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Computing Isophotes on Free-Form Surfaces Based on Support Function Approximation

  • M. Aigner
  • L. Gonzalez-Vega
  • B. Jüttler
  • M. L. Sampoli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5654)

Abstract

The support function of a free-form-surface is closely related to the implicit equation of the dual surface, and the process of computing both the dual surface and the support function can be seen as dual implicitization. The support function can be used to parameterize a surface by its inverse Gauss map. This map makes it relatively simple to study isophotes (which are simply images of spherical circles) and offset surfaces (which are obtained by adding the offsetting distance to the support function).

We present several classes of surfaces which admit a particularly simple computation of the dual surfaces and of the support function. These include quadratic polynomial surfaces, ruled surfaces with direction vectors of low degree and polynomial translational surfaces of bidegree (3,2).

In addition, we use a quasi-interpolation scheme for bivariate quadratic splines over criss-cross triangulations in order to formulate a method for approximating the support function. The inverse Gauss maps of the bivariate quadratic spline surfaces are computed and used for approximate isophote computation. The approximation order of the isophote approximation is shown to be 2.

Keywords

Support Function Rational Curf Freeform Surface Translational Surface Parabolic Point 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Aigner
    • 1
  • L. Gonzalez-Vega
    • 2
  • B. Jüttler
    • 1
  • M. L. Sampoli
    • 3
  1. 1.Johannes Kepler UniversityLinzAustria
  2. 2.University of CantabriaSantanderSpain
  3. 3.University of SienaItaly

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