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1.128

Computational Geometry

Graduate · Historical course

Spring 2003

Topics

  • Introduction; Classification of Geometric Modeling Forms
  • Differential Geometry of Curves
  • Differential Geometry of Surfaces (Demo)
  • Introduction to Spline Curves
  • B-splines (Uniform and Non-uniform)
  • Non-Uniform B-splines, Spline Surfaces
  • Non-Uniform Rational B-spline Curves and Surfaces (Demo) (Demo Program)
  • Physically-Based Deformable Surfaces (Demo)
  • Fairing; Generalized Cylinders
  • Blending Surfaces
  • Intersections
  • Surface Intersections; Nonlinear Solvers
  • Interval Methods, Robustness
  • Offset Curves and Surfaces
  • B-rep and CSG
  • B-rep and Non-Manifold Mixed Dimension Models
  • Computer Graphics Techniques
  • Reverse Engineering, Reconstructing the Past
  • Mechanical Tolerances
  • Decomposition Models; Integral Properties of Solids
  • Advanced Topics in Differential Geometry (Geodesics, Developable Surfaces, Umbilics, Parabolic Line, Ridge Line, Sub-Parabolic Line)
  • Localization, Inspection and Model Matching
  • Discrete Differential Geometry
  • F. E. and B. E. Meshing Algorithms (Demo)
  • Machining Automation (Guest Lecturer) (Demo)

Readings

  • Patrikalakis, N. M., T. Maekawa, and W. Cho. Shape Interrogation for Computer Aided Design and Manufacturing . New York, NY: Springer Verlag, 2010. ISBN: 978-3642040733. (Available from Springer & ResearchGate: printed , electronic ) ↗
    Required
  • Beach, R. C. An Introduction to Curves and Surfaces of Computer Aided Design . Van Nostrand Reinhold, 1991.
    Listed reading
  • Ding, Q. Surface Engineering Geometry for Computer Aided Design and Manufacture . Halsted Press, 1987.
    Listed reading
  • Farin, G. E. Curves and Surfaces for Computer Aided Geometric Design. 3rd ed. Academic Press, 1993.
    Listed reading
  • Faux, I. D., and M. Pratt. Computational Geometry for Design and Manufacture . Halsted Press,1979.
    Listed reading
  • Hoschek, J., and D. Lasser. Fundamentals of Computer Aided Geometric Design . Wellesley, MA: A. K. Peters Ltd., 1993.
    Listed reading
  • Lawrence, J. D. A Catalog of Special Plane Curves . Dover, 1972.
    Listed reading
  • Mortensen, M. E. Geometric Modeling . J. Wiley, 1985.
    Listed reading
  • Piegl, L., and W. Tiller. The NURBS Book . Springer, 1995.
    Listed reading
  • Rogers, D. F. An Introduction to NURBS: With Historical Perspective . 1st ed. Morgan Kaufmann Publishers, 2000.
    Listed reading
  • Yamaguchi, F. Curves and Surfaces in Computer Aided Geometric Design . Springer, 1988.
    Listed reading
  • -—–. Computer-Aided Geometric Design. Springer Verlag, 2002.
    Listed reading
  • Hoffmann, C. Geometric and Solid Modeling . Morgan Kaufman, 1989.
    Listed reading
  • Mantyla, M. An Introduction to Solid Modeling . Computer Science Press, 1988.
    Listed reading
  • Foley, J. D. Computer Graphics . 2nd ed. Addison-Wesley, 1990.
    Listed reading
  • Rogers, D. F. Mathematical Elements for Computer Graphics . 2nd ed. McGraw-Hill, 1990.
    Listed reading
  • Do Carmo, M. P. Differential Geometry of Curves and Surfaces . Prentice Hall, 1976.
    Listed reading
  • Gray, A. Modern Differential Geometry of Curves and Surfaces . CRC Press, 1993.
    Listed reading
  • Struik, D. J. Lectures on Classical Differential Geometry. Addison-Wesley, 1950.
    Listed reading
  • Dahlquist, G., and A. Bjorck. Numerical Methods . Prentice Hall, 1974.
    Listed reading
  • Press, W. H., et al. Numerical Recipes in C: The Art of Scientific Computing . Cambridge University Press, 1988.
    Listed reading
Sources