Smooth surface interpolation using patches with rational offsets

TL;DR

The paper introduces a novel local patch-based method for interpolating data points and normals to create smooth surfaces with rational offsets, leveraging dual space isotropic models for G1 continuity.

Contribution

It proposes a dual approach using isotropic models and bicubic Coons patches for smooth, rational offset surface interpolation, ensuring local control and global G1 continuity.

Findings

Achieves smooth surface interpolation with rational offsets.

Ensures G1 continuity in the resulting surfaces.

Uses dual space isotropic models for construction.

Abstract

We present a new method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. We give some arguments why a dual approach is the most convenient for these surfaces, which are traditionally called Pythagorean normal vector (PN) surfaces. Our construction is based on the isotropic model of the dual space to which the original data are pushed. Then the bicubic Coons patches are constructed in the isotropic space and then pulled back to the standard three dimensional space. As a result we obtain the patch construction which is completely local and produces surfaces with the global G1~continuity.