🤖 AI Summary
This work proposes a novel surface representation framework that addresses the lack of effective smooth interpolation methods for non-quadrilateral faces in arbitrarily topologized closed meshes. By integrating local polygonal quadratic interpolation with rational curve parameterization, the method constructs smoothly connected quadrilateral patches and introduces a specialized rational-curve-based parameterization strategy for triangular and general polygonal faces. Through sub-patch blending and surface stitching techniques, the approach achieves globally C¹-continuous, high-quality surface reconstruction. Notably, this is the first unified framework capable of effectively handling smooth interpolation across faces with arbitrary numbers of edges, significantly enhancing both the quality and flexibility of surface generation for complex-topology meshes.
📝 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.