Bicubic B-spline blending patches with optimized shape

  • Authors:
  • Przemysław Kiciak

  • Affiliations:
  • -

  • Venue:
  • Computer-Aided Design
  • Year:
  • 2011

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Abstract

Two constructions of bicubic B-spline patches with fixed boundary conditions are described. Their goal is to minimize functionals taken for measures of patch badness. The first construction is numerically solving the triharmonic equation -@D^3p=0. The functional minimized in the second construction is the sum of a term determined by the surface shape (the distribution of mean curvature) and a term introduced to overcome the problem of ambiguity of minimum of the first term. In addition to boundary conditions one can impose constraints, e.g. fix constant parameter curves of the patch.