Abstract
An algorithm for the local interpolation of a mesh of cubic curves with 3- and 4-sided facets by a piecewise cubic C 1 surface is stated and illustrated by an implementation. Precise necessary and sufficient conditions for oriented tangent-plane continuity between adjacent patches are derived, and the explicit constructions are characterized by the degree of the three scalar weight functions that relate the versal to the two transversal derivatives. The algorithm fully exploits the possibility of reparametrization by choosing all three weight functions nonconstant and not just degree-raising polynomials. The construction is local and consists mainly of averaging. The only systems to be solved are linear and of size 2 × 2. The algorithm guarantees interpolating surfaces without cusps and has a simple, implemented extension to n-sided facets.
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