JOURNAL PUBLICATIONS

1. q-Blossoming for Analytic Functions, with P. Simeonov, to appear in NumericalcAlgorithms.

2. Combining Complementary Methods for Implicitizing Rational Tensor Product Surfaces, with L. Shen, Computer Aided Design (2018), Vol. 104, pp. 100-112, https://doi.org/10.1016/j.cad.2018.07.002.

3. A Polynomial Blossom for the Askey-Wilson Operator, with P. Simeonov, Constructive Approximation (2018), https://doi.org/10.1007/s00365-018-9439-1.

4. Rational curves over generalized complex numbers, with J. Du and X. Wang, to appear in Journal of Symbolic Computation.

5. de Boor-suitable (DS) T-splines, with Y. Zhang and V. Pataranutaporn, to appear in Graphical Models (GMOD).

6. Detecting when an Implicit Equation or a Rational Parametrization defines a Conical or Cylindrical Surface, or a Surface of Revolution, with J. Alcazar, to appear in IEEE Transactions on Visualization and Computer Graphics.

7. Implicitizing Ruled Translational Surfaces, with H. Wang, Computer Aided Geometric Design, Vol. 59, pp. 98-106.

8. Syzygies for Translational Surfaces, with H. Wang, to appear in the Journal of Symbolic Computation.

9. Applications of the Shorgin Identity for Bernstein Type Operators, with X.W. Xu and Q. B. Cai, Results in Mathematics (2018), Vol. 73, No. 1, https://doi.org/10.1007/s00025-018-0764-2.

10. Using Dual Quaternions to Study Translational Surfaces, with H. Wang, Mathematics in Computer Science (2018), Vol. 12, pp. 69-75. {DOI 10.1007/s11786-018-0330-z}

11. Implicitizing Rational Tensor Product Surfaces by the Resultant of Three Moving Planes, with L. Shen, Transactions on Graphics (TOG 2017), Vol. 36, No. 5, 167, doi>10.1145/3119909.2

12. Modeling 3D Geometry in the Clifford Algebra 𝑅(4,4), with J. Du and S. Mann, Advances in Applied Clifford Algebras (2017), Vol. 27, No. 4, pp. 3039-3062.

13. Shape preserving properties of Univariate Lototsky-Bernstein Operators, with X.W. Xu and X.M. Zeng, Journal of Approximation Theory (2017), Vol. 224C, pp. 13-42.

14. Strong 𝜇-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity, with L. Shen, SIAM Journal on Applied Algebra and Geometry (SIAGA 2017), Vol. 1, No. 1, pp. 328-351.

15. Algorithms for Computing Strong 𝜇-Bases for Rational Tensor Product Surfaces, with L. Shen, Special Issue of Computer Aided Geometric Design for the Proceedings of Geometric Modeling and Processing (GMP 2017), Vols. 52-53, pp. 48-62.

16. An Asymmetric Distributed Method for Sorting a Robot Swarm, with Y. Zhou and J. McLurkin, IEEE Robotics and Automation Letters (2017), Vol. 2, No. 1, pp. 261-268.

17. A Unified Approach to Non-Polynomial B-spline Curves based on a Novel Variant of Polar Forms, with C. Disibuyuk, Calcolo (2016), Vol. 53, pp. 751-781.

18. Finding the Axis of Revolution of an Algebraic Surface of Revolution, with J. Alcazar, IEEE Transactions on Visualization and Computer Graphics (2016), Vol. 22, pp. 2082-2093.

19. Algebraic Surfaces Invariant under Scissor Shears, with J. Alcazar and C. Hermoso, Graphical Models (2016), Vol. 87, pp. 23-34.

20. Generalized Quantum Splines, with P. Simeonov, Computer Aided Geometric Design, (2016), Vol. 47, pp. 29-54.

21. Birational 2D Free-Form Deformation of Degree 1 Å~ n , with T. Sederberg and X. Wang, Computer Aided Geometric Design (2016), Vol. 44, pp. 1-9.

22. Novel Polynomial Bernstein Bases and Bezier Curves Based on a General Notion of Polynomial Blossoming, Numerical Algorithms (2016), Vol. 72, pp. 605-634.

23. Two Additional Advantages of Complex μ-Bases for Non-Ruled Real Quadric Surfaces (Short Communication), with X. Wang, Computer Aided Geometric Design (2016), Vol. 42, pp. 31-33.3

24. Explicit μ-Bases for Conic Sections and Planar Rational Cubic Curves, with X. Wang and T. Sederberg, Computer Aided Geometric Design (2016), Vol. 41, pp. 62-75.

25. Quaternion Rational Surfaces: Rational Surfaces Generated from the Quaternion Product of Two Rational Space Curves, with X. Wang, Graphical Models (2015), Vol. 81, pp. 18-32.

26. Best Polynomial Degree Reduction on q-Lattices with Applications to q-OrthogonalPolynomials, with R. Ait-Haddou, Journal of Applied Mathematics and Computation (2015), Vol. 266, pp. 267-276.

27. A Unifying Functional Structure for Polar Forms and for Functional Bernstein Bezier Curves, with C. Disibuyuk, Journal of Approximation Theory (2015), Vol. 192, pp. 234-249.

28. Complex μ-Bases for Real Quadric Surfaces, with T. Sederberg and X. Wang, Computer Aided Geometric Design (2015), Vol. 37, pp. 57-68.

29. Two Essential Properties of (𝑞, ℎ)-Bernstein-Bezier Curves, with P. Simeonov, Applied Numerical Mathematics (2015), Vol. 96, pp. 82-93.

30. Quantum Bernstein Bases and Quantum Bezier Curves, with P. Simeonov, Journal of Computational and Applied Mathematics (2015), Vol. 288, pp. 284-303.

31. Extending Fundamental Formulas from Classical B-splines to Quantum B-splines, with G. Budakci, C. Disibuyuk, and H. Oruc, Advances in Computational Mathematics (2015), Vol. 282, pp. 17-33.

32. R(4,4) as a Computational Framework for 3-Dimensional Computer Graphics, with S. Mann, Advances in Applied Clifford Algebras (2015), Vol. 25, No. 1, pp. 113-149.

33. Generating Functions for B-Splines with Knots in Geometric or Affine Progression, with C. Disibuyuk, G. Budakci, and H. Oruc, Calcolo (2014), Vol. 51, No. 4, pp. 599-613.

34. Generating Functions for the q-Bernstein Bases, with P. Simeonov and Y. Simsek, SIAM Journal on Discrete Mathematics (2014), Vol. 28, pp. 1009-1025.

35. Computing Perspective Projections in 3-Dimensions using Rotors in the Homogeneous and Conformal Models of Clifford Algebra, with S. Mann and X. Jia, Advances in Applied Clifford Algebras (2014), Vol. 24, No. 2, pp. 465-491.4

36. Using a Bihomogeneous Sparse Resultant to Find the Singularities of Rational Space Curves, with X. Shi and X. Jia, Journal of Symbolic Computation (2013), Vol. 53, pp. 1-25.

37. μ-Bases for Complex Rational Curves, with X. Wang, Computer Aided Geometric Design (2013), Vol. 30, pp. 623-635.

38. Quantum B-splines, with P. Simeonov, BIT Numerical Mathematics (2013), Vol. 53, pp. 193–223.

39. Modeling Perspective Projections in 3-Dimensions by Rotations in 4-Dimensions, Graphical Models (2013), Vol. 75, pp. 41-55.

40. Formulas and Algorithms for Quantum Differentiation of Quantum Bernstein Bases and Quantum Bezier Curves Based on Quantum Blossoming, with P. Simeonov, GraphicalModels (2012), Special Issue of selected papers from the 8th Dagstuhl Seminar on Geometric Modeling 2011, Vol. 74, pp. 326–334.

41. Using μ-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.

42. Implicitizing Rational Surfaces of Revolution using μ-Bases, with X. Shi, Computer Aided Geometric Design (2012), Vol. 29, pp. 348-362.

43. 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.

44. 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.

45. 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.

46. 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. 67-86.5

47. Understanding Quaternions, Graphical Models (2011), Vol. 73, pp. 21-49.

48. 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.

49. Minimal Generators for the Rees Algebra of Rational Space Curves of Type (1,1,d-2), with J. Hoffman, H. Wang, and X. Jia, European Journal of Pure and Applied Mathematics (2010), Vol. 3, No. 4, pp. 602-632.

50. Set-Theoretic Generators of Rational Space Curves, with X. Jia and H. Wang, Journal of Symbolic Computation (2010), Vol. 45, pp. 414-433.

51. Mu-bases and Singularities of Rational Planar Curves, with X. Jia, Computer Aided Geometric Design (2009), Vol. 26, pp. 970-988.

52. 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.

53. 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.

54. Mu-Bases for Polynomial Systems in One Variable, with N. Song, Computer Aided Geometric Design (2009), Vol. 26, pp. 217-230.

55. Non-Uniform Subdivision for B-splines of Arbitrary Degree, with S. Schaefer, Computer Aided Geometric Design (2009), Vol. 26, pp. 75-81.

56. Division Algorithms for Bernstein Polynomials, with L. Buse, Computer Aided Geometric Design (2008), Vol. 25, pp. 850-865.

57. Nonlinear Subdivision Through Nonlinear Averaging, with S. Schaefer and E. Vouga, Computer Aided Geometric Design (2008), Vol. 25, pp. 162-180.

58. Axial Moving Lines and Singularities of Rational Planar Curves, with N. Song and F. Chen, Computer Aided Geometric Design (2007), Vol. 24, pp. 200-209.

59. Two Blossoming Proofs of the Lane-Riesenfeld Algorithm, with E. Vouga, Computing (2007), Vol. 79, pp. 153-162.6

60. 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.

61. Curvature Formulas for Implicit Curves and Surfaces, Special Issue of CAGD on Geometric Modeling and Differential Geometry (2005), Vol. 22, pp. 632-658.

62. 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.

63. Recursive Turtle Programs and Iterated Affine Transformations, with T. Ju and S. Schaefer, Computers and Graphics (2004), Vol. 28, pp. 991-1004.

64. Turtle Geometry in Computer Graphics and Computer-Aided Design, with T. Ju and S. Schaefer, Computer-Aided Design (2004), Vol. 36, pp. 1471-1482.

65. Multisided Arrays of Control Points for Multisided Bezier Patches, Computer Aided Geometric Design (2004), Vol. 21, pp. 243-261.

66. Enhancing Levin’s Method for Computing Quadric-Surface Intersections, with W. Wang and C. Tu, Computer Aided Geometric Design (2003), Vol. 20, pp. 401-422.

67. Deriving Linear Transformations in 3-Dimensions, IEEE Computer Graphics and Applications (2003), Vol. 23, pp. 66-71.

68. 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.

69. Compositional Synthesis of Optical Imaging Systems, with D. Subramanian, Research in Engineering Design (2002), Vol. 13, pp. 183-198.

70. The Affine Invariant Analytic Blossom, with G. Morin, Computer Aided Geometric Design (2002). Vol. 19, pp. 621-623.

71. On the Algebraic and Geometric Foundations of Computer Graphics, Transactions on Graphics (2002), Vol. 21, pp. 1-35.

72. Fast Computation of the Bezout and Dixon Resultant Matrices, with E. Chionh and M. Zhang, Journal of Symbolic Computation (2002), Vol. 33, pp. 13-29.7

73. 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.

74. Trimming Analytic Functions Using Right Sided Poisson Subdivision, with G. Morin, Computer-Aided Design, (2001), Vol. 33, pp. 813-824.

75. Blossoming and Divided Difference, Geometric Modeling, Computing [Suppl], (2001), Vol. 14, pp. 155-184.

76. Baseball Arithmetic and the Laws of Pseudoperspective, IEEE Computer Graphics and Applications, (2001), Vol. 21, pp. 70-78.

77. A Subdivision Scheme for Poisson Curves and Surfaces, with G. Morin, Computer Aided Geometric Design, (2000), Vol. 17, pp. 813-833.

78. Spline Functions of Negative Degree, with G. Walz, CALCOLO, (2000), Vol. 37, pp. 125- 137.

79. 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.

80. The Ambient Space of Computer Graphics and Geometric Modeling, IEEE Computer Graphics and Applications, (2000), Vol. 20, pp. 76-84.

81. The Rational Bernstein Bases and the Multirational Blossoms, Computer Aided Geometric Design, (1999), Vol. 16, pp. 701-738.

82. Blossoming with Cancellation, Special Issue of Computer Aided Geometric Design dedicated to P. de Casteljau, (1999), Vol. 16, pp. 671-689.

83. 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.

84. 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. 59-99.8

85. On the Linear Independence of the Bivariate Discrete Convolution Blending Functions, with Y. Stefanus, Australian Computer Science Communications, (1998), Vol. 20, pp. 231-244.

86. Rational Quadratic Parametrizations of Quadrics, with W. Wang and B. Joe, International Journal of Computational Geometry and Applications, (1997), Vol. 7, pp. 599-619.

87. A Unified Approach to Evaluation Algorithms for Multivariate Polynomials, with S. Lodha, Mathematics of Computation, (1997), Vol. 66, pp. 1521-1553.

88. 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.

89. 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.

90. Theories of Contact Specified by Connection Matrices, with A. Habib, Computer Aided Geometric Design, (1996), Vol. 13, pp. 905-929.

91. 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.

92. Some Applications of Discrete Unimodality to Problems for Parametric Curves, with P. Barry, Annals of Numerical Mathematics, (1996), Vol. 3, pp. 83-90.

93. 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.

94. Change of Basis Algorithms for Surfaces in CAGD, with S. Lodha, Computer Aided Geometric Design, (1995), Vol. 12, pp. 801-824.

95. Elimination and Resultants Part 1: Elimination and Bivariate Resultants, with E. Chionh, IEEE Computer Graphics and Applications, (1995), Vol. 15, pp. 69-77.

96. Elimination and Resultants Part 2: Multivariate Resultants, with E. Chionh, IEEEComputer Graphics and Applications, (1995), Vol. 15, pp. 60-69.9

97. 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.

98. Unimodal Properties of Generalized Ball Bases, with P. Barry, Computing, Computing Suppl., Vol. 10, (1995), pp. 35-41.

99. Dual Polynomial Bases, Journal of Approximation Theory, (1994), Vol. 79, pp. 311-346.

100. 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.

101. 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.

102. Functional Composition Algorithms via Blossoming, with T. DeRose, H. Hagen, and S. Mann, Transactions on Graphics, (1993), Vol. 12, pp. 113-135.

103. An Extension of Chaiken’s 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.

104. Unimodal Properties of B-Splines and Bernstein Basis Functions, with P. Barry and J. Beatty, Computer-Aided Design, (1992), Vol. 24, pp. 627-636.

105. Blossoming Marsden’s Identity, with Y. Stefanus, Computer Aided Geometric Design, (1992), Vol. 9, pp. 73-84.

106. Degree, Multiplicity, and Inversion Formulas for Rational Surfaces Using u-Resultants, with E. Chionh, Computer Aided Geometric Design, (1992), Vol. 9, pp. 93-108.

107. Using Multivariate Resultants to Find the Implicit Equation of a Rational Surface, with E. Chionh, The Visual Computer, (1992), Vol. 8, pp. 171-180.

108. 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.

109. Using Multivariate Resultants to Find the Intersection of Three Quadric Surfaces, with E. Chionh and J. Miller, Transactions on Graphics, (1991), Vol. 10, pp. 378-400.10

110. 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.

111. Shape Parameter Deletion for Polya Curves, with P. Barry, Numerical Algorithms, (1991), Vol. 1, pp. 121-137.

112. B-Splines, Polya Curves, and Duality, with P. Barry and T. DeRose, Journal of Approximation Theory, (1991), Vol. 65, pp. 3-21.

113. 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.

114. Blossoming and Knot Insertion Algorithms for B-Spline Curves, Computer Aided Geometric Design, (1990), Vol. 7, pp. 69-81.

115. Recursive Polynomial Curve Schemes and Computer Aided Geometric Design, with P. Barry, Constructive Approximation, (1990), Vol. 6, pp. 65-96.

116. 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.

117. Urn Models, Approximations, and Splines, Journal of Approximation Theory, (1988), Vol. 54, No. 1, pp. 1-66.

118. Urn Models and B-Splines, Constructive Approximation, (1988), Vol. 4, pp. 265-288.

119. A Recursive Proof of Boehm’s Knot Insertion Technique, with P. Barry, Computer- Aided Design, (1988), Vol. 20, No. 4, pp. 181-182.

120. De Casteljau Type Subdivision is Peculiar to Bezier Curves, with P. Barry, Computer-Aided Design, (1988), Vol. 20, No. 3, pp. 114-116.

121. 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. 122. Conversion from Bezier Rectangles to Bezier Triangles, with D. Filip, Computer-Aided Design, (1987), Vol. 19, No. 1, pp. 25-28.11

123. Recursive Subdivision Without the Convex Hull Property, with T. DeRose, ComputercAided Geometric Design, (1986), Vol. 3, No. 4, pp. 247-265.

124. Algebraic Geometry for Computer-Aided Geometric Design, with T. Sederberg, IEEEcComputer Graphics and Applications, (1986), Vol. 6, No. 6, pp. 52-59.

125. 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.)

126. 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.

127. 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.)

128. Illicit Expressions in Vector Algebra, Transactions on Graphics, (1985), Vol. 4, No. 3, pp. 223-243.

129. Implicitization, Inversion, and Intersection of Planar Rational Cubic Curves, with T. Sederberg, Computer Vision, Graphics, and Image Processing, (1985), Vol. 31, pp. 89-102.

130. Markov Chains and Computer Aided Geometric Design Part II — Examples and Subdivision Matrices, Transactions on Graphics, (1985), Vol. 4, No. 1, pp. 12-40.

131. Polya’s Urn Model and Computer Aided Geometric Design, SIAM Journal on Algebraic and Discrete Methods, (1985), Vol. 6, No. 1, pp. 1-28.

132. 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.

133. Linear Subdivision is Strictly a Polynomial Phenomenon, with D. Heath, Computer Aided Geometric Design, (1984), Vol. 1, No. 3, pp. 269-278.12

134. 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.

135. Markov Chains and Computer Aided Geometric Design Part I — Problems and Constraints, Transactions on Graphics, (1984), Vol. 3, No. 3, pp. 204-222.

136. 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).

137. Two Approaches to a Computer Model for Quadric Surfaces, IEEE Computer Graphics and Applications, (1983), Vol. 3, No. 6, pp. 21-24.

138. Subdivision Algorithms for Bezier Triangles, Computer-Aided Design, (1983), Vol. 15, No. 3, pp. 159-166.

139. Quadrics of Revolution, IEEE Computer Graphics and Applications, (1983), Vol. 3, No. 3, pp. 68-76.

140. Using Degenerate Bezier Triangles and Tetrahedra to Subdivide Bezier Curves, Computer-Aided Design, (1982), Vol. 14, No. 6, pp. 307-311.

141. The Holonomy Ring on the Leaves of Foliated Manifolds, Journal of Differential Geometry (1976), Vol. 11, No. 3, pp. 411-449.

ARTICLES UNDER SUBMISSION

1. Lototsky-Bernstein Operators Preserving Arbitrary Increasing Functions, with X.W. Xu and X.M. Zeng, Submitted to Journal of Approximation Theory.

2. Modeling Craniosynostosis Severity and Progression in Infants using Hidden Markov Models, with Salem Karani, Enoch Tsai, Mathew Kurian, John Phillips, Brooke French, and David Khechoyan, submitted to the Journal of Plastic, Reconstructive and Aesthetic Surgery.

3. A Novel Computational Framework for Evaluating Outcomes in Craniosynostosis Reconstruction, with R.D. Wagner, M.S. Lloyd, B. Yuan and D.Y. Khechoyan, submitted to the Journal of Craniofacial Surgery. 13

4. Revisiting the Properness of Parametric Supports, with L. Shen, submitted to Computer Aided Geometric Design.

5. Using Rotations and Shears in 4-Dimensions to Model Translations and Perspective Projections in 3-Dimensions, with J. Du and S. Mann, submitted to IEEE Computer Graphics and Applications (IEEE CG&A).

6. Quaternions and their Associated Clifford Algebras, with J. Du, submitted to Graphical Models (GMOD).

7. Affine differential geometry and affine rotation surfaces: algebraic surfaces invariant under non-Euclidean affine rotations, with J. Alcazar, submitted to Graphical Models (GMOD).

8. High order smoothness of non-linear Lane-Riesenfeld algorithms in the functional setting, with N. Dyn and D. Levin, submitted to Computer Aided Geometric Design.

9. Rational B-splines and Multirational Blossoms, submitted to Advances in Computational Mathematics.

10. The Multirational Blossom, submitted to Constructive Approximation.

11. Differentiation and Integration Identities for B-splines of Negative Degree, submitted to Mathematics of Computation.

12. A Survey of Urn Models in Computer Aided Geometric Design, with P. Barry, submitted to IEEE Computer Graphics and Applications.

13. Bounding the Arclength of Integral and Rational Bezier Curves, with C. Micchelli, W. Png, and J. Warren, submitted to Computer-Aided Design.

14. Wiggle, submitted to Journal of Computing.

TECHNICAL REPORTS

1. Modeling Affine and Projective Transformations in 3-Dimensions by Linear Transformations in 4-Dimensions, with J. Du and S. Mann, University of WaterlooTechnical Report CS-2018-05.14

2. 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.

3. 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.

4. 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.

5. 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.

6. Detecting and Calculating Conic Sections in the Intersection of Two Natural Quadric Surfaces, Part I: Theoretical Analysis, with Jim Miller, Technical Report TR–93–1, Department of Computer Science, University of Kansas, 1992.

7. 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 TR–93–2, Department of Computer Science, University of Kansas, 1992.

8. 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.

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

1. A Homogeneous Model for Three-Dimensional Computer Graphics based on the Clifford Algebra for 𝑅!, Guide to Geometric Algebra in Practice, edited by L. Dorst and J. Lasenby, Springer, London (2011), pp. 329-352.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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. 305-314.16

7. Identities for the Univariate and Bivariate Bernstein Basis Functions, Graphics Gems V, edited by Alan Paeth, Academic Press, (1995), pp. 149-162.

8. Identities for the B-Spline Basis Functions, Graphics Gems V, edited by Alan Paeth, Academic Press, (1995), pp. 163-167.

9. 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.

10. Knot Insertion Using Forward Differencing, with P. Barry, Graphics Gems IV, edited by Paul Heckbert, Academic Press, (1994), pp. 251-255.

11. 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.

12. 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.

13. 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.

14. Cross Product in 4-Dimensions and Beyond, Graphics Gems III, edited by David Kirk, Academic Press, (1992), pp. 84–88.

15. Decomposing Projective Transformations, Graphics Gems III, edited by David Kirk, Academic Press, (1992), pp. 98–107.

16. Decomposing Linear and Affine Transformations, Graphics Gems III, edited by David Kirk, Academic Press, (1992), pp. 108–116.

17. 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.) 17

18. 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.)

19. 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.)

20. 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.)

21. Area of Planar Polygons and Volume of Polyhedra, Graphics Gems II, edited by Jim Arvo, Academic Press, (1991), pp. 170-171.

22. Recovering the Data from the Transformation Matrix, Graphics Gems II, edited by Jim Arvo, Academic Press, (1991), pp. 324-331.

23. Transformations as Exponentials, Graphics Gems II, edited by Jim Arvo, Academic Press, (1991), pp. 332-337.

24. More Matrices and Transformations: Shear and Pseudoperspective, Graphics Gems II, edited by Jim Arvo, Academic Press, (1991), pp. 338-341.

25. 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.

26. Triangles, Graphics Gems, edited by Andrew Glassner, Academic Press, (1990), pp. 20-23.

27. Intersection of Two Lines in Three Space, Graphics Gems, edited by Andrew Glassner, Academic Press, (1990), pp. 304.

28. Intersection of Three Planes, Graphics Gems, edited by Andrew Glassner, AcademicPress, (1990), pp. 305.18

29. Matrices and Transformations, Graphics Gems, edited by Andrew Glassner, Academic Press, (1990), pp. 472-475.

30. Some Properties of Bezier Curves, Graphics Gems, edited by Andrew Glassner, Academic Press, (1990), pp. 587-593.

31. Integration of Bernstein Basis Functions, Graphics Gems, edited by Andrew Glassner, Academic Press, (1990), pp. 604-606.

32. 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.

33. 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.)

34. 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.).

35. 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.)

36. 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.

37. 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.) 19

DISSERTATION

1. Characteristic Classes on the Leaves of Foliated Manifolds, Ph.D. Thesis, Johns Hopkins University, Department of Mathematics, 1973.

CONFERENCE PROCEEDINGS

1. A New Objective Automatic Computational Framework for Evaluating and Visualizing the Results of Infant Cranial Surgery, with B. Yuan, and D. Khechoyan, Proceedings of BioMedCom2014: The Third ASE International Conference on Biomedical Computing, Cambridge, Massachusetts, December 2014.

2. Generating Functions for Uniform B-Splines, Proceedings of the Eighth International Conference on Mathematical Methods for Curves and Surfaces (2014), M. Floater, T. Lyche, M-L Mazure, K. Morken, and L. Schumaker (eds.), Springer, pp. 172-188.

3. 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.

4. 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.

5. 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.

6. 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.

7. Hodograph Turtles, with T. Ju, Proceedings of the IASTED Conference on Computer Graphics, Kauai, Hawaii, August 2004.

8. 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. 81-89.20

9. 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.

10. The Fractal Nature of Bezier Curves, Proceedings of Geometric Modeling and Processing: Theory and Applications, GMP2004, pp. 3-11.

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.

12. Morphing Rational B-spline Curves and Surfaces Using Mass Distributions, with T. Ju, Eurographics 2003, Short Presentations, Granada, Spain, September 2003, pp. 61-68.

13. 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.

14. Algorithms for Analytic Functions in Geometric Modeling, with G. Morin, Proceedings of Journees du Groupe de Travail en Modelisation Geometrique, Dijon, France, 2001.

15. 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.

16. 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.

17. 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.

18. 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.

19. Poisson Approximation, with G. Morin, Proceedings of Geometric Modeling and Processing 2000, Hong Kong, April 2000, pp. 141-149. 21

20. 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.

21. 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.

22. 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.

23. 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.

24. Two Surfaces Suffice, with Hang Du, Eurographics Workshop on Computer Graphics and Mathematics, Santa Margherita Ligure, Genova, Italy, October 1991.

25. 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.

26. Pruned Bezier Curves, with P. Barry and T. DeRose, Proceedings Graphics Interface 90, June 1990, pp. 229-238.

27. β-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.

28. A Recursive Evaluation Algorithm for a Class of Catmull-Rom Splines, with P. Barry, Proceedings Siggraph ’88, August 1988, pp. 199-204.

CONFERENCE PRESENTATIONS

1. Implicitizing Rational Tensor Product Surfaces Using the Resultant of Three Moving Planes, with L. Shen, Siggraph 2018, Vancouver, Canada, August 2018.

2. Syzygies and Implicitization for Translational Surfaces, with H. Wang, 8th International Conference on Curves and Surfaces, Arcachon, France, June 2018. 22

3. de Boor-suitable T-splines: Freeform Surfaces that Support Efficient Evaluation, with Visit Pataranutaporn, International Congress on Mathematical Software – ICMS 2018, Notre Dame, July 2018.

4. Implicitizing Rational Tensor Product Surfaces (I): Using the Resultant of Strong 𝜇- Bases, with L. Shen, SIAM Conference on Applied Algebraic Geometry, August 2017.

5. Implicitizing Rational Tensor Product Surfaces (II): Using the Resultant of Three Moving Planes, with L. Shen, SIAM Conference on Applied Algebraic Geometry, August 2017.

6. De Boor Suitable T-Splines, with Yang Zhang and Visit Pataranutaporn, Dagstuhl Seminar on Geometric Modeling, Dagstuhl, Germany, May 2017.

7. Algorithms for Computing Strong 𝜇-Bases for Rational Tensor Product Surfaces, with L. Shen, Geometric Modeling and Processing (GMP 2017), Best Paper Award, Xiamen, China, April 2017.

8. A Polynomial Blossom for the Askey–Wilson Operator, with P. Simeonov, Workshop on High Dimensional Data Fitting and Approximation Theory, University of Central Florida, March, 2017.

9. An Asymmetric Distributed Method for Sorting a Robot Swarm, with Y. Zhou and J. McLurkin, Twelfth IEEE International Conference on Automation Science and Engineering (CASE 2016), San Antonio, August 2016.

10. Algebraic Surfaces of Revolution and Algebraic Surfaces Invariant Under Scissor Shear: Similarities and Differences, with J. Alcazar, Computational Algebra and GeometricModeling, Oaxaca, Mexico, August 2016.

11. Strong 𝜇-Bases for Rational Tensor Product Surfaces, with L. Shen, Computational Algebra and Geometric Modeling, Oaxaca, Mexico, August 2016.

12. Complex, Hyperbolic, and Parabolic Rational Curves, with J. Du and X. Wang, Computational Algebra and Geometric Modeling, Oaxaca, Mexico, August 2016.

13. Algebraic Surfaces of Revolution and Algebraic Surfaces Invariant Under Scissor Shear: Similarities and Differences, with J. Alcazar, Ninth International Conference on Mathematical Methods for Curves and Surfaces, Tonsberg, Norway, June 2016.

14. Blossoming in Arbitrary Function Spaces, with P. Simeonov, Sixth Conference on Numerical Analysis and Applications, Lozenets, Bulgaria, June 2016.23

15. Generating a 3D Normative Infant Cranial Model, with B. Yuan and D. Khechoyan, International Conference on Computational Science, (ICCS 2016), San Diego, June 2016

16. Complex 𝜇-Bases for Real Quadric Surfaces, with T. Sederberg and X. Wang, International Conferences on Geometric Modeling and Processing (GMP 2016), San Antonio, April 2016.

17. Homogenous Models of Clifford Algebra Minisymposium on Perspective Projection in

Conformal Clifford Algebra, SIAM Conference on Geometric and Physical Modeling

(GD/SPM), Salt Lake City, October 2015.

18. Introduction to Clifford Algebra, Minisymposium on Perspective Projection in Conformal Clifford Algebra, SIAM Conference on Geometric and Physical Modeling (GD/SPM), Salt Lake City, October 2015.

19. Quaternion Rational Surfaces, with X, Wang, ICIAM 2015 (8th International Congress on Industrial and Applied Mathematics), Beijing, China, August 2015.

20. A Visual and Computational Framework for Evaluating the Effeictiveness of Surgery on Infants Born with Craniosynostosis, with B. Yuan and D. Khechoyan, ICIAM 2015 (8th International Congress on Industrial and Applied Mathematics), Beijing, China, August 2015.

21. Complex μ-Bases for Real Quadric Surfaces, SIAM Conference on Applied Algebraic Geometry (AG15), National Institute for Mathematical Sciences, Daejeon, South Korea, August 2015.

22. Explicit μ-Bases for Low Degree Rational Curves, SIAM Conference on Applied Algebraic Geometry (AG15), National Institute for Mathematical Sciences, Daejeon, South Korea, August 2015.

23. Algebraic and Geometric Extensions of the Lane-Riesenfeld Subdivision Algorithm (Invited Presentation), Workshop on Numerical Methods and Applied Geometry, Weizmann Institute of Science, Israel, May 2015.

24. A New Objective Automatic Computational Framework for Evaluating and Visualizing the Results of Infant Cranial Surgery, with B. Yuan and D. Khechoyan, BioMedCom2014, Cambridge, Massachusetts, December 2014. 24

25. A Unifying Functional Structure for Polar Forms and for Functional Bernstein=Bezier Curves, with C. Disibuyuk, Eighth International Conference on Curves and Surfaces, Paris, France, June 2014.

26. Geometric Variations of the Lane-Riesenfeld Algorithm, with N. Dyn and D. Levin, Dagstuhl Conference on Geometric Modeling, Dagstuhl, Germany, May 2014.

27. Generalized Quantum Splines (Invited Presentation), with P. Simeonov, IMA Conference on the Mathematics of Surfaces, Birmingham, England, September 2013.

28. Towards an Algebra for Rational Curves and Surfaces in Two and Three Dimensions, with Wang, SIAM Conference on Applied Algebraic Geometry, Ft. Collins, Colorado, August 2013.

29. Towards a General Unified Theory of Classical and Quantum Splines, with P. Simeonov, 14th International Conference on Approximation Theory, San Antonio, Texas, April 2013.

30. Extending Fundamental Formulas from Classical B-splines to Quantum B-splines, with G. Budakci, C. Disibuyuk, and H. Oruc, 14th International Conference on Approximation Theory, San Antonio, Texas, April 2013.

31. μ-Bases for Complex Rational Curves, with X. Wang, Algebraic Geometry and Geometric Modeling (AGGM 2013), Banff, Canada, January 2013.

32. 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.

33. Generating Functions for Uniform B-splines, Eighth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway, July 2012.

34. Using μ-Bases to Implicitize Rational Surfaces with a Pair of Orthogonal Directrices, with Shi and X. Wang, Geometric Modeling and Processing (GMP 2012), Huangshan, China, June 2012.

35. Quaternions and Dual Quaternions (Tutorial), International Conference on Shape Modeling and Applications (SMI), College Station, Texas, May 2012.

36. Quantum Splines, New Trends in Approximation Theory, Ein Gedi, Israel, January 2012. 25

37. The Role of Algebraic Geometry in Geometric Modeling, SIAM Conference on Applied Algebraic Geometry, Raleigh, North Carolina, October 2011.

38. Understanding Quaternions: Rotation, Reflection and Perspective Projection — Invited Presentation, Third Annual Fall School: Shapes, Geometry, and Algebra (SAGA), Vilnius, Lithuania, September 2011.

39. Introduction to Clifford Algebra — Invited Presentation, Third Annual Fall School: Shapes, Geometry, and Algebra (SAGA), Vilnius, Lithuania, September 2011.

40. Polynomials and Fractals: Polynomials as Attractors, Fractals with Control Points (Invited Presentation), 24th International Conference of the Jangjeon Mathematical Society, Konya, Turkey, July 2011.

41. Quantum Bezier Curves, Dagstuhl Conference on Geometric Design, Dagstuhl, Germany, May 2011.

42. Convergence of the Lane-Riesenfeld Algorithm with Nonlinear Averages, Minisymposium on Nonlinear Subdivision, Seventh International Conference on Curves and Surfaces, Avignon, France, June 2010.

43. Rethinking the Classical Paradigm of the Clifford Algebra fo 3-Dimensions: Presenting a Simple Homogeneous Model for Computer Graphics, Applied Geometric Algebras in Computer Science and Engineering 2010, Amsterdam, Netherlands, June 2010.

44. 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.

45. 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.

46. Nonlinear Lane–Riesenfeld Algorithms with Nonlinear Averaging Rules, Research Workshop on Subdivision and Refinability, Pontignano, Italy, October 2009.

47. 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. 26

48. 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.

49. 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.

50. 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.

51. An Introduction to Geometric Modeling (Invited Presentation), Second International Workshop on Algebraic Geometry and Approximation Theory, Towson, Maryland, April 2009.

52. B-Splines with Knots in the Complex Plane, (Invited Presentation), with K. Tsianos, Second International Workshop on Algebraic Geometry and Approximation Theory, Towson, Maryland, April 2009.

53. 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.

54. 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.

55. Global Knot Insertion Algorithms, with S. Schaefer, Foundations of Computational Mathematics (FoCM 2008), Workshop on Approximation Theory (Invited Presentation), Hong Kong, June 2008.

56. 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.

57. 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 2007.27

58. 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.

59. 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.

60. Subdivision Algorithms for Circular Arcs, with S. Schaefer and E. Vouga, SIAM Conference on Geometric Design and Computing, Phoenix, Arizona, November 2005.

61. 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.

62. Subdivision Schemes and Attractors, with S. Schaefer and D. Levin, Symposium on Geometric Processing (SGP) 2005, Vienna, Austria, July 2005.

63. Blossoming and the Lane-Riesenfeld Algorithm, Dagstuhl Conference on Geometric Modelling, Dagstuhl, Germany, May 2005.

64. Algebraic Geometry and Geometric Modeling: Insight and Computation, (Invited Presentation), Workshop on Algebraic Geometry and Geometric Modeling, Nice, France, September 2004.

65. Hodograph Turtles, with T. Ju, IASTED Conference on Computer Graphics, Kauai, Hawaii, August 2004.

66. 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.

67. 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.

68. 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 2004.28

69. 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.

70. Fractal Algorithms for Polynomial Curves, Coastal Workshop on Geometric Modeling, June 2004.

71. An Introduction to Multisided Toric Bezier Patches, (Invited Presentation), International Workshop on Geometric and Visual Computing, Jinan, China, April 2004.

72. The Fractal Nature of Bezier Curves, (Invited Presentation), Geometric Modeling and Processing 2004, Beijing, China, April 2004.

73. Introduction to Geometric Modeling, (Invited Presentation), MSRI Workshop on Real Algebraic Geometry and Geometric Modeling, Berkeley, California, April 2004.

74. Toric Bezier Patches, SIAM Conference on Geometric Design and Computing, Seattle, Washington, November 2003.

75. Blossoming Analytic Functions, SIAM Conference on Geometric Design and Computing, Seattle, Washington, November 2003.

76. Computer Graphics in its Fifth Decade: Ferment at the Foundations, (Invited Presentation), Pacific Graphics 2003, Canmore, Canada, October 2003.

77. Fractal Bezier, 2003 Pacific Workshop on Geometric Modeling, Calgary, Canada, October 2003.

78. Curvature Formulas for Implicit Curves and Surfaces, Workshop on Geometric Modeling

and Differential Geometry, Erbach, Germany, October 2003.

79. Morphing Rational B-spline Curves and Surfaces Using Mass Distributions, with T. Ju, Eurographics 2003, Short Presentation, Granada, Spain, September 2003.

80. Two Multisided Bernstein/Bezier/Barycentric Schemes: S–Patches and Toric Bezier Patches, Oberwolfach Conference on Mathematical Methods in Geometric Design, Oberwolfach, Germany, October 2002.

81. Blossoming, Workshop on Algebraic Geometry and Geometric Modeling, Vilnius, Lithuania, July 2002.29

82. The Sylvester Resultant Matrix for Bernstein Polynomials, with J. Winkler, Fifth International Conference on Curves and Surfaces, St. Malo, France, July 2002.

83. Musings on Multisided Bezier Patches, Dagstuhl Conference on Geometric Modeling, Dagstuhl, Germany, May 2002.

84. A New Approach to Sparse Resultant Matrices for Bivariate Polynomials with Applications in Geometric Modeling (Invited Presentation), with E. Chionh, Journées de Cloture Visi3D et CoSTIC, Paris, France, December 2001.

85. Analytic Functions in Geometric Modeling, with G. Morin, Journées de Cloture Visi3D et CoSTIC, Paris, France, December 2001.

86. Three Implicitization Methods for Rational Surfaces, SIAM Conference on Geometric Design and Computing, Sacramento, California, November 2001.

87. An Extended Domain for the Analytic Blossom, with G. Morin, SIAM Conference on Geometric Design and Computing, Sacramento, California, November 2001.

88. Multisided Bezier Patches (Invited Presentation), Hong Kong University Workshop on Geometric Computing, Hong Kong, China, June 2001.

89. Algorithms for Analytic Functions in Geometric Modeling, with G. Morin, Journees du Groupe de Travail, Modelisation Geometrique, Dijon, France, March 2001.

90. 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.

91. Rectangular Corner Cutting and Sylvester A-Resultants, with M. Zhang, International Symposium on Symbolic and Algebraic Computation (ISSAC), St Andrews University, Scotland, August 2000.

92. Baseball and Bezier, The Fifth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway, July 2000.

93. Blossoming Poisson Curves, with G. Morin, The Fifth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway, July 2000.30

94. 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.

95. 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.

96. Discrete Approximations of Bezier Derivatives, with G. Morin, Trends in ApproximationTheory, Vanderbilt University, Nashville, Tennessee, May 2000.

97. Poisson Approximation (Invited Presentation), with G. Morin, Geometric Modeling and Processing 2000, Hong Kong, April 2000.

98. Implicitization by Dixon A-resultants, with E. Chionh and M. Zhang, Geometric Modeling and Processing 2000, Hong Kong, April 2000.

99. From Bezier to Poisson, Joint Australia-Taiwan Workshop on Analysis and Applications, Taipei, April 2000.

100. Implicitization by Moving Quadrics Almost Always Succeeds, with M. Zhang, Sixth SIAM Conference on Geometric Modeling, Albequerque, New Mexico, Nov. 2-5, 1999.

101. Trimming using Subdivision for Poisson Curves and Surfaces, with G. Morin, Sixth SIAM Conference on Geometric Modeling, Albequerque, New Mexico, Nov. 2-5, 1999.

102. 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.

103. 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.

104. The Ambient Spaces of Computer Aided Design, MSRI Workshop on Mathematical Foundations of CAD, Berkeley, California, June, 1999.

105. Blossoming, the Cancellation Axiom, and Divided Difference, Dagstuhl Conference on Geometric Modelling, Dagstuhl, Germany, May 1999. 31

106. Fast Computation of the Entries of the Bezout and Dixon Resultants (Invited Presentation), with E. Chionh and M. Zhang, Surface Approximation and Visualization Conference, Christchurch, New Zealand, February 1999.

107. Hybrid Dixon Resultants, with E. Chionh and M. Zhang, Eighth IMA Conference on the Mathematics of Surfaces, August 1998.

108. Complex Contour Integration and B-splines of Negative Degree, Oberwolfach Conference on Freeform Curves and Surfaces, Oberwolfach, Germany, June 1998.

109. On the Linear Independence of the Bivariate Discrete Convolution Blending Functions, with Y. Stefanus, 4th Australian Theory Symposium, CATS ‘98, Perth, Australia, February 1998.

110. A Trimming Algorithm for Bezier Surfaces, with Suresh Lodha, The Fourth International Conference on Mathematical Methods for Curves and Surfaces, Lillehammer, Norway, July 1997.

111. Rational B-splines?, (Invited Presentation), The Fourth International Conference on Mathematical Methods for Curves and Surfaces, Lillehammer, Norway, July 1997

112. Rational Bezier?, International Workshop on Computer Aided Geometric Design: New Trends and Applications, Anogia, Crete, June 1997.

113. 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.

114. 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.

115. Dual de Casteljau Subdivision Algorithm, with S. Lodha, Dagstuhl Conference on Geometric Modeling, Dagstuhl, Germany, May 1996.

116. 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. 32

117. A New Approach to Implicitizing Rational Curves and Surfaces, with Tom Sederberg, Oberwolfach Conference on Freeform Curves and Surfaces, Oberwolfach, Germany, June 1995.

118. Discrete Unimodality of B-Spline and Bernstein Bases, (Invited Presentation), International Conference on Computer Aided Geometric Design, Penang, Malaysia, July 1994.

119. Point-Line Duality for Surfaces in CAGD, with S. Lodha, International Conference on Computer Aided Geometric Design, Penang, Malaysia, July 1994.

120. Dual Properties of B-Patches and L-Patches, with S. Lodha, Third International Conference on Mathematical Methods in CAGD, Ulvik, Norway, June 1994.

121. Evaluation Algorithms for Surfaces in CAGD, with S. Lodha, Third International Conference on Mathematical Methods in CAGD, Ulvik, Norway, June 1994.

122. An Axiomatic Approach to Geometric Continuity, with A. Habib, Third International Conference on Mathematical Methods in CAGD, Ulvik, Norway, June 1994.

123. An Introduction to Polar Forms, Third SIAM Conference on Geometric Design, Tempe, Arizona, November 1993.

124. Polar Forms and Knot Insertion for B-spline Curves, Third SIAM Conference on Geometric Design, Tempe, Arizona, November 1993.

125. Recursive Techniques in CAGD, Third SIAM Conference on Geometric Design, Tempe, Arizona, November 1993.

126. What is Wiggle?, Dagstuhl Conference on Geometric Modeling, Dagstuhl, Germany, July 1993.

127. 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.

128. Dual Polynomial Bases, (Invited Presentation), International Conference on Advances in Computational Mathematics, New Delhi, India, January 1993.33

129. Implicitizing Techniques for Rational Surfaces, with E. Chionh, 5th International Conference on Engineering Computer Graphics and Descriptive Geometry, Melbourne, Australia, August 1992.

130. 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.

131. An Extension of Chaikin’s Algorithm, with J. Warren, Second SIAM Conference on Geometric Design, Tempe, Arizona, November 1991.

132. Blossoming and B-splines, ACM Siggraph Tutorial, Las Vegas, Nevada, July 1991.

133. Knot Insertion Algorithms, ACM Siggraph Tutorial, Las Vegas, Nevada, July 1991.

134. Wonderful Triangle, with P. Barry, (Invited Presentation), Conference on Curves, Surfaces, CAGD, and Image Processing, Biri, Norway, June 1991.

135. 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.

136. Tensor Product Slices, with R. Bartels and R. Pfeifle, Conference on Curves, Surfaces CAGD, and Image Processing, Biri, Norway, June 1991.

137. On Discrete Convolution Curves, with Y. Stefanus, Conference on Curves, Surfaces, CAGD, and Image Processing, Biri, Norway, June 1991.

138. 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.

139. 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.

140. Fast Knot Insertion, with P. Barry, A.F.A. International Conference on Curves and Surfaces, Chamonix, France, June 1990. 34

141. Methods of Knot Insertion for B-spline Curves, with P. Barry, A.F.A. International Conference on Curves and Surfaces, Chamonix, France, June 1990.

142. 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.

143. 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.

144. Polya Polynomials and B-Spline Curves, (Invited Presentation), NATO Advanced Study Institute, Puerto de la Cruz, Canary Islands, Spain, July 1989.

145. 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.

146. Algorithms in the Style of Boehm and Sablonniere, with P. Barry, Oberwolfach Conference on Computer Aided Geometric Design, Oberwolfach, Germany, April 1989.

147. Recursive Curves and Surfaces, ACM Siggraph Tutorial, August 1988. (Repeated again at Graphics Interface in June 1989 and at Siggraph in August 1989).

148. Three Examples of Dual Properties of Bezier Curves, with P. Barry, Oslo Conference on Mathematical Methods in CAGD, Oslo, Norway, June 1988.

149. What is the Natural Generalization of a Bezier Curve?, with P. Barry, Oslo Conference on Mathematical Methods in CAGD, Oslo, Norway, June 1988.

150. 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.

151. Probabilistic Approaches to Computer-Aided Geometric Design, Minisyposium with P. Barry and T. DeRose, SIAM Conference on Applied Geometry, Albany, July 1987. 35

152. Future Directions in Geometric Modeling: A Preview of Coming Attractions, (Invited Presentation), Wayne State Conference on Applied Geometry, Detroit, Michigan, May 1987.

153. Conversion Between Bezier Rectangles and Bezier Triangles, with D. Filip, Symposium on Topics in Computer Aided Geometric Design, Braunschweig, West Germany, June 1986.

154. Vector Geometry: A Coordinate Free Approach, ACM Siggraph Tutorial, July 1985. Repeated again at Siggraph in July 1986 and 1987).

155. The Role of Surfaces in Solid Modeling, (Invited Presentation), SIAM Conference on Geometric Modeling and Robotics, Albany, July 1985. 156. Urn Models and Beta-Splines, NASA International Conference on Computational Geometry and Computer Aided Design, New Orleans, June 1985.

157. Some Applications of Resultants to Problems in Computational Geometry, with T. Sederberg, International Conference on Engineering and Computer Graphics, Beijing, China, August 1984.

158. Geometry and Probability, ACM Siggraph Tutorial, July 1984.

159. An Intuitive Approach to Bezier and Other Random Curves and Surfaces, ACM Siggraph Tutorial, July 1983.

160. An Urnful of Blending Functions, NASA Symposium on Computer Aided Geometry and Modeling, Langley, Virginia, April 1983.

161. The Perfect Surface, Engineering Society of Detroit, Detroit, Michigan, 1979.