On approximating contours of the piecewise trilinear interpolant using triangular rationalquadratic bézier patches

Bernd Hamann, Issac J. Trotts, Gerald E. Farin

Research output: Contribution to journalArticle

16 Scopus citations


Given a three-dimensional (3D) array of function values Fi,j,k on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x, y, z) = T. We describe the construction of a C0 -continuous surface consisting of rational-quadratic surface patches interpolating the triangles in T. We determine the Bézier control points of a single rational-quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.

Original languageEnglish (US)
Pages (from-to)215-227
Number of pages13
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number3
StatePublished - Dec 1 1997



  • Approximation
  • Contour
  • Isosurface
  • Marching cubes
  • Rational bézier curve
  • Rational bézier surface
  • Triangular patch
  • Triangulation
  • Trilinear interpolation
  • Visualization

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

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