Geometric path planning in rapid prototyping

  • Avner Friedman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 67)


Rapid prototyping encompasses a family of recently developed technologies that are concerned with the automatic generation of 3D prototype parts from computerized geometric descriptions. The prototype parts are expected to be dimensionally accurate, but need not possess the strength, rigidity, surface finish or other physical properties of the final product.


Rapid Prototype Voronoi Diagram Rational Curf Polynomial Curve Pythagorean Hodograph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Ashley, Rapid prototyping systems, Mechanical Engineering, April 1991, 34–43.Google Scholar
  2. [2]
    T. Wohler, Chrysler compares rapid prototyping systems, Computer-Aided Engineering, October 1992, 84–90.Google Scholar
  3. [3]
    A. Friedman, J. Glimm and J. Lavery, The Mathematical and Computational Sciences in Emerging Manufacturing Technologies and Management Practices, SIAM, Philadelphia (1992).Google Scholar
  4. [4]
    R.T. Farouki and C.A. Neff, Analytic properties of plane offset curves, Computer Aided Geometric Design, 7 (1990), 83–99.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    G. Salmon, A Treatise of the Higher Plane Curves, Chelsea, New York (1879) (preprint).Google Scholar
  6. [6]
    R.T. Farouki and C.A. Neff, Algebraic properties of plane offset curves, Comput. Aided Geom. Design, 7 (1990), 101–127.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    R.T. Farouki and T. Sakkalis, Pythagorean hodographs, IBM Journal of Research and Development, 34 (1990), 736–752.MathSciNetCrossRefGoogle Scholar
  8. [8]
    K.K. Kubota, Pythagorean triples in unique factorization domains, Amer. Math. Monthly, 79 (1972), 503–505.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    R.T. Farouki, The conformal map z --> z2 of the hodograph plane, Preprint.Google Scholar
  10. [10]
    R.T. Farouki and V.T. Rajan, On the numerical condition of polynomials in Bernstein form, Comput. Aided Geom. Design, 4 (1987), 191–216.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, New York, 1988.zbMATHGoogle Scholar
  12. [12]
    R.T. Farouki and C.A. Neft, Hermite Interpolation by Pythagoreanhodograph quintics, IBM Research Division, RC 19234, October 1993.Google Scholar
  13. [13]
    B. Pham, Offset curves and surfaces: a brief survey, Computer-Aided Design, 24 (1992), 223–229.CrossRefGoogle Scholar
  14. [14]
    R.T. Farouki, Exact offset procedures for simple solids, Computer Aided Geometric Design 2 (1985), 257–280.zbMATHCrossRefGoogle Scholar
  15. [15]
    R.T. Farouki, The approximation of non degenerate offset surfaces, Computer Aided Geometric Design, 3 (1986), 15–44.zbMATHCrossRefGoogle Scholar
  16. [16]
    R.T. Farouki, K. Tarabanis, J.U. Korein, J.S. Batchelder, and S.R. Abrams, Offset curves in layered manufacturing, IBM Research Division, RC 19408, February 1994.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations