Dr. Farouki's Papers in CADCAM and Physics

• None

• Albrecht, G., and Farouki, R. T., Construction of C2 Pythagorean-Hodograph Interpolating Splines by the Homotopy Method, Advances in Computational Mathematics, Vol. 5, 1996, pp. 417-442.
• Albrecht, G., and Farouki, R. T., Construction of C_SP_2 Pythagorean-Hodograph Interpolating Splines by the Homotopy Method, Advances in Computational Mathematics, Vol. 5, No. 4, 1996, pp. 417-442.
• Dalvie, M., Pavarino, L. F., and Farouki, R. T., Boundary-Condition Refinement of the Child-Langmuir Law for Collisionless dc Plasma Sheaths, Journal of Applied Physics, Vol. 68, 1990, pp. 106-116.
• Dalvie, M., Farouki, R. T., and Hamaguchi, S., Flux Integration in 2D vs. 3D Feature Evolution Models of Plasma Processing, Proceedings of the 1991 IEEE International Conference on Plasma Science, 1991, pp. 138.
• Dalvie, M., Farouki, R. T., and Hamaguchi, S., Flux Considerations in the Coupling of Monte Carlo Plasma Sheath Simulations with Feature Evolution Models, IEEE Transactions on Electron Devices, Vol. 39, No. 5, 1992, pp. 1090-1099.
• Farouki, R. T., and Hinds, J. K., A Hierarchy of Geometric Forms, IEEE Computer Graphics and Applications, Vol. 5, No. 5, 1985, pp. 51-78.
• Farouki, R. T., Exact Offset Procedures for Simple Solids, Computer Aided Geometric Design, Vol. 2, No. 4, 1985, pp. 257-279.
• Farouki, R. T., The Characterization of Parametric Surface Sections, Computer Vision, Graphics, and Image Processing, Vol. 33, No. 2, 1986, pp. 209-236.
• Farouki, R. T., The Approximation of Non-Degenerate Offset Surfaces, Computer Aided Geometric Design, Vol. 3, No. 1, 1986, pp. 15-43.
• Farouki, R. T., and Rajan, V. T., On the Numerical Condition of Polynomials in Bernstein Form, Computer Aided Geometric Design, Vol. 4, No. 3, 1987, pp. 191-216.
• Farouki, R. T., Trimmed Surface Algorithms for the Evaluation and Interrogation of Solid Boundary Representations, IBM Journal of Research and Development, Vol. 31, No. 3, 1987, pp. 314-334.
• Farouki, R. T., Direct Surface Section Evaluation, Geometric Modeling, SIAM Publishers, 1987, pp. 319-334.
• Farouki, R. T., Graphical Methods for Surface Differential Geometry, The Mathematics of Surfaces II, Oxford University Press, 1987, pp. 363-385.
• Farouki, R. T., and Rajan, V. T., Algorithms for Polynomials in Bernstein Form, Computer Aided Geometric Design, Vol. 5, No. 1, 1988, pp. 1-26.
• Farouki, R. T., Computational Issues in Solid Boundary Evaluation, Information Sciences, Vol. 44, No. 2, 1988, pp. 87-171.
• Farouki, R. T., and Rajan, V. T., On the Numerical Condition of Algebraic Curves and Surfaces: 1. Implicit Equations, Computer Aided Geometric Design, Vol. 5, No. 3, 1988, pp. 215-252.
• Farouki, R. T., Neff, C. A., and O'Conner, M. A., Automatic Parsing of Degenerate Quadric-Surface Intersections, ACM Transactions on Graphics, Vol. 8, No. 3, 1989, pp. 174-203.
• Farouki, R. T., Hierarchical Segmentations of Algebraic Curves and Some Applications, Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L. Schumaker Eds., Academic PRess, 1989, pp. 239-248.
• Farouki, R. T., Numerical Stability in Geometric Algorithms and Representations, Mathematics of Surfaces III, Oxford University Press, 1989, pp. 83-113.
• Farouki, R. T., a nd Neff, C. A., On the Numerical Condition of Bernstein-Bezier Subdivision Processes, Mathematics of Computation, Vol. 55, No. 192, 1990, pp. 637-647.
• Farouki, R. T., and Neff. C. A., Algebraic Properties of Plane Offset Curves, Computer Aided Geometric Design, Vol. 7, No. 1-4, 1990, pp. 101-127.
• Farouki, R. T., and Neff, C. A., Analytic Properties of Plane Parametric Curves, Computer Aided Geometric Design, Vol. 7, No. 1-4, 1990, pp. 83-99.
• Farouki, R. T., and Sakkalis, T., Pythagorean Hodographs, IBM Journal of Research and Development, Vol. 34, No. 5, 1990, pp. 736-752.
• Farouki, R. T., Computing with Barycentric Polynomials, Mathematics Intelligencer, Vol. 13, No. 4, 1991, pp. 61-69.
• Farouki, R. T., On the Stability of Transformations Between Power and Bernstein Polynomial Forms, Computer Aided Geometric Design, Vol. 8, No. 1, 1991, pp. 29-36.
• Farouki, R. T., and Sakkalis, T., Real Rational Curves are Not "Unit Speed", Computer Aided Geometric Design, Vol. 8, No. 2, 1991, pp. 151-157.
• Farouki, R. T., Hamaguchi, S., and Dalvie, M., Hydrodynamic Analysis of Electron Motion In the Cathode Fall Using a Monte Carlo Simulation, Journal of Applied Physics, Vol. 72, 1992, pp. 2620-2631.
• Farouki, R. T., and Johnstone, J. K., Computing Point/Curve and Curve/Curve Bisectors, Design and Application of Curves and Surfaces, Oxford University Press, 1992, pp. 327-354.
• Farouki, R. T., and Chastang, J-C. A., Curves and Surfaces in Geometrical Optics, Mathematical Methods in Computer Aided Geometric Design II, Academic Press, 1992, pp. 239-260.
• Farouki, R. T., Pythagorean Hodograph Curves in Practical Use, Geometry Processing for Design and Manufacturing, SIAM Publishers, 1992, pp. 3-33.
• Farouki, R. T., and Sakkalis, T., Pythagorean-Hodograph Space Curves, Advances in Computational Mathematics, Vol. 2, 1994, pp. 41-66.
• Farouki, R. T., The Conformal Map Z tp Z_SP_2 of the Hodograph Plane, Computer Aided Geometric Design, Vol. 11, No. 4, 1994, pp. 363-390.
• Farouki, R. T., and Johnstone, J. K., The Bisector of a Point and a Plane Parametric Curve, Computer Aided Geometric Design, Vol. 11, No. 2, 1994, pp. 117-151.
• Farouki, R. T., Watch Your Parametric Speed, Computer Aided Surface Geometry and Design, Oxford University Press, 1994, pp. 69-95.
• Farouki, R. T., and Neff, C. A., Hermite Interpolation by Pythagorean-Hodograph Quintics, Mathematics of Computation, Vol. 64, No. 212, 1995, pp. 1589-1609.
• Farouki, R. T., Konig, T., and Tarabanis, K., Path Planning With Offset Curves for Layered Fabrication Processes, Journal of Manufacturing Systems, Vol. 14, No. 5, 1995, pp. 355-368.
• Farouki, R. T., and Sederberg, T. W., Analysis of the Offset to a Parabola, Computer Aided Geometric Design, Vol. 12, No. 6, 1995, pp. 639-645.
• Farouki, R. T., The Elastic Bending Energy of Pythagorean Hodograph Curves, Computer Aided Geometric Design, Vol. 13, 1996, pp. 227-241.
• Farouki, R. T., and Peters, J., Smooth Curve Design with Double Tschirnhausen Cubics, Annals of Numerical Mathematics, Vol. 3, No. 1-4, 1996, pp. 63-82.
• Farouki, R. T., and Pottmann, H., Polynomial and Rational Pythagorean Curves Reconciled, The Mathematics of Surfaces VI, Oxford University Press, 1996, pp. 355-378.
• Farouki, R. T., and Konig, T., Computational Methods for Rapid Prototyping of Analytic Solid Models, Rapid Prototyping Journal, Vol. 2, No. 3, 1996, pp. 41-48.
• Farouki, R. T., and Shah, S., Real-Time CNC Interpolators for Pythagorean Hodograph Curves, Computer Aided Geometric Design, Vol. 13, No. 7, 1996, pp. 583-600.
• Farouki, R. T., and Goodman, T. N. T., On the Optimal Stability of Bernstein Basis, Mathematics of Computation, Vol. 65, No. 216, 1996, pp. 1533-1566.
• Farouki, R. T., and Rampersad, J., Cycles Upon Cycles: An Anecdotal History of Higher Curves in Science and Engineering, Mathematical Methods for Curves and Surfaces II, Vanderbilt University Press, 1997, pp. 95-116.
• Farouki, R. T., Conic Approximation of Conic Offsets, Journal of Symbolic Computation, Vol. 23, No. 2-3, 1997, pp. 301-313.
• Farouki, R. T., Optimal Parametrizations, Computer Aided Geometric Design, Vol. 14, No. 2, 1997, pp. 153-168.
• Farouki, R. T., Pythagorean-Hodograph Quintic Transition Curves of Monotone Curvature, Computer Aided Geometric Design, Vol. 29, No. 9, 1997, pp. 601-606.
• Farouki, R. T., Saitou, K., and Y-F., Tsai, Least-Squares Tool Path Approximation with Pythagorean-Hodograph Curves for High-Speed Machinning, Proceedings of the IMA Mathematics of Surfaces VIII Conference, R. Cripps Eds., Information Geometers Press, 1998.
• Farouki, R. T., Manjunathaiah, J., and Jee, S., Design of Rational Cam Profiles with Pythagorean Hodograph Curves, Mechanism and Machine Theory, Vol. 33, No. 6, 1998, pp. 669-682.
• Farouki, R. T., On Integrating Lines of Curvature, Computer Aided Geometric Design, Vol. 15, No. 2, 1998, pp. 187-192.
• Farouki, R. T., and Ramamurthy, R., Degenerate Point/Curve and Curve/Curve Bisectors Arising in Medial Axis Computations for Planar Domains with Curved Boundaries, Computer Aided Geometric Design, Vol. 15, No. 6, 1998, pp. 615-635.
• Farouki, R. T., and Ramamurthy, R., Specified-Precision Computation of Curve-Curve Bisectors, International Journal of Computational Geometry and Applications, Vol. 8, No. 5., 1998, pp. 599-617.
• Farouki, R. T., Tsai, Y-F., and Yuan, G-F., Contour Machining of Free-Form Surfaces with Real-Time Pythagorean-Hodograph Curve CNC Interpolators, Computer Aided Geometric Design, Vol. 16, No. 1, 1999, pp. 61-76.
• Farouki, R. T., Manjunathaiah, J., and Yuan, G-F., G-Codes for the Specification of Pythagorean-Hodograph Tool Paths and Associated Feedrate Functions on Open Architecture CNC Machines, International Journal of Machine Tools and Manufacture, Vol. 39, No. 1, 1999, pp. 123-142.
• Hamaguchi, S., Dalvie, M., and Farouki, R. T., The Ion Distribution Function in Weakly Collisional Sheaths, Proceedings of the 1991 IEEE International Conference on Plasma Science, 1991, pp. 137-138.
• Hamaguchi, S., Dalvie, M., and Farouki, R. T., A Shock-Tracking Algorithm for Surface Evolution Under Reactive Ion Etching, Journal of Applied Physics, Vol. 74, 1993, pp. 5172-5184.
• Hamaguchi, S., and Farouki, R. T., Dynamics of Charged Particulates in Plasmas, Proceedings of the 1994 IEEE International Conference on Plasma Science, 1994, pp. 218.
• Hamaguchi, S., Farouki, R. T., and Dubin, D. H. E., Phase Diagram of Yukawa Systems Near the One-Component Plasma Limit Revisited, Journal of Chemical Physics, Vol. 105, No. 17, 1996, pp. 7641-7647.
• Kaul, A., and Farouki, R. T., Computing Minkowski Sums of Plane Curves, International Journal of Computational Geometry and Applications, Vol. 5, No. 4, 1995, pp. 413-432.
• Sakkalis, T., and Farouki, R. T., Singular Points of Algebraic Curves, Journal of Symbolic Computation, Vol. 9, No. 4, 1990, pp. 405-421.
• Sakkalis, T., and Farouki, R. T., Algebraically Rectifiable Parametric Curves, Computer Aided Geometric Design, Vol. 10, No. 6, 1993, pp. 551-569.
• Sederberg, T. W., and Farouki, R. T., Approximation by Interval Bezier Curves, IEEE Computer Graphics and Applications, September 1992, pp. 87-95.

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