
rotationminimizing
frames
for
spatial
Pythagoreanhodograph
curves
Graphical Models 64, 382395 (2002)
Hermite
interpolation
by
rotationinvariant
spatial
Pythagoreanhodograph
curves
(with M. alKandari and T. Sakkalis), Advances in Computational
Mathematics 17,
369383 (2002)
Structural
invariance
of
spatial
Pythagorean
hodographs (with M. alKandari
and T. Sakkalis), Computer Aided Geometric
Design 19, 395407 (2002)
Pythagoreanhodograph curves, Handbook
of Computer Aided Geometric Design
(G. Farin, J. Hoschek, and MS. Kim, eds.), North Holland,
405427 (2002)
Exact
Minkowski products of N complex disks (with H. Pottmann),
Reliable Computing 8, 4366 (2002)
Optimal
slicing
of
freeform
surfaces (with M. alKandari, H. Pottmann, and
T. S. Smith),
Computer Aided Geometric Design 19, 4364 (2002)
Computation
of
optimal
composite
parameterizations (with P. Costantini,
C. Manni, and A. Sestini), Computer Aided Geometric Design 18,
875897
(2001)
Gauss
map
computation
for
freeform
surfaces (with T. S. Smith),
Computer Aided Geometric Design 18, 831850 (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, 3560 (2001)
ALGORITHM
812:
BPOLY:
An
objectoriented
software
library
of
algorithms
for
polynomials
in
Bernstein
form (with YF. Tsai), ACM Transactions
on Mathematical
Software 27, 267296 (2001)
Realtime
CNC
interpolators
for
Bezier
conics (with C. Manni and
A. Sestini),
Computer Aided Geometric Design 18, 639655 (2001)
Minkowski
geometric
algebra
of
complex
sets (with H. P. Moon and
B. Ravani),
Geometriae Dedicata 85, 283315
(2001)
Sliding mode control of two arms manipulating a
flexible beam (with A. S. alYahmadi
and T. C. Hsia), Proceedings, 32nd International Symposium on Robotics,
April 1921, 2001,
Seoul, Korea (2001)
Performance
analysis
of
CNC
interpolators
for
timedependent
feedrates
along
PH
curves
(with YF. Tsai and B. Feldman), Computer Aided Geometric Design 18,
245265
(2001)
Construction
and
shape
analysis
of
PH
quintic
Hermite
interpolants (with H. P.
Moon
and H. I. Choi), Computer Aided Geometric Design 18,
93115 (2001)
Exact
Taylor
series
coefficients
for
variablefeedrate
CNC
curve
interpolators
(with YF. Tsai), Computer Aided Design 33, 155165
(2001)
Bipolar and multipolar coordinates (with H.
P. Moon), The Mathematics of Surfaces IX
(R. Cippola and R. Martin eds.), Springer, 348371 (2000)
Minkowski roots of complex sets (with W. Gu
and H. P. Moon), Geometric Modeling
and Processing 2000, IEEE Computer Society Press, 287300 (2000)
Algorithms
for
Minkowski
products
and
implicitlydefined
complex
sets
(with H. P. Moon and B. Ravani), Advances in Computational
Mathematics
13, 199229 (2000)
Curves from motion, motion from curves, Curve
and
Surface
Design:
SaintMalo
1999
(PJ. Laurent, P. Sablonniere, and L. L. Schumaker, eds.), Vanderbilt
Univ. Press,
6390 (2000)
Physical
constraints
on
feedrates
and
feed
accelerations
along
curved
tool
paths
(with YF. Tsai and C. Wilson), Computer Aided Geometric Design 17,
337359
(2000)
LegendreBernstein
basis
transformations,
Journal of Computational and Applied Mathematics 119,
145160 (2000)
Convergent
inversion
approximations
for
polynomials
in
Bernstein
form,
Computer Aided Geometric Design 17, 179196 (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, 253277 (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, 119141 (1999)
Contour
machining
of
freeform
surfaces
with
realtime
PH
curve
CNC
interpolators
(with YF. Tsai and GF. Yuan), Computer Aided Geometric
Design 16, 6176 (1999)
G
codes
for
the
specification
of
Pythagoreanhodograph
tool
paths
and
associated
feedrate
functions
on
openarchitecture
CNC
machines (with J. Manjunathaiah and GF.
Yuan),
International Journal of Machine Tools and
Manufacture 39, 123142 (1999)
Leastsquares tool path approximation with Pythagoreanhodograph
curves for highspeed
CNC machining (with K. Saitou and YF. Tsai),
The Mathematics of Surfaces VIII
(R. Cripps, ed.), Information Geometers, 245264 (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 79, 1998, Bookplus Press, 126 (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, 95116
(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, 615635 (1998)
Variablefeedrate
CNC
interpolators
for
constant
material
removal
rates
along
Pythagoreanhodograph
curves (with J. Manjunathaiah, D. Nicholas, GF. Yuan,
and S. Jee), Computer Aided Design 30, 631640 (1998)
Design
of
rational
cam
profiles
with
Pythagoreanhodograph
curves (with S.
Jee
and J. Manjunathaiah), Mechanism and Machine Theory 33,
669682 (1998)
On integrating lines of curvature, Computer Aided Geometric Design 15, 187192 (1998)
Specifiedprecision computation of curve/curve bisectors (with R.
Ramamurthy),
International Journal of Computational Geometry and Applications 8,
599617
(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 2125, 1996,
Goa, INDIA, World Scientific Press, Singapore, 8795 (1997)
Triple point of Yukawa systems (with S. Hamaguchi and D. H. E.
Dubin),
Physical Review E 56, 46714682
(1997)
Pythagoreanhodograph
quintic
transition
curves
of
monotone
curvature,
Computer Aided Design 29, 601606 (1997)
Optimal parameterizations, Computer Aided Geometric Design 14, 153168 (1997)
Conic
approximation of conic offsets, Journal of Symbolic Computation
23, 301313 (1997)
Phase
diagram
of
Yukawa
systems
near
the
onecomponentplasma
limit
revisited
(with
S. Hamaguchi and D. H. E. Dubin), Journal of Chemical Physics 105,
76417647
(1996)
Construction of C2 Pythagoreanhodograph interpolating splines by
the
homotopy method
(with G. Albrecht), Advances in Computational Mathematics 5,
417442
(1996)
On the optimal
stability of the Bernstein basis (with T. N. T. Goodman),
Mathematics of Computation 65, 15531566 (1996)
Realtime
CNC
interpolators
for
Pythagoreanhodograph
curves (with S. Shah),
Computer Aided Geometric Design 13, 583600 (1996)
Approximation
of
rollingball
blends
for
freeform
parametric
surfaces
(with R. Sverrisson), Computer Aided Design 28, 871878
(1996)
Computational methods for rapid prototyping of analytic solid models
(with T. Koenig),
Rapid Prototyping Journal 2 (3), 4148 (1996)
Smooth curve design with doubleTschirnhausen cubics (with J.
Peters),
Annals of Numerical Mathematics 3, 6382 (1996)
Polynomial and rational Pythagoreanhodograph curves reconciled
(with
H. Pottmann),
The Mathematics of Surfaces VI (G. Mullineux, ed.), Oxford Univ.
Press, 355378 (1996)
The
elastic
bending
energy
of
Pythagoreanhodograph
curves,
Computer Aided Geometric Design 13, 227241 (1996)
Computing Minkowski sums of plane curves (with A. Kaul), International
Journal
of Computational Geometry and Applications 5, 413432
(1995)
Hermite interpolation by Pythagoreanhodograph quintics (with C. A.
Neff),
Mathematics of Computation 64, 15891609 (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,
355368 (1995)
Analysis
of
the
offset
to
a
parabola (with T. W. Sederberg),
Computer Aided Geometric Design 12, 639645 (1995)
Thermodynamics of stronglycoupled Yukawa systems near the
onecomponentplasma
limit II. Molecular dynamics simulations (with S. Hamaguchi), Journal
of
Chemical
Physics
101, 98859893 (1994)
Thermodynamics of stronglycoupled Yukawa systems near the
onecomponentplasma
limit I. Derivation of the excess energy (with S. Hamaguchi), Journal
of
Chemical
Physics
101, 98769884 (1994)
Spline approximation of "effective" potentials under periodic
boundary conditions
(with S. Hamaguchi), Journal of Computational Physics 115,
276287
(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,
PEDVol. 682
(Proceedings of the 1994 International Mechanical Engineering Congress
and Exposition),
557568, 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, 327354 (1994)
The conformal map z to z^2 of the hodograph plane, Computer
Aided Geometric Design 11,
363390 (1994)
Plasmaparticulate interactions in nonuniform plasmas with finite
flows (with S. Hamaguchi),
Physics of Plasmas 1, 21102118
(1994)
The BoltzmannPoisson 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, 1731, Springer
(1994)
Polarization force on a charged particulate in a nonuniform plasma
(with S. Hamaguchi),
Physical Review E 49, 44304441
(1994)
Mass segregation, relaxation, and the Coulomb logarithm in Nbody
systems (again)
(with E. E. Salpeter), Astrophysical Journal 427,
676683 (1994)
The bisector of a point and a plane parametric curve (with J. K.
Johnstone),
Computer Aided Geometric Design 11, 117151 (1994)
Pythagoreanhodograph space curves (with T. Sakkalis),
Advances in Computational Mathematics 2, 4166 (1994)
Watch your (parametric) speed!, ComputerAided Surface Geometry
and Design
(The Mathematics of Surfaces IV) (A. Bowyer, ed.), Oxford Univ.
Press, 6995 (1994)
Algebraically rectifiable parametric curves (with T. Sakkalis),
Computer Aided Geometric Design 10, 551569 (1993)
A shocktracking algorithm for surface evolution under reactiveion
etching (with M. Dalvie,
S. Hamaguchi, and S. Sethuraman), Journal of Applied Physics 74,
51725184
(1993)
Thermal energy of the crystalline onecomponent plasma from
dynamical
simulations
(with S. Hamaguchi), Physical Review E
47, 43304336 (1993)
Phase transitions of dense systems of charged "dust" grains in
plasmas (with S. Hamaguchi),
Applied Physics Letters 61, 29732975 (1992)
Dynamical Nbody simulations of Coulomb scattering in plasma sheaths
(with M. Dalvie,
S. Hamaguchi, and M. Surendra), Physical Review A 46,
78157829 (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, 26202631
(1992)
Exact equations of "simple" wavefronts (with J.C. Chastang), Optik 91, 109121 (1992)
Approximation by interval Bezier curves (with T. W. Sederberg),
IEEE Computer Graphics and Applications 12 (5), 8795
(1992)
Selfconsistent Monte Carlo simulation of the cathode fall including
treatment of negative
glow electrons (with M. Dalvie and S. Hamaguchi), Physical Review A
46, 10661077 (1992)
Ion energetics in collisionless sheaths of rf process plasmas (with
M. Dalvie and S. Hamaguchi),
Physics of Fluids B 4, 23622367 (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,
239260 (1992)
Analysis of a kinematic model for ion transport in rf plasma sheaths
(with M. Dalvie
and S. Hamaguchi), Physical Review A 45, 59135928
(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, 10901099 (1992)
Pythagoreanhodograph curves in practical use, Geometry
Processing
for Design and Manufacturing
(R. E. Barnhill, ed.), SIAM, Philadelphia, 333 (1992)
Ponderomotive force and ion energy distributions in an rf sheath
(with M. Dalvie and S. Hamaguchi),
Physical Review Letters 68, 4447 (1992)
The mathematical evolution of wavefronts (with J.C. Chastang),
Optics and Photonics News 3, 2023 (1992)
Computing with barycentric polynomials, The Mathematical Intelligencer 13, 6169 (1991)
Ion distribution function in a weakly collisional sheath (with M.
Dalvie and S. Hamaguchi),
Physical Review A 44, 38043821
(1991)
Monte Carlo simulations of spacechargelimited ion transport
through
collisional plasma
sheaths (with M. Dalvie and S. Hamaguchi), Physical Review A 44,
26642681
(1991)
Real rational curves are not "unit speed" (with T. Sakkalis),
Computer Aided Geometric Design 8, 151157 (1991)
On the stability of transformations between power and Bernstein
polynomial forms,
Computer Aided Geometric Design 8, 2936 (1991)
Boundarycondition refinement of the ChildLangmuir law for
collisionless dc plasma sheaths
(with M. Dalvie and L. F. Pavarino), Journal of Applied Physics 68,
61066116
(1990)
Pythagorean hodographs (with T. Sakkalis),
IBM Journal of Research and Development 34, 736752
(1990)
On the numerical condition of BernsteinBezier subdivision processes
(with C. A. Neff),
Mathematics of Computation 55, 637647 (1990)
Algebraic properties of plane offset curves (with C. A. Neff),
Computer Aided Geometric Design 7, 101127 (1990)
Analytic properties of plane offset curves (with C. A. Neff),
Computer Aided Geometric Design 7, 8399 (1990)
Singular points of algebraic curves (with T. Sakkalis),
Journal of Symbolic Computation 9, 405421 (1990)
Numerical stability in geometric algorithms and representations, The
Mathematics
of
Surfaces
III
(D. C. Handscomb, ed.), Oxford Univ. Press, 83113 (1989)
Automatic parsing of degenerate quadric surface intersections (with
C. A. Neff
and M. A. O'Connor), ACM Transactions on Graphics 8,
174203 (1989)
Hierarchical segmentations of algebraic curves and some
applications,
Mathematical Methods
in Computer Aided Geometric Design, (T. Lyche & L. L.
Schumaker, eds.), Academic Press,
239248 (1989)
On the numerical condition of algebraic curves and surfaces 1.
Implicit equations
(with V. T. Rajan), Computer Aided Geometric Design 5,
215252 (1988)
Algorithms for polynomials in Bernstein form (with V. T. Rajan),
Computer Aided Geometric Design 5, 126 (1988)
Computational issues in solid boundary evaluation, Information
Sciences 44, 87171 (1988)
Graphical methods for surface differential geometry, The
Mathematics of Surfaces II
(R. R. Martin, ed.), Oxford Univ. Press, 363385 (1987)
On the numerical condition of polynomials in Bernstein form (with V.
T. Rajan),
Computer Aided Geometric Design 4, 191216 (1987)
Direct surface section evaluation, Geometric Modeling:
Algorithms and New Trends
(G. Farin, ed.), SIAM, 319334 (1987)
Trimmed surface algorithms for the evaluation and interrogation of
solid boundary
representations, IBM Journal of Research and Development 31,
314334
(1987)
Surface analysis methods (with J. M. Beck and J. K. Hinds),
IEEE Computer Graphics and Applications 6 (12), 1836
(1986)
The characterization of parametric surface sections,
Computer Vision, Graphics, and Image Processing 33,
209236 (1986)
The approximation of nondegenerate offset surfaces,
Computer Aided Geometric Design 3, 1543 (1986)
Exact offset procedures for simple solids,
Computer Aided Geometric Design 2, 257279 (1985)
A hierarchy of geometric forms (with J. K. Hinds),
IEEE Computer Graphics and Applications 5 (5), 5178
(1985)
Do cosmic magnetic monopoles cause rapid decay of the galactic
magnetic field?
(with S. L. Shapiro and I. Wasserman), Comments on Astrophysics 10,
257265
(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,
282298
(1984)
The collapse and violent relaxation of Nbody systems: mass
segregation and the secondary
maximum (with G. L. Hoffman and E. E. Salpeter), Astrophysical
Journal 271, 1121 (1983)
Simulations of galaxy mergers: cannibalism and dynamical friction
(with M. J. Duncan and S. L. Shapiro), Astrophysical Journal 271,
2231
(1983)
Computational astrophysics on the array processor (with S. L.
Shapiro
and S. A. Teukolsky),
IEEE Computer 16 (6), 7383 (1983)
Hierarchical merging and the structure of elliptical galaxies (with
M. J. Duncan
and S. L. Shapiro), Astrophysical Journal 265, 597605
(1983)
Simulations of merging disk galaxies (with S. L. Shapiro),
Astrophysical Journal 259, 103115 (1982)
Mass segregation, relaxation, and the Coulomb logarithm in Nbody
systems
(with E. E. Salpeter), Astrophysical Journal 253,
512519 (1982)
Computer simulations of environmental influences on galaxy evolution
in dense clusters
II. Rapid tidal encounters (with S. L. Shapiro), Astrophysical
Journal 243, 3241 (1981)
Computer simulations of environmental influences on galaxy evolution
in dense clusters
I. Rampressure stripping (with S. L. Shapiro), Astrophysical
Journal 241, 928945 (1980)