Polyhedral design with blended $n$-sided interpolants

TL;DR

This paper introduces a novel parametric surface representation that interpolates mesh vertices of arbitrary topology using blended multi-sided interpolants, enabling smooth connections across complex mesh structures.

Contribution

It presents a new blending technique for multi-sided quadratic interpolants and a specialized parameterization method for non-quadrilateral patches.

Findings

Successfully interpolates vertices of arbitrary mesh topology

Creates smooth, connected quadrilateral patches

Handles triangular subpatches effectively

Abstract

A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In the non-four-sided case, this requires a special parameterization technique involving rational curves. Appropriate handling of triangular subpatches and alternative subpatch representations are also discussed.