JOURNAL PUBLICATIONS
- Modeling Perspective Projections in 3-Dimensions
by Rotations in 4-Dimensions, accepted to appear in Graphical Models.
- Using a Bivariate Sparse Resultant to Find
the Singularities of Rational Space Curves, with X. Shi and X. Jia, accepted to appear in
the Journal of Symbolic Computation.
- Quantum B-splines, with P. Simeonov,
accepted to appear in BIT Numerical Mathematics.
- Formulas and Algorithms
for Quantum Differentiation of Quantum Bernstein Bases and Quantum
Bezier Curves Based on Quantum Blossoming, with P. Simeonov, Graphical
Models (2012), Special Issue of selected papers from the 8th Dagstuhl Seminar
on Geometric Modeling 2011, Vol. 74, pp.326-334.
- Using ”-Bases to Implicitize Rational Surfaces
with a Pair of Orthogonal Directrices, with X. Shi and X. Wang, Computer Aided Geometric Design (2012),
Special Issue on GMP 2012, Vol. 29, pp. 541-554.
- Implicitizing Rational Surfaces
of Revolution using ”-Bases, with X. Shi, Computer Aided Geometric
Design (2012), Vol. 29, pp. 348-362.
- Using Smith Normal Forms and
Mu-bases to Compute All the Singularities of Rational Planar Curves, with
X. Jia, Computer Aided Geometric Design (2012), Vol. 29, pp. 296-314.
- q-Blossoming: A New
Approach to Algorithms and Identities for q-Bernstein Bases and q-Bezier
Curves, with P. Simeonov and V. Zafiris, Journal of Approximation Theory (2012),
Vol. 164, pp. 77-104.
- h-Blossoming: A New Approach
to Algorithms and Identities for h-Bernstein Bases and h-Bezier
Curves, with P. Simeonov and V. Zafiris, Computer Aided Geometric Design,
(2011), Vol. 28, No.9, pp.549-565.
- Bezier and B-spline Curves with Knots in the
Complex Plane, with K. Tsianos, Fractals Complex Geometry, Patterns, and
Scaling in Nature and Society (2011), Vol. 19, pp. 67-86.
- Understanding Quaternions, Graphical
Models (2011), Vol. 73, pp.21-49.
- Convergence and Smoothness
of Nonlinear Lane-Riesenfeld Algorithms in the Functional Setting, with N.
Dyn, Foundations of Computational Mathematics (2011), Vol. 11,
No. 1, pp. 79-94.
- Minimal Generators for the
Rees Algebra of Rational Space Curves of Type (1,1d-2), with J. Hoffman,
H. Wang, and X. Jia, European Journal of Pure and Applied Mathematics
(2010), Vol. 3,No.4,pp. 602-632.
- Set-Theoretic Generators of
Rational Space Curves (with X. Jia and H. Wang), accepted to appear in the
Journal of Symbolic Computation.
- Mu-bases and Singularities
of Rational Planar Curves (with X. Jia), Computer Aided Geometric Design (2009), Vol. 26, pp. 970-988.
- Axial Moving Planes and
Singularities of Rational Space Curves (with H. Wang and X. Jia), Computer Aided Geometric Design
(2009), Vol. 26, pp. 300-316.
- On the Smoothness of
Real-Valued Functions Generated by Subdivision Schemes Using Nonlinear
Binary Averaging (with E. Vouga and S. Schaefer), Computer Aided Geometric Design
(2009), Vol. 26, pp. 231-242.
- Mu-Bases for Polynomial
Systems in One Variable, with N. Song, Computer
Aided Geometric Design (2009), Vol. 26, pp. 217-230.
- Non-Uniform Subdivision for
B-splines of Arbitrary Degree (with S. Schaefer),
accepted to appear in Computer Aided Geometric Design (2009), Vol.
26, pp. 75-81.
- Division Algorithms for
Bernstein Polynomials (with L. Buse), accepted to appear in Computer
Aided Geometric Design (2008), vol. 25, pp. 850-865.
- Nonlinear Subdivision Through Nonlinear Averaging (with S. Schaefer and E. Vouga), accepted to appear in Computer
Aided Geometric Design (2008), Vol. 25, pp. 162-180.
- Axial Moving Lines and
Singularities of Planar Rational Curves (with N. Song and F. Chen),
accepted to appear in Computer Aided Geometric Design (2007), Vol.
24, pp.200-209.
- Two Blossoming Proofs of
the Lane-Riesenfeld Algorithm (with E. Vouga),
Computing (2007), Vol. 79, pp. 153-162.
- Improving Conformational
Searches by Geometric Screening (with M. Zhang, R. White, L. Wang, L.
Kavraki, and B. Hassett), Journal of Bioinformatics (2005), Vol. 21, pp. 624-630.
- Curvature Formulas for
Implicit Curves and Surfaces, Special Issue of CAGD on Geometric
Modeling and Differential Geometry (2005), Vol. 22, pp. 632-658.
- Using Invariants to Extract
Geometric Characteristics of Conic Sections from Rational Quadratic
Parametrizations (with W. Wang),
International Journal of Computational Geometry and Applications (2004),
Vol. 14, pp. 161-187.
- Recursive Turtle Programs
and Iterated Affine Transformations (with T. Ju and S.
Schaeffer), Computers and Graphics (2004), Vol. 28, pp.
991-1004.
- Turtle Geometry in Computer
Graphics and Computer-Aided Design (with T. Ju and S.
Schaeffer), Computer-Aided Design (2004), Vol.
36, pp. 1471-1482.
- Multisided Arrays of
Control Points for Multisided Bezier Patches, Computer Aided Geometric
Design (2004), Vol. 21, pp. 243-261.
- Enhancing Levinâs Method
for Computing Quadric-Surface Intersections (with W.
Wang and C. Tu), Computer Aided Geometric Design (2003),
Vol. 20, pp. 401-422.
- Deriving Linear
Transformations in 3-Dimensions, IEEE Computer Graphics and
Applications (2003), Vol. 23, pp. 66-71.
- Computing Quadric Surface
Intersections Based on an Analysis of Plane Cubic Curves (with W. Wang and B. Joe), Graphical Models (2003),
Vol. 64. pp. 335-367.
- Compositional Synthesis of
Optical Imaging Systems (with D. Subramanian), Research in Engineering Design
(2002), Vol. 13, pp. 183-198.
- The Affine Invariant
Analytic Blossom (with G. Morin), Computer Aided Geometric Design (2002).
Vol. 19, pp. 621-623.
- On the Algebraic and
Geometric Foundations of Computer Graphics, Transactions on Graphics (2002),
Vol. 21, pp. 1-35.
- Fast Computation of the
Bezout and Dixon
Resultant Matrices (with E. Chionh and M.
Zhang), Journal of Symbolic Computation (2002), Vol. 33, pp.
13-29.
- On the Smooth Convergence
of Subdivision and Degree Elevation for Bezier Curves (with G. Morin), Computer
Aided Geometric Design, (2001), Vol. 18, pp. 657-666.
- Trimming Analytic Functions
Using Right Sided Poisson Subdivision (with G. Morin), Computer-Aided
Design, (2001), Vol. 33, pp. 813-824.
- Blossoming and Divided
Difference, Geometric Modeling, Computing [Suppl.], (2001), Vol.
14, pp. 155-184.
- Baseball Arithmetic and the
Laws of Pseudoperspective, IEEE Computer Graphics and Applications, (2001),
Vol. 21, pp. 70-78.
- A Subdivision Scheme for
Poisson Curves and Surfaces (with G. Morin), Computer Aided Geometric
Design, (2000), Vol. 17, pp. 813-833.
- Spline Functions of
Negative Degree (with G. Walz), CALCOLO, (2000), Vol. 37, pp.
125-137.
- On the Validity of
Implicitization by Moving Quadrics for Rational Surfaces with No Base Points
(with D. Cox and M. Zhang), Journal of Symbolic Computation, (2000),
Vol. 29, pp. 419-440.
- The Ambient Space of
Computer Graphics and Geometric Modeling, IEEE Computer Graphics and
Applications, (2000), Vol. 20, pp. 76-84.
- The Rational Bernstein Bases
and the Multirational Blossoms, Computer Aided Geometric Design, (1999),
Vol. 16, pp. 701-738.
- Blossoming with
Cancellation, Special Issue of Computer Aided Geometric Design
dedicated to P. de Casteljau, (1999), Vol. 16, pp. 671-689.
- On a Relationship Between
the Moving Line and Moving Conic Coefficient Matrices (with E. Chionh and
M. Zhang), Computer Aided Geometric Design, (1999), Vol. 16, pp.
517-527.
- Lattices and Algorithms for
Bivariate Bernstein, Lagrange, Newton and
Other Related Polynomial Bases Based on Duality between L-bases and
B-bases (with S. Lodha), Journal of Approximation Theory, (1998),
Vol. 93, pp. 59-99.
- On the Linear Independence
of the Bivariate Discrete Convolution Blending Functions (with Y.
Stefanus), Australian Computer Science Communications, (1998), Vol.
20, pp. 231-244.
- Rational Quadratic
Parametrizations of Quadrics (with W. Wang
and B. Joe), International Journal of Computational Geometry and
Applications, Vol. 7, (1997), pp 599-619.
- A Unified Approach to
Evaluation Algorithms for Multivariate Polynomials (with S. Lodha), Mathematics of
Computation, (1997), Vol. 66, pp. 1521-1553.
- The Dual Basis Functions
for the Generalised Ball Basis of Odd Degree (with W.A. Othman), Computer
Aided Geometric Design, (1997), Vol. 14, pp. 571-582.
- Implicitizing Rational
Curves by the Method of Moving Algebraic Curves (with T. Sederberg and H.
Du), Journal of Symbolic Computation, (1997), Vol. 23, pp. 153-175.
- Theories of Contact
Specified by Connection Matrices (with A. Habib), Computer Aided
Geometric Design, (1996), Vol. 13, pp. 905-929.
- A Recursive Algorithm for
Hermite Interpolation over a Triangular Grid (with A. Habib and T. Lyche),
Journal of Computational and Applied Mathematics, (1996), Vol. 73,
pp. 95-118.
- Some Applications of
Discrete Unimodality to Problems for Parametric Curves (with P. Barry), Annals
of Numerical Mathematics, (1996), Vol. 3, pp. 83-90.
- A Ladder Recurrence
Algorithm for the Evaluation of L-Patches (with S.
Lodha and J.Warren), Annals of Numerical Mathematics, (1996),
Vol. 3, pp. 209-219.
- Change of Basis Algorithms
for Surfaces in CAGD (with S. Lodha),
Computer Aided Geometric Design, (1995), Vol. 12, pp. 801-824.
- Elimination and Resultants
Part 1: Elimination and Bivariate Resultants (with E. Chionh), IEEE Computer Graphics
and Applications, (1995), Vol. 15, pp. 69-77.
- Elimination and Resultants
Part 2: Multivariate Resultants (with E. Chionh),
IEEE Computer Graphics and Applications, (1995), Vol. 15, pp.
60-69.
- Geometric Algorithms for Detecting
and Calculating All Conic Sections in the Intersection of Any Two Natural
Quadric Surfaces (with J. Miller), CVGIP: Graphical Models and Image
Processing, (1995), Vol. 57, pp. 55-66.
- Unimodal Properties of
Generalized Ball Bases (with P. Barry), Computing, Computing Suppl., Vol.
10, (1995), pp. 35-41.
- Dual Polynomial Bases, Journal
of Approximation Theory, (1994), Vol. 79, pp. 311-346.
- On the Existence and
Coefficients of the Implicit Equation of Rational Surfaces (with E. Chionh), CVGIP: Graphical Models and Image
Processing, (1994), Vol. 56, pp. 19-24.
- Knot Insertion Algorithms
for Piecewise Polynomial Spaces Determined by Connection Matrices (with P.
Barry and C. Micchelli), Advances in Computational Mathematics,
(1993), Vol. 1, pp. 139-171.
- Functional Composition
Algorithms via Blossoming (with T. DeRose, H. Hagen, and S. Mann), Transactions
on Graphics, (1993), Vol. 12, pp. 113-135.
- An Extension of Chaikenâs
Algorithm to B-spline Curves with Knots in Geometric Progression (with J.
Warren), CVGIP: Graphical Models and Image Processing, (1993), Vol.
55, pp. 58-62.
- Unimodal Properties of
B-Splines and Bernstein Basis Functions (with P. Barry and J. Beatty), Computer-Aided
Design, (1992), Vol. 24, pp. 627-636.
- Blossoming Marsdenâs
Identity (with Y. Stefanus), Computer Aided Geometric Design,
(1992), Vol. 9, pp. 73-84.
- Degree, Multiplicity, and
Inversion Formulas for Rational Surfaces Using u-Resultants (with E. Chionh), Computer Aided Geometric Design,
(1992), Vol. 9, pp. 93-108.
- Using Multivariate
Resultants to Find the Implicit Equation of a Rational Surface (with E. Chionh), The Visual Computer,
(1992), Vol. 8, pp. 171-180.
- Using Tangent Balls to Find
Plane Sections of Natural Quadric Surfaces (with Jim Miller), Computer
Graphics and Applications, (1992), Vol. 12, No. 2, pp. 68-82.
- Using Multivariate
Resultants to Find the Intersection of Three Quadric Surfaces (with E. Chionh and J. Miller), Transactions
on Graphics, (1991), Vol. 10, pp. 378-400.
- Polynomial Identities for
Piecewise Polynomial Spaces Determined by Connection Matrices (with P.
Barry, N. Dyn, and C. Micchelli), Aequationes Mathematicae, (1991),
Vol. 42, pp. 123-136.
- Shape Parameter Deletion
for Polya Curves (with P. Barry), Numerical Algorithms, (1991),
Vol. 1, pp. 121-137.
- B-Splines, Polya Curves,
and Duality (with P. Barry and T. DeRose), Journal of Approximation
Theory, (1991), Vol. 65, pp. 3-21.
- Interpolation and
Approximation of Curves and Surfaces Using Polya Polynomials (with P.
Barry), Computer Vision, Graphics, and Image Processing, (1991),
Vol. 53, pp. 137-148.
- Blossoming and Knot
Insertion Algorithms for B-Spline Curves, Computer Aided Geometric
Design, (1990), Vol. 7, pp. 69-81.
- Recursive Polynomial Curve
Schemes and Computer Aided Geometric Design (with P. Barry), Constructive
Approximation, (1990), Vol. 6, pp. 65-96.
- A Recursive Proof of a
B-Spline Identity for Degree Elevation, (1988) (with P. Barry), Computer
Aided Geometric Design, Vol. 5, No. 2, pp. 173-175.
- Urn Models, Approximations,
and Splines, Journal of Approximation Theory, (1988), Vol. 54, No.
1, pp. 1-66.
- Urn Models and B-Splines, Constructive
Approximation, (1988), Vol. 4, pp. 265-288.
- A Recursive Proof of
Boehm's Knot Insertion Technique (with P. Barry), Computer-Aided Design,
(1988), Vol. 20, No. 4, pp. 181-182.
- De Casteljau Type
Subdivision is Peculiar to Bezier Curves (with P. Barry), Computer-Aided
Design, (1988), Vol. 20, No. 3, pp. 114-116.
- An Analytic Approach to the
Intersection of All Piecewise Parametric Rational Cubic Curves (with T.
Sederberg), Computer-Aided Design, (1987), Vol. 19, No. 6, pp.
282-292.
- Conversion from Bezier
Rectangles to Bezier Triangles (with D. Filip), Computer-Aided Design,
(1987), Vol. 19, No. 1, pp. 25-28.
- Recursive Subdivision Without the Convex Hull
Property (with T. DeRose), Computer Aided Geometric Design, (1986),
Vol. 3, No. 4, pp. 247-265.
- Algebraic Geometry for
Computer-Aided Geometric Design (with T. Sederberg), IEEE Computer
Graphics and Applications, (1986), Vol. 6, No. 6, pp. 52-59.
- Urn Models and
Beta-Splines, IEEE Computer Graphics and Applications, (1986), Vol.
6, No. 2, pp. 57-64. (First delivered orally at the NASA International
Conference on Computational Geometry and Computer Aided Design, New
Orleans, June 1985.)
- The Method of Resolvents: A
Technique for the Implicitization, Inversion, and Intersection of
Non-Planar, Parametric, Rational Cubic Curves, Computer Aided Geometric
Design, (1985), Vol. 2, No. 4, pp. 237-255.
- Some Applications of
Resultants to Problems in Computational Geometry (with T. Sederberg), The Visual Computer, (1985), Vol. 1, No.
2, pp. 101-107. (First delivered orally at the International Conference on
Engineering and Computer Graphics, Beijing, China, August 1984.)
- Illicit Expressions in
Vector Algebra, Transactions on Graphics, (1985), Vol. 4, No. 3,
pp. 223-243.
- Implicitization, Inversion,
and Intersection of Planar Rational Cubic Curves, with T. Sederberg, Computer
Vision, Graphics, and Image Processing, (1985), Vol. 31, pp. 89-102.
- Markov Chains and Computer
Aided Geometric Design Part II -- Examples and Subdivision Matrices, Transactions
on Graphics, (1985), Vol. 4, No. 1, pp. 12-40.
- Polya's Urn Model and
Computer Aided Geometric Design, SIAM
Journal on Algebraic and Discrete Methods, (1985), Vol. 6, No. 1, pp.
1-28.
- Vector Elimination: A
Technique for the Implicitization, Inversion, and Intersection of Planar,
Parametric, Rational Polynomial Curves (with T. Sederberg and D.
Anderson), Computer Aided Geometric Design, (1984), Vol. 1, No. 4,
pp. 327-356.
- Linear Subdivision is Strictly a Polynomial Phenomenon (with D. Heath), Computer
Aided Geometric Design, (1984), Vol. 1, No. 3, pp. 269-278.
- Implicit Representation of
Parametric Curves and Surfaces (with T. Sederberg and D. Anderson),
Computer Vision, Graphics, and Image Processing, (1984), Vol. 28,
pp. 72-84.
- Markov Chains and Computer
Aided Geometric Design Part I -- Problems and Constraints, Transactions
on Graphics, (1984), Vol. 3, No. 3, pp. 204-222.
- An Urnful of Blending
Functions, IEEE Computer Graphics and Applications, (1983), Vol. 3,
No. 7, pp. 49-54. (First delivered orally at the NASA Symposium on
Computer Aided Geometry and Modeling, Langley, Virginia, April 1983).
- Two Approaches to a
Computer Model for Quadric Surfaces, IEEE Computer Graphics and
Applications, (1983), Vol. 3, No. 6, pp. 21-24.
- Subdivision Algorithms for
Bezier Triangles, Computer-Aided Design, (1983), Vol. 15, No. 3,
pp. 159-166.
- Quadrics of Revolution, IEEE
Computer Graphics and Applications, (1983), Vol. 3, No. 3, pp. 68-76.
- Using Degenerate Bezier
Triangles and Tetrahedra to Subdivide Bezier Curves, Computer- Aided
Design, (1982), Vol. 14, No. 6, pp. 307-311.
- The Holonomy Ring on the
Leaves of Foliated Manifolds, Journal of Differential Geometry (1976),
Vol. 11, No. 3, pp. 411-449
ARTICLES UNDER SUBMISSION
- Computing Perspective Projections in
3-Dimensions using Rotors in the Homogeneous and Conformal Models of Clifford Algebra, with S. Mann
and X. Jia, submitted to Advances in Applied Clifford Algebras.
- ”-Bases for Complex Rational Curves,
with X. Wang, submitted to Computer Aided Geometric Design.
- Generating Functions for B-Splines
with Knots in Geometric or Affine Progression, with C. Disibuyuk, G. Budakci, and H. Oruc,
submitted to Advances in Computational Mathematics.
- Generating Functions for Uniform
B-Splines, submitted to Proceedings of the Eighth International Conference on Mathematical Methods
for Curves and Surfaces.
- Rational B-splines and Multirational Blossoms,
submitted to Advances in Computational Mathematics.
- The Multirational Blossom, submitted to Constructive
Approximation.
- Differentiation and Integration
Identities for B-splines of Negative Degree, submitted to Mathematics of
Computation.
- A Survey of Urn Mmodels in Computer
Aided Geometric Design, with P. Barry, submitted to IEEE Computer
Graphics and Applications.
- Bounding the Arclength of Integral and Rational
Bezier Curves, with C. Micchelli, W. Png, and J. Warren, submitted to Computer-Aided Design.
- Wiggle, submitted to Journal of Computing.
TECHNICAL REPORTS
- Transformations and
Transitions from the Sylvester to the Bezout Resultant, with E. Chionh and
M. Zhang, Technical Report TR99-343, Department of Computer Science, Rice
University, 1999.
- A Set of Convolution
Identities Relating the Blocks of Two Dixon Resultant Matrices, with E.
Chionh and M. Zhang, Technical Report TR99-342, Department of Computer
Science, Rice University, 1999.
- The Block Structure of
Three Dixon Resultants and Their Accompanying Transformation Matrices,
with E. Chionh and M. Zhang, Technical Report TR99-341, Department of
Computer Science, Rice University, 1999.
- Vector Algebraic Representations
of Natural Quadrics with Applications to Ray Tracing, with Jim Miller,
DesignLab Technical Report DL-1997-01, Department of Computer Science, University
of Kansas, 1997.
- Detecting and Calculating Conic
Sections in the Intersection of Two Natural Quadric Surfaces, Part I:
Theoretical Analysis, with Jim Miller, Technical Report TRâ93â1,
Department of Computer Science, University
of Kansas, 1992.
- Detecting and Calculating
Conic Sections in the Intersection of Two Natural Quadric Surfaces, Part
II: Geometric Constructions for Detection and Calculation, with Jim
Miller, Technical Report TRâ93â2, Department of Computer Science, University
of Kansas, 1992.
- A Sufficient Condition for
the Intersection of Two Quadrics of Revolution to Degenerate into a Pair
of Conic Sections, with Joe Warren, Department of Computer Science, Rice
University.
BOOKS
- Rethinking Quaternions: Theory and
Computation, Synthesis Lectures on Computer Graphics and Animation, ed.
Brian A. Barsky, No. 13. San Rafael: Morgan & Claypool Publishers, 2010.
- An Integrated Introduction to Computer Graphics and Geometric
Modeling, CRC Press, Taylor and Francis, New York, 2009.
- Geometric Modeling,
Dagstuhl 2002, S. Hahmann, G. Brunnett, G. Farin, and R. Goldman
(eds.), Springer-Verlag, 2004.
- Topics in Algebraic
Geometry and Geometric Modeling, co-edited with R. Krasauskas, AMS
Contemporary Mathematics, Vol. 334, 2003.
- Pyramid Algorithms: A
Dynamic Programming Approach to Curves and Surfaces for Geometric
Modeling, Morgan Kaufmann Publishers, Academic Press, San Diego, 2002.
- Knot Insertion and
Deletion Algorithms for B-spline Curves and Surfaces, co-edited with
Tom Lyche, SIAM,
1993.
BOOK
REVIEW
1. After the
Revolution: Geometric Algebra for Computer Scientists in the Twenty-First
Century, Computer-Aided Design (2008), Vol. 40, pp. 655-656.
ARTICLES IN BOOKS
- A Homogeneous Model for Three-
Dimensional Computer Graphics based on the Clifford Algebra for R3,
Guide to Geometric Algebra in Practice, edited by L. Dorst and J.
Laenby, Springer, London (2011), pp. 329-352.
- Counting Pruned Bezier
Curves (with S. Mann), Mathematical Methods for Curves and Surfaces:
Tromso 2004, edited by M. Daehlen, K. Morken, and L. Schumaker,
Nashboro Press, (2005), pp. 169-178.
- Polar Forms in Geometric
Modeling and Algebraic Geometry, Topics in Algebraic Geometry and
Geometric Modeling, edited by R. Goldman and R. Krasauskas, AMS
Contemporary Mathematics, Vol. 334, (2003), pp. 3-24.
- Toric Bezier Patches with
Depth (with R. Krasauskas), Topics in Algebraic Geometry and Geometric
Modeling, edited by R. Goldman and R. Krasauskas, AMS Contemporary
Mathematics, Vol. 334, (2003), pp. 65-91.
- Notions of Geometric
Continuity Based on Geometric Invariants (with A. Habib), Mathematical
Methods for Curves and Surfaces, edited by M. Daehlen, T. Lyche, and
L. Schumaker, Vanderbilt University Press, (1995), pp. 187-201.
- Duality Between Degree
Elevation and Differentiation for B-bases and L-bases (with S. Lodha), Mathematical
Methods for Curves and Surfaces, edited by M. Daehlen, T. Lyche, and
L. Schumaker, Vanderbilt University
Press, (1995), pp. 305-314.
- Identities for the
Univariate and Bivariate Bernstein Basis Functions, Graphics Gems V, edited
by Alan Paeth, Academic Press, (1995), pp. 149-162.
- Identities for the B-Spline
Basis Functions, Graphics Gems V, edited by Alan Paeth, Academic
Press, (1995), pp. 163-167.
- A Multivariate
Generalization of the de Boor-Fix Formula (with S. Lodha), Curves and
Surfaces in Geometric Design, edited by Pierre-Jean Laurent, Alain Le
Mehaute, and Larry Schumaker, A.K. Peters, Ltd., (1994), pp. 301-310.
- Knot Insertion Using
Forward Differencing (with P. Barry), Graphics Gems IV, edited by
Paul Heckbert, Academic Press, (1994), pp. 251-255.
- Algorithms for Progressive
Curves: Extending B-Spline and Blossoming Techniques to the Monomial,
Power, and Newton Dual Bases (with
P. Barry), Knot Insertion and Deletion Algorithms for B-spline Curves
and Surfaces, co-edited by Ron Goldman and Tom Lyche, SIAM, (1993),
pp. 11-63.
- Factored Knot Insertion (with
P. Barry), Knot Insertion and Deletion Algorithms for Bspline Curves
and Surfaces, co-edited by Ron Goldman and Tom Lyche, SIAM,
(1993), pp. 65-88.
- Knot Insertion Algorithms (with
P. Barry), Knot Insertion and Deletion Algorithms for Bspline Curves
and Surfaces, co-edited by Ron Goldman and Tom Lyche, SIAM,
(1993), pp. 89-133.
- Cross Product in
4-Dimensions and Beyond, Graphics Gems III, edited by David Kirk, Academic
Press, (1992), pp. 84-88.
- Decomposing Projective
Transformations, Graphics Gems III, edited by David Kirk, Academic
Press, (1992), pp. 98â107.
- Decomposing Linear and
Affine Transformations, Graphics Gems III, edited by David Kirk,
Academic Press, (1992), pp. 108â116.
- Discrete Convolution
Schemes (with Y. Stefanus), Mathematical Methods in Computer Aided
Geometric Design II, edited by Tom Lyche and Larry Schumaker, Academic
Press, (1992), pp. 585-596. (First delivered orally by Y. Stefanus at the
Oslo Conference on Curves, Surfaces, CAGD, and Image Processing,
June 1991.)
- Wonderful Triangle: A
Simple, Unified, Algorithmic Approach to Change of Basis Procedures in
Computer Aided Geometric Design (with P. Barry), Mathematical Methods
in Computer Aided Geometric Design II, edited by Tom Lyche and Larry
Schumaker, Academic Press, (1992), pp. 297-320. (First delivered orally at
the Oslo Conference on Curves, Surfaces, CAGD, and Image Processing,
June 1991.)
- Implicitizing Rational
Surfaces with Base Points by Applying Perturbations and the Factors of
Zero Theorem (with E. Chionh), Mathematical Methods in Computer Aided
Geometric Design II, edited by Tom Lyche and Larry Schumaker, Academic
Press, (1992), pp. 101-110. (First delivered orally by E. Chionh at the
Oslo Conference on Curves, Surfaces, CAGD, and Image Processing,
June 1991.)
- Tensor Product Slices (with
R. Bartels and R. Pfeifle), Mathematical Methods in Computer Aided
Geometric Design II, edited by Tom Lyche and Larry Schumaker, Academic
Press, (1992), pp. 431-440. (First delivered orally by R. Bartels at the
Oslo Conference on Curves, Surfaces, CAGD, and Image Processing,
June 1991.)
- Area of Planar Polygons and
Volume of Polyhedra, Graphics Gems II, edited by Jim Arvo, Academic
Press, (1991), pp. 170-171.
- Recovering the Data from
the Transformation Matrix, Graphics Gems II, edited by Jim Arvo,
Academic Press, (1991), pp. 324-331.
- Transformations as
Exponentials, Graphics Gems II, edited by Jim Arvo, Academic Press,
(1991), pp. 332-337.
- More Matrices and
Transformations: Shear and Pseudoperspective, Graphics Gems II,
edited by Jim Arvo, Academic Press, (1991), pp. 338-341.
- A Tutorial Introduction to
Blossoming, with T. DeRose and J. Lounsbery, Geometric Modeling,
edited by H. Hagen and D. Roller, Springer-Verlag, (1991), pp. 267-286.
- Triangles, Graphics Gems,
edited by Andrew Glassner, Academic Press, (1990), pp. 20-23.
- Intersection of Two Lines
in Three Space, Graphics Gems, edited by Andrew Glassner, Academic
Press, (1990), pp. 304.
- Intersection of Three
Planes, Graphics Gems, edited by Andrew Glassner, Academic Press,
(1990), pp. 305.
- Matrices and
Transformations, Graphics Gems, edited by Andrew Glassner, Academic
Press, (1990), pp. 472-475.
- Some Properties of Bezier
Curves, Graphics Gems, edited by Andrew Glassner, Academic Press,
(1990), pp. 587-593.
- Integration of Bernstein
Basis Functions, Graphics Gems, edited by Andrew Glassner, Academic
Press, (1990), pp. 604-606.
- Recursive Triangles, Computation
of Curves and Surfaces, edited by W. Dahmen, M. Gasca, and C.
Micchelli, NATO ASI Series, Series C: Mathematical and Physical Sciences,
Vol. 307, Kluwer Academic Publishers, (1990), pp. 27-72.
- Three Examples of Dual
Properties of Bezier Curves (with P. Barry), Mathematical Methods in
Computer Aided Geometric Design, edited by Tom Lyche and Larry
Schumaker, Academic Press, (1989), pp. 61-69. (First delivered orally by
P. Barry at the Oslo Conference on Mathematical Methods in CAGD, June
1988.)
- What is the Natural Generalization
of a Bezier Curve? (with P. Barry), Mathematical Methods in Computer
Aided Geometric Design, edited by Tom Lyche and Larry Schumaker,
Academic Press, (1989), pp. 71-85. (First delivered orally by R. Goldman
at the Oslo Conference on Mathematical Methods in CAGD, June 1988.).
- On Beta Continuous
Functions and Their Application to the Construction of Geometrically
Continuous Curves and Surfaces, with B. Barsky, Mathematical Methods in
Computer Aided Geometric Design, edited by Tom Lyche and Larry
Schumaker, Academic Press, (1989), pp. 299-311. (First delivered orally by
B. Barsky at the Oslo Conference on Mathematical Methods in CAGD, June
1988.)
- Algebraic Aspects of
Geometric Continuity (with C. Micchelli), Mathematical Methods in
Computer Aided Geometric Design, edited by Tom Lyche and Larry
Schumaker, Academic Press, (1989), pp. 313-332.
- The Role of Surfaces in
Solid Modeling, Geometric Modeling: Algorithms and Trends, edited
by Gerald Farin, SIAM, (1987), pp. 69-90. (First delivered orally as an
invited presentation at the SIAM Conference on Geometric Modeling and
Robotics, Albany, July 1985.)
DISSERTATION
- Characteristic Classes on
the Leaves of Foliated Manifolds, Ph.D. Thesis, Johns Hopkins
University, Department of Mathematics, 1973.
CONFERENCE PROCEEDINGS
- Freeform Curves on Spheres
of Arbitrary Dimension (with Scott Schaefer), Proceedings of Pacific
Graphics 2005, Edited by E. Wu, D. Minocha, and C. Gotsman, Macau,
China, October 2005, pp. 160-162.
- Algebraic Geometry and
Geometric Modeling: Insight and Computation, to appear in the Proceedings
of the Workshop on Algebraic Geometry and Geometric Modeling, Nice,
France, September
2004.
- Subdivision Schemes and
Attractors (with S. Schaefer and D. Levin), Proceedings
of Symposium on Geometric Processing (SGP) 2005, edited by M. Desbrun
and H. Pottmann, Vienna, Austria, July 2005, pp. 171-180.
- Blossoming Analytic Functions
Using the Paired Algebras of Forms and Sites (with L. Ramshaw and G. Morin),
Geometric Modeling and Computing: Seattle 2003, edited by M. Lucian
and M. Neamtu, Nashboro Press, Brentwood, pp.
249-278.
- Hodograph Turtles (with T.
Ju), Proceedings of the IASTED Conference on Computer Graphics, Kauai,
Hawaii, August 2004.
- A Computational Method for
Constructing Sylvester-style Sparse Resultants (with N. Song), Proceedings
of the Tenth International Conference on Applications of Computer Algebra
(ACA-2004), Beaumont, Texas, July 2004, pp. 81-89.
- Sylvester A-Resultants for
Bivariate Polynomials with Planar Newton Polygons (with A. Khetan and N.
Song), Proceedings of the 2004 International Symposium on Symbolic and
Algebraic Computation (ISSAC), Santander, Spain, July 2004.
- The Fractal Nature of
Bezier Curves, Proceedings of Geometric Modeling and Processing: Theory
and Applications, GMP2004, pp. 3-11.
- Computer Graphics in its
Fifth Decade: Ferment at the Foundations, (Invited paper), Proceedings
of Pacific Graphics 2003, Canmore, Canada,
October 2003, pp. 4-21.
- Morphing Rational B-spline
Curves and Surfaces Using Mass Distributions (with T. Ju), Eurographics
2003, Short Presentations, Granada, Spain,
September 2003, pp. 61-68.
- The Sylvester Resultant
Matrix for Bernstein Polynomials (with J. Winkler), accepted to appear in
the Proceedings of the Fifth International Conference on Curves and
Surfaces, St. Malo, France,
July 2002.
- Algorithms for Analytic
Functions in Geometric Modeling, with G. Morin, Proceedings of Journees du
Groupe de Travail en Modelisation Geometrique, Dijon, France, 2001.
- The Analytic Blossom, with
G. Morin, Proceedings of the Fifth International Conference on
Mathematical Methods for Curves and Surfaces, Oslo, Norway, July 2000,
pp. 325- 346.
- Beta-Continuity Revisited:
Determining Bezier Control Vertices for the Construction of Geometrically
Continuous Curves and Surfaces (with B. Barsky), Proceedings of the
Fifth International Conference on Mathematical Methods for Curves and
Surfaces, Oslo, Norway,
July 2000, pp. 35-44.
- Efficient Implicitization
of Rational Surfaces by Moving Planes (with M. Zhang and E. Chionh), Proceedings
of the Fourth Asian Symposium on Computer Mathematics (ASCM 2000), Chiang
Mai, Thailand, December 2000, Lecture Notes Series on Computing Vol. 8,
Computer Mathematics, World Scientific, Singapore, pp. 142-151.
- Rectangular Corner Cutting
and Sylvester A-Resultants (with M. Zhang), Proceedings of the 2000
International Symposium on Symbolic and Algebraic Computation (ISSAC), St.
Andrews University, Scotland, August 2000, pp. 301-308.
- Poisson Approximation (with
G. Morin), Proceedings of Geometric Modeling and Processing 2000, Hong
Kong, April 2000, pp. 141-149.
- Implicitization by Dixon
A-resultants (with E. Chionh and M. Zhang), Proceedings
of Geometric Modeling and Processing 2000, Hong Kong, April 2000,
pp.310-318.
- Implicitization Matrices in
the Style of Sylvester with the Order of Bezout (with E. Chionh and M.
Zhang), Proceedings of the Fourth International Conference on Curves
and Surfaces, St. Malo, France,
July 1999, pp. 17-26.
- Hybrid Dixon
Resultants (with E. Chionh and M. Zhang), Proceedings of the Eighth IMA
Conference on the Mathematics of Surfaces, August 1998, pp. 193-212.
- Resolvents and their
Applications in Computer Aided Geometric Design (with Hang Du), SPIE
Conference on Advances in Intelligent Robotic Systems: Curves and Surfaces
in Computer Vision and Graphics II, November 1991.
- Two Surfaces Suffice (with
Hang Du), Eurographics Workshop on Computer Graphics and Mathematics,
Santa Margherita Ligure, Genova, Italy,
October 1991.
- Combining Algebraic Rigor
with the Geometric Robustness for the Detection and Calculation of Conic Sections
in the Intersection of Two Natural Quadric Surfaces, with Jim Miller, Proceedings
of the Symposium on Solid Modeling Foundations and CAD/CAM Applications,
Austin, Texas,
June 1991, pp. 221-231.
- Pruned Bezier Curves (with
P. Barry and T. DeRose), Proceedings Graphics Interface 90, June
1990, pp. 229-238.
- b-Continuity and Its Application
to Rational Beta-Splines (with B. Barsky), Proceedings of the Fourth
Computer Graphics Conference, Smolenice, Czechoslovakia, May 1989, pp.
5-10.
- A Recursive Evaluation
Algorithm for a Class of Catmull-Rom Splines (with P. Barry), Proceedings
Siggraph '88, August 1988, pp. 199-204.
CONFERENCE PRESENTATIONS
- Perspective Projection in the
Homogeneous and Conformal Models Using Rotors, with X. Jia, Applied Geometric
Algebras in Computer Science and Engineering 2012 (AGACSE 2012), La Rochelle,
France, July 2012.
- Generating Functions for
Uniform B-splines, Eighth International Conference on Mathematical Methods for
Curves and Surfaces, Oslo, Norway, July 2012.
- Using ”-Bases to Implicitize Rational
Surfaces with a Pair of Orthogonal Directrices, with X. Shi and X. Wang, Geometric
Modeling and Processing (GMP 2012), Huangshan, China, June 2012.
- Quaternions and Dual Quaternions (Tutorial),
International Conference on Shape Modeling and Applications (SMI), College
Station, Texas, May 2012.
- Quantum Splines, New Trends
in Approximation Theory, Ein Gedi, Israel, January 2012.
- The Role of Algebraic Geometry
in Geometric Modeling, SIAM Conference on Applied Algebraic Geometry, Raleigh, North
Carolina, October 2011.
- Understanding Quaterions: Rotation, Refection and
Perspective Projection -- Invited Presentation, Third Annual Fall School: Shapes, Geometry,
and Algebra (SAGA), Vilnius, Lithuania, September 2011.
- Introduction to Clifford Algebra --
Invited Presentation, Third Annual Fall School: Shapes, Geometry, and Algebra (SAGA),
Vilinius, Lithuania, September 2011.
- Polynomials and Fractals: Polynomials as Attractors,
Fractals with Control Points (Invited Presentation), 24th International Conference of the Jangjeon
Mathematical Society, Konya, Turkey, July 2011.
- Quantum Bezier Curves, Dagstuhl Conference on Geometric
Design, Dagstuhl, Germany, May 2011.
- Convergence of the Lane-Riesenfeld
Algorithm with Nonlinear Averages, Minisymposium on Nonlinear Subdivision,
Seventh International Conference on Curves and Surfaces, Avignon, France, June 2010.
- Rethinking the Classical Paradigm of the Clifford Algebra
for 3-Dimensions: Presenting a Simple Homogeneous Model for Computer Graphics, Applied
Geometric Algebras in Computer Science and Engineering 2010, Amsterdam, Netherlands, June 2010.
- Towards Three Theories of
Bezier Curves: D-Theory, Q-Theory and H-Theory (with V. Zafiris and P.
Simeonov), 13th
International Conference on Approximation Theory, San Antonio, Texas, March 2010.
- Set Theoretical Generators
of Rational Space Curves (with X. Jia and H. Wang), International Workshop on New Trends in Applied Geometry, Bad Herrenalb,
Germany, February 2010.
- Nonlinear Lane-Riesenfeld
Algorithms with Nonlinear Averaging Rules: The Functional Setting (with
Nira Dyn), SIAM Conference on
Geometric and Physical Modeling, San Francisco, California, October
2009.
- Nonlinear Lane-Riesenfeld
Algorithms with Nonlinear Averaging Rules, Research Workshop on Subdivision and Refinability, Pontignano,
Italy, October 2009.
- Set Theoretic Generators of
Rational Space Curves (with Haohao Wang and Xiaohong Jia). The Fourth International Workshop on
Algebraic Geometry and Geometric Modeling (AGGM 2009), Lijiang, China,
July 2009.
- Computing Singularity Trees
of Rational Planar Curves Using μ
Bases (with Xiaohong Jia), The
Fourth International Workshop on Algebraic Geometry and Geometric Modeling
(AGGM 2009), Lijiang, China, July 2009.
- Four Open Mathematical
Problems Related to Computer Graphics and Geometric Modeling (Keynote
Presentation), International
Conference on Computational and Information Sciences, NTNU and WSEAS, Houston,
Texas, May 2009.
- An Introduction to
Geometric Modeling (Invited Presentation), Second International Workshop on Algebraic Geometry and
Approximation Theory, Towson, Maryland, April 2009.
- B-Splines with Knots in the
Complex Plane (Invited Presentation), Second
International Workshop on Algebraic Geometry and Approximation Theory,
Towson, Maryland, April 2009.
- Axial Moving Planes and
Singularities of Rational Space Curves (with H. Wang and X. Jia), Applications of Computer Algebra
(ACA) 2008, RISC, Austria, July 2008.
- Three Computational
Advantages of Mu-Bases in the Analysis of Rational Planar Curves (with X.
Jia), Seventh International
Conference on Mathematical Methods for Curves and Surfaces, Tonsberg,
Norway, June 2008.
- Global Knot Insertion
Algorithms (with S. Schaefer), Foundations of Computational Mathematics
(FoCM 2008), Workshop on
Approximation Theory (Invited Presentation), Hong Kong, June 2008.
- An Analogue of the
Lane-Riesenfeld Subdivision Algorithm for B-splines with Non-Uniform Knots
(with S. Schaefer), Dagstuhl
Workshop on Geometric Design, Dagstuhl, Germany, May 2008.
- Mu-Bases for Polynomial
Systems in One Variable OR What About Non-Planar
Curves? (with N. Song, X. Jia, and D. Cox),
(Invited presentation), Oberwolfach Mini-Workshop on Surface Modeling
and Syzygies, Oberwolfach, Germany,
November 2007.
- A Simple Class of
Non-Linear Subdivision Schemes (with S. Schaefer and E. Vouga), Sixth
International Conference on Curves and Surfaces, Avignon, France, June
2006.
- Modeling Analytic Functions
with Poles: Extending the Poisson Representation to Laurent Series (with
G. Morin), SIAM Conference on
Geometric Design and Computing, Phoenix,
Arizona, November 2005.
- Subdivision Algorithms for
Circular Arcs (with S. Schaefer and E. Vouga), SIAM
Conference on Geometric Design and Computing, Phoenix,
Arizona, November 2005.
- Axial Moving Lines and
Singularities of Rational Planar Curves (with F. Chen and N. Song), SIAM
Conference on Geometric Design and Computing, Phoenix, Arizona,
November 2005.
- Subdivision Schemes and
Attractors (with S. Schaefer and D. Levin), Symposium on Geometric
Processing (SGP) 2005, Vienna, Austria,
July 2005.
- Blossoming and the
Lane-Riesenfeld Algorithm, Dagstuhl Conference on Geometric Modelling,
Dagstuhl, Germany,
May 2005.
- Algebraic Geometry and Geometric
Modeling: Insight and Computation, (Invited presentation), Workshop on
Algebraic Geometry and Geometric Modeling, Nice,
France, September
2004.
- Hodograph Turtles (with T.
Ju), IASTED Conference on Computer Graphics, Kauai,
Hawaii, August 2004.
- Applications of Computer
Algebra: Some Challenges for the Next Decade, (Invited presentation), Tenth
International Conference on Applications of Computer Algebra (ACA-2004), Beaumont,
Texas, July 2004.
- A Computational Method for
Constructing Sylvester-style Sparse Resultants (with N. Song), Tenth
International Conference on Applications of Computer Algebra (ACA-2004), Beaumont,
Texas, July 2004.
- Sylvester A-Resultants for
Bivariate Polynomials with Planar Newton
Polygons (with A. Khetan and N. Song), International Symposium on
Symbolic and Algebraic Computation (ISSAC), Santander, Spain, July
2004.
- A Combinatorial Approach to
Counting Pruned Bezier Curves, with S. Mann, Sixth International
Conference on Mathematical Methods for Curves and Surfaces, Tromso,
Norway, July 2004.
- Fractal Algorithms for
Polynomial Curves, Coastal Workshop on Geometric Modeling, June
2004.
- An Introduction to
Multisided Toric Bezier Patches, (Invited presentation), International
Workshop on Geometric and Visual Computing, Jinan,
China, April 2004.
- The Fractal Nature of
Bezier Curves, (Invited presentation), Geometric Modeling and
Processing 2004, Beijing, China,
April 2004.
- Introduction to Geometric
Modeling, (Invited presentation), MSRI Workshop on Real Algebraic
Geometry and Geometric Modeling, Berkeley,
California, April 2004.
- Toric Bezier
Patches, SIAM
Conference on Geometric Design and Computing, Seattle,
Washington, November 2003.
- Blossoming
Analytic Functions, SIAM
Conference on Geometric Design and Computing, Seattle,
Washington, November 2003.
- Computer Graphics in its
Fifth Decade: Ferment at the Foundations, (Invited presentation), Pacific
Graphics 2003, Canmore, Canada,
October 2003.
- Fractal Bezier, 2003 Pacific
Workshop on Geometric Modeling, Calgary,
Canada, October
2003.
- Curvature Formulas for
Implicit Curves and Surfaces, Workshop on Geometric Modeling and
Differential Geometry, Erbach, Germany,
October 2003.
- Morphing Rational B-spline
Curves and Surfaces Using Mass Distributions (with T. Ju), Eurographics
2003, Short Presentation, Granada, Spain,
September 2003.
- Two Multisided
Bernstein/Bezier/Barycentric Schemes: SâPatches and Toric Bezier
Patches, Oberwolfach Conference on Mathematical Methods in Geometric
Design, Oberwolfach, Germany, October 2002.
- Blossoming, Workshop on
Algebraic Geometry and Geometric Modeling, Vilnius,
Lithuania, July
2002.
- The Sylvester Resultant
Matrix for Bernstein Polynomials (with J. Winkler), Fifth International
Conference on Curves and Surfaces, St. Malo, France,
July 2002.
- Musings on Multisided
Bezier Patches, Dagstuhl Conference on Geometric Modelling, Dagstuhl,
Germany, May 2002.
- A New Approach to Sparse
Resultant Matrices for Bivariate Polynomials with Applications in
Geometric Modeling (Invited presentation) (with E. Chionh), Journales
de Cloture Visi3D et CoSTIC, Paris,
France, December
2001.
- Analytic Functions in
Geometric Modeling, with G. Morin, Journales de Cloture Visi3D et CoSTIC, Paris, France, December 2001.
- Three Implicitization
Methods for Rational Surfaces, SIAM
Conference on Geometric Design and Computing, Sacramento,
California, November 2001.
- An Extended Domain for the
Analytic Blossom (with G. Morin), SIAM
Conference on Geometric Design and Computing, Sacramento,
California, November 2001.
- Multisided Bezier Patches
(Invited presentation), Hong Kong University
Workshop on Geometric Computing, Hong Kong,
China, June 2001.
- Algorithms for Analytic
Functions in Geometric Modeling (with G. Morin), Journees du Groupe de
Travail, Modelisation Geometrique, Dijon, France, March 2001.
- Efficient Implicitization
of Rational Surfaces by Moving Planes (with M. Zhang and E. Chionh), Fourth
Asian Symposium on Computer Mathematics (ASCM 2000), Chiang Mai,
Thailand, December 2000.
- Rectangular Corner Cutting
and Sylvester A-Resultants (with M. Zhang), International Symposium on
Symbolic and Algebraic Computation (ISSAC), St Andrews University, Scotland,
August 2000.
- Baseball and Bezier, The Fifth International Conference on
Mathematical Methods for Curves and Surfaces, Oslo,
Norway, July 2000.
- Blossoming Poisson Curves (with
G. Morin), The Fifth International Conference
on Mathematical Methods for Curves and Surfaces, Oslo,
Norway, July 2000.
- Extracting the Geometric
Features of Conic Sections from Rational Quadratic Parametrizations (with
W. Wang), The Fifth International Conference
on Mathematical Methods for Curves and Surfaces, Oslo,
Norway, July 2000.
- Beta-Continuity Revisited:
Determining a Set of Bezier Control Vertices for the Construction of
Geometrically Continuous Curves and Surfaces (with B. Barsky), The Fifth
International Conference on Mathematical Methods for Curves and Surfaces, Oslo,
Norway, July 2000.
- Discrete Approximations of
Bezier Derivatives (with G. Morin), Trends in Approximation Theory, Vanderbilt
University, Nashville, Tennessee, May 2000.
- Poisson Approximation (with
G. Morin), (Invited presentation) Geometric Modeling and Processing
2000, Hong Kong, April 2000.
- Implicitization by Dixon
A-resultants (with E. Chionh and M. Zhang), Geometric Modeling and
Processing 2000, Hong Kong, April 2000.
- From Bezier to Poisson, Joint
Australia-Taiwan Workshop on Analysis and Applications, Taipei,
April 2000.
- Implicitization by Moving
Quadrics Almost Always Succeeds, (with M. Zhang), Sixth SIAM
Conference on Geometric Modeling, Albequerque,
New Mexico, Nov. 2-5, 1999.
- Trimming using Subdivision
for Poisson Curves and Surfaces (with G. Morin), Sixth SIAM Conference
on Geometric Modeling, Albequerque, New Mexico, Nov. 2-5, 1999.
- Subdivision for Analytic
Functions Based on the Poisson Representation (with G. Moran), Fourth
International Conference on Curves and Surfaces, Organized by AFA, Saint-Malo,
France, July 1-7,
1999.
- Implicitization Matrices in
the Style of Sylvester with the Order of Bezout (with E. Chionh and M.
Zhang), Fourth International Conference on Curves and Surfaces, Organized
by AFA, Saint-Malo, France, July 1-7, 1999.
- The Ambient Spaces of
Computer Aided Design, MSRI Workshop on Mathematical Foundations of
CAD, Berkeley, California,
June, 1999.
- Blossoming, the
Cancellation Axiom, and Divided Difference, Dagstuhl Conference on
Geometric Modelling, Dagstuhl, Germany,
May 1999.
- Fast Computation of the
Entries of the Bezout and Dixon Resultants (with E.
Chionh and M. Zhang), (Invited presentation), Surface
Approximation and Visualization Conference, Christchurch, New Zealand, February
1999.
- Hybrid Dixon
Resultants (with E. Chionh and M. Zhang), Eighth
IMA Conference on the Mathematics of Surfaces, August 1998.
- Complex Contour Integration
and B-splines of Negative Degree, Oberwolfach Conference on Freeform
Curves and Surfaces, Oberwolfach, Germany, June 1998.
- On the Linear Independence
of the Bivariate Discrete Convolution Blending Functions (with Y. Stefanus),
4th Australian Theory Symposium, CATS â98, Perth,
Australia, February
1998.
- A Trimming Algorithm for
Bezier Surfaces (with Suresh Lodha), The Fourth International
Conference on Mathematical Methods for Curves and Surfaces, Lillehammer,
Norway, July 1997.
- Rational B-splines?, (Invited presentation), The Fourth International
Conference on Mathematical Methods for Curves and Surfaces, Lillehammer,
Norway, July 1997.
- Rational Bezier?, International Workshop on Computer Aided
Geometric Design: New Trends and Applications, Anogia, Crete,
June 1997.
- Evaluation Algorithms for
Polynomial Surfaces (with S. Lodha), (Invited presentation), Seventh
IMA Conference on The Mathematics of Surfaces, University
of Dundee, Dundee,
Scotland, September
1996.
- A Tale of Two Resultants: Implicitizing
Rational Curves by the Method of Moving Conics Even in the Presence of
Base Points (with T. Sederberg), Dagstuhl Conference on Geometric
Modeling, Dagstuhl, Germany,
May 1996.
- Dual de Casteljau
Subdivision Algorithm (with S. Lodha), Dagstuhl Conference on Geometric
Modeling, Dagstuhl, Germany, May 1996.
- Using Moving Curves and
Surfaces to Implicitize Rational Curves and Surfaces with Base Points (with
T. Sederberg), Fourth SIAM
Conference on Geometric Design, Nashville,
Tennessee, November 1995.
- A New Approach to
Implicitizing Rational Curves and Surfaces (with Tom Sederberg), Oberwolfach
Conference on Freeform Curves and Surfaces, Oberwolfach, Germany, June
1995.
- Discrete Unimodality of
B-Spline and Bernstein Bases, (Invited presentation), International
Conference on Computer Aided Geometric Design, Penang,
Malaysia, July 1994.
- Point-Line Duality for
Surfaces in CAGD (with S. Lodha), International Conference on Computer
Aided Geometric Design, Penang, Malaysia, July 1994.
- Dual Properties of
B-Patches and L-Patches (with S. Lodha), Third International Conference
on Mathematical Methods in CAGD, Ulvik, Norway, June 1994.
- Evaluation Algorithms for
Surfaces in CAGD (with S. Lodha), Third International Conference on
Mathematical Methods in CAGD, Ulvik, Norway, June 1994.
- An Axiomatic Approach to
Geometric Continuity ( with A. Habib), Third
International Conference on Mathematical Methods in CAGD, Ulvik, Norway,
June 1994.
- An Introduction to Polar
Forms, Third SIAM Conference
on Geometric Design, Tempe, Arizona,
November 1993.
- Polar Forms and Knot
Insertion for B-spline Curves, Third SIAM Conference on Geometric
Design, Tempe, Arizona, November 1993.
- Recursive Techniques in
CAGD, Third SIAM Conference on
Geometric Design, Tempe, Arizona,
November 1993.
- What is Wiggle?, Dagstuhl Conference on Geometric Modeling, Dagstuhl,
Germany, July 1993.
- Change of Basis Algorithms
for Surfaces in Computer Aided Design (with S. Lodha),
A.F.A. Second International Conference on Curves and Surfaces, Chamonix,
France, June 1993.
- Dual Polynomial Bases,
(Invited presentation), International Conference on Advances in
Computational Mathematics, New Delhi, India,
January 1993.
- Implicitizing Techniques
for Rational Surfaces (with E. Chionh), 5th International Conference on
Engineering Computer Graphics and Descritptive Geometry, Melbourne,
Australia, August
1992.
- Bounding the Arclength and
Surface Area of Bezier Curves and Surfaces (with W. Png, C. Micchelli, and
J. Warren), Oberwolfach Conference on Curves and Surfaces, Oberwolfach,
Germany, June 1992.
- An Extension of Chaikinâs
Algorithm (with J. Warren), Second SIAM Conference on Geometric Design,
Tempe, Arizona, November 1991.
- Blossoming and B-splines, ACM
Siggraph Tutorial, Las Vegas, Nevada,
July 1991.
- Knot Insertion Algorithms, ACM
Siggraph Tutorial, Las Vegas, Nevada,
July 1991.
- Wonderful Triangle (with P.
Barry), (Invited presentation), Conference on Curves, Surfaces, CAGD, and
Image Processing, Biri, Norway,
June 1991.
- Implicitizing Rational
Surfaces with Base Points by Applying Perturbations and the Factors of
Zero Theorem (with E. Chionh), Conference on Curves, Surfaces, CAGD,
and Image Processing, Biri, Norway, June 1991.
- Tensor Product Slices (with
R. Bartels and R. Pfeifle), Conference on Curves, Surfaces CAGD, and
Image Processing, Biri, Norway, June 1991.
- On Discrete Convolution
Curves (with Y. Stefanus), Conference on Curves, Surfaces, CAGD, and
Image Processing, Biri, Norway,
June 1991.
- Some Applications of
Elimination Theory to Solving Problems in Computer Aided Geometric Design,
(Invited presentation), NSF/CBMS Regional Conference on Curves and
Surfaces, Kent State University, Kent, Ohio, December 1990.
- A Resolvent Method for
Implicitization and Inversion of Non-Planar Parametric Curves (with H. Du),
Course on Geometric Modeling and Robotics, Institute Leonardo
Fibonacci, Trento, Italy,
June 1990.
- Fast Knot Insertion (with
P. Barry), A.F.A. International Conference on Curves and Surfaces, Chamonix,
France, June 1990.
- Methods of Knot Insertion
for B-spline Curves (with P. Barry), A.F.A. International Conference on
Curves and Surfaces, Chamonix, France, June 1990.
- The Algebraic Structure of
Sets of Functions with Fixed Connection Matrices, SIAM Conference on
Geometric Design, Tempe, Arizona,
November, 1989 and again at the A.F.A. International Conference on
Curves and Surfaces, Chamonix, France,
June 1990.
- An Introduction to
Recursive Schemes in Computer Aided Geometric Design, (Invited
presentation), NATO Advanced Study Institute, Puerto de la Cruz,
Canary Islands, Spain, July 1989.
- Polya Polynomials and
B-Spline Curves, (Invited presentation), NATO Advanced Study Institute,
Puerto de la Cruz, Canary Islands, Spain, July 1989.
- Dual Functionals and Knot
Insertion Algorithms for B-Spline Curves, (Invited presentation), NATO
Advanced Study Institute, Puerto de la Cruz, Canary Islands, Spain,
July 1989.
- Algorithms in the Style of
Boehm and Sablonniere (with P. Barry), Oberwolfach Conference on
Computer Aided Geometric Design, Oberwolfach, Germany, April 1989.
- Recursive Curves and
Surfaces, ACM Siggraph Tutorial, August 1988. (Repeated again at
Graphics Interface in June 1989 and at Siggraph in August 1989).
- Three Examples of Dual
Properties of Bezier Curves (with P. Barry), Oslo Conference on
Mathematical Methods in CAGD, Oslo, Norway, June 1988.
- What is the Natural Generalization
of a Bezier Curve? (with P. Barry), Oslo
Conference on Mathematical Methods in CAGD, Oslo,
Norway, June 1988.
- Some Basic Results on Beta
Continuous Functions and Their Application to the Construction of
Geometrically Continuous Curves and Surfaces (with B. Barsky), Oslo
Conference on
Mathematical Methods in CAGD, Oslo,
Norway, June 1988.
- Probabilistic Approaches to
Computer-Aided Geometric Design, Minisyposium (with P. Barry and T. DeRose),
SIAM Conference on Applied
Geometry, Albany, July
1987.
- Future Directions in Geometric
Modeling: A Preview of Coming Attractions, (Invited presentation), Wayne
State Conference on Applied Geometry, Detroit,
Michigan, May 1987.
- Conversion Between Bezier
Rectangles and Bezier Triangles (with D. Filip), Symposium on Topics in
Computer Aided Geometric Design, Braunschweig, West Germany,
June 1986.
- Vector Geometry: A
Coordinate Free Approach, ACM Siggraph Tutorial, July 1985.
(Repeated again at Siggraph in July 1986 and 1987).
- The Role of Surfaces in
Solid Modeling, (Invited presentation), SIAM
Conference on Geometric Modeling and Robotics, Albany,
July 1985.
- Urn Models and
Beta-Splines, NASA International Conference on Computational Geometry
and Computer Aided Design, New Orleans,
June 1985.
- Some Applications of
Resultants to Problems in Computational Geometry, with T. Sederberg, International
Conference on Engineering and Computer Graphics, Beijing,
China, August 1984.
- Geometry and Probability, ACM
Siggraph Tutorial, July 1984.
- An Intuitive Approach to Bezier
and Other Random Curves and Surfaces, ACM Siggraph Tutorial, July
1983.
- An Urnful of Blending
Functions, NASA Symposium on Computer Aided Geometry and Modeling, Langley,
Virginia, April 1983.
- The Perfect Surface, Engineering
Society of Detroit, Detroit,
Michigan, 1979.
#