Interpolation of subdivision features for curved geometry modeling

TL;DR

This paper introduces a nodal interpolation method for subdivision models that accurately represents curved geometries with sharp and smooth features, enhancing simulation fidelity without relying on underlying curved models.

Contribution

The method automatically identifies and preserves sharp features while smoothing others, enabling high-order polynomial interpolation of subdivision-based curved geometries.

Findings

Converges geometrically with polynomial degree

Effectively preserves sharp features during interpolation

Successfully applied to high-order volume mesh boundaries

Abstract

We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to maintain the necessary sharp features and smooth the indicated ones. This sharp-to-smooth modeling capability handles unstructured configurations of the simulation points, curves, and surfaces. The surfaces correspond to initial linear triangulations that determine the sharp point and curve features. The method automatically suggests a subset of sharp features to smooth which the user modifies to obtain a limit model preserving the initial points. This model reconstructs the curvature by subdivision of the initial mesh, with no need of an underlying curved geometry model. Finally, given a polynomial degree and a nodal distribution, the method generates a piece-wise polynomial representation interpolating the limit model. We show numerical evidence that this approximation, naturally aligned to the subdivision features, converges to the model geometrically with the polynomial degree for nodal distributions with sub-optimal Lebesgue constant. We also apply the method to prescribe the curved boundary of a high-order volume mesh. We conclude that our sharp-to-smooth modeling capability leads to curved geometry representations with enhanced preservation of the simulation intent.