Fair Surface Reconstruction Using Quadratic Functionals

Andreas Kolb*, Helmut Pottmann, Hans‐Peter ‐P Seidel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


An algorithm for surface reconstruction from a polyhedron with arbitrary topology consisting of triangular faces is presented. The first variant of the algorithm constructs a curve network consisting of cubic Bézier curves meeting with tangent plane continuity at the vertices. This curve network is extended to a smooth surface by replacing each of the networks facets with a split patch consisting of three triangular Bézier patches. The remaining degrees of freedom of the curve network and the split patches are determined by minimizing a quadratic functional. This optimization process works either for the curve network and the split patches separately or in one simultaneous step. The second variant of our algorithm is based on the construction of an optimized curve network with higher continuity. Examples demonstrate the quality of the different methods.

Original languageEnglish (US)
Pages (from-to)469-479
Number of pages11
JournalComputer Graphics Forum
Issue number3
StatePublished - Aug 1995
Externally publishedYes

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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