“Smoothing polyhedra using implicit algebraic splines” by Bajaj and Ihm

  • ©Chandrajit Bajaj and Insung Ihm

Conference:


Type:


Title:

    Smoothing polyhedra using implicit algebraic splines

Presenter(s)/Author(s):



Abstract:


    No abstract available.

References:


    1. Afield, P.,. Scattered Data Interpolation in Three or More Variables. In T. Lyche and L. Schumaker, editors, Mathematical Methods in Computer Aided Geometric Design, pages 1-34. Academic Press, 1989.
    2. Anupam, A., and Bajaj, C., and Royappa, A. The SHAS- TRA Distributed and Collaborative Geometric Design Environment. Computer Science Technical Report, CAPO-91-38, Purdue University, 1991.
    3. Bajaj, C. Geometric modeling with algebraic surfaces. In D. Handscomb, editor, The Mathematics of Surfaces III, pages 3–48. Oxford Univ. Press, 1988.
    4. Bajaj, C. Electronic Skeletons: Modeling Skeletal Structures with Piecewise Algebraic Surfaces. In Curves and Surfaces in Computer Vision and Graphics 11, pages 230-237, Boston, MA, 1991.
    5. Bajaj, C., and Ihm, I. Algebraic surface design with Hermite interpolation. ACM Transactions on Graphics, 19(1 ):61-91, January 1992.
    6. Beeker, E. Smoothing of Shapes Designed with Free Form Surfaces. Computer Aided Design, 18(4):224-232, 1986.
    7. Chiyokura, H., and Kimura, E Design of SoLids with Freeform Surfaces. Computer Graphics, 17(3):289-298, 1983.
    8. Chui, C. Multivariate Splines. Regional Conference Series in Applied Mathematics, 1988.
    9. Dahmen, W. Smooth piecewise quadratic surfaces. In T. Lyche and L. Schumaker, editors, Mathematical Methods in Computer Aided Geometric Design, pages 181-193. Academic Press, Boston, 1989.
    10. Dahmen, W. and Michelli, C. Recent Progress in Multivariate Splines. In L. Schumaker C. Chui and J. Word, editors, Approximation Theory IV, pages 27-121. Academic Press, 1983.
    11. deBoor, C., and Hollig, K., and Sabin, M. High Accuracy Geometric Hermite Interpolation, Computer Aided Geometric Design, 4(00):269-278, 1987.
    12. Farin, G. Triangular Bemstein-B~zier patches. Computer Aided Geometric Design, 3:83-127, 1986.
    13. Garrity, T., and Warren, J. Geometric continuity. Computer Aided Geometric Design, 8:51-65, 1991.
    14. Golub, G., and Van Loan, C. Matrix Computation. The Johns Hopkins Univ. Press, Baltimore, MD, 1983.
    15. Gregory, J., and Charrot, P. A C’l Triangular Interpolation Patch for Computer Aided Geometric Design. Computer Graphics and Image Processing, 13:80-87, 1980.
    16. Hagen, H., and Pottmann, H. Curvature Continuous Triangulax Interpolants. Mathematical Methods in Computer Aided Geometric Design, pages 373-384, 1989.
    17. Herron, G. Smooth Closed Surfaces with Discrete Triangular Interpolants. Computer Aided Geometric Design, 2(4):297- 306, 1985.
    18. Hollig, K. Multivariate Splines. SIAM J. on Numerical Analysis, 19:1013-1031, 1982.
    19. Ihm, I.,. Surface Design with Implicit Algebraic Surfaces. PhD thesis, Purdue University, August 1991.
    20. Lee, E. The rational B6zier representation for conics. In G. Farin, editor, Geometric Modeling : Algorithms and New Trends, pages 3-19. SIAM, Philadelphia, 1987.
    21. Liu, D., andHoschek, J. GCt Continuity Conditions Between Adjacent Rectangular and Triangular Bezier Surface Patches. Computer Aided Design, 21:194-200, 1989.
    22. Lorensen, W., and Cline, H. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics, 21:163-169, 1987.
    23. Moore, D., and Warren, J. Approximation of dense scattered data using algebraic surfaces. In Proc. of the 24th Hawaii Intl. Conference on System Sciences, pages 681-690, Kauai, Hawaii, 1991.
    24. Nielson, G. A Transfinite Visually Continuous Triangular lnterpolant. In O. Farin, editor, Geometric Modeling Applications and New Trends. SIAM, 1986.
    25. Patrikalakis, N., and Kriezis, G. Representation of piecewise continuous algebraic surfaces in terms of B-splines. The V/sua/ Computer, 5(6):360-374, Dec. 1989.
    26. Peters, J. Local Cubic and BiCubic CI Surface Interpolation with Linearly Varying Boundary Normal. Computer Aided Geometric Design, 7:499-516, 1990.
    27. Peters, j. Smooth interpolation of a mesh of curves. Constructive Approximation, 7:221-246,1991.
    28. Peters, J. Parametrizing singularly to enclose data points by a smooth parametric surface. In Proc. of Graphics Interface, Calgary, Alberta, June 1991. Graphics Interface ’91.
    29. Piper, B. Visually Smooth Interpolation with Triangular Bezier Patches. In G. Farin, editor, Geometric Modeling: Algorithms and New Trends. SIAM, 1987.
    30. Powell, M., and Sabin, M. Piecewise Quadratic Approximations on Triangles.ACM Trans. on Math. Software,3:316-325, 1977.
    31. Preparata, F., and Shamos, M. Computational Geometry, Aa Introduction. Springer Verlag, 1985.
    32. Ramshaw, L. Beziers and B-splines as Multiaf6ne Maps. In Theoretical Foundations of Computer Graphics and CAD. Springer Verlag, 1988.
    33. Sarraga, R. G1 interpolation of generally unrestricted cubic B~zier curves. Computer Aided Geometric Design, 4:23-39, 1987.
    34. Sederberg, T. Piecewise Algebraic Surface Patches. Computer Aided Geometric Design, 2:53-59,1985.
    35. Seidel, H-P. A New Multiaffine Approach to B-splines. Computer Aided Geometric Design, 6:23-32,1989.
    36. Semple, J., and Roth, L. Introduction to Algebraic Geometry. Oxford University Press, Oxford, U.K., 1949.
    37. Shirman, L., and Sequin, C. Local Surface Interpolation with Bezier Patches. Computer Aided Geometric Design, 4:279- 295, 1987.
    38. Walker, R. Algebraic Curves. Springer Verlag, New York, 1978.


ACM Digital Library Publication:



Overview Page: