Fair Surface Reconstruction Using Quadratic Functionals

Abstract

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 Bezier 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 Bezier 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.