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High-order surface reconstruction is an important technique for CAD-free,mesh-based geometric and physical modeling, and for high-order numericalmethods for solving partial differential equations (PDEs) in engineeringapplications. In this paper, we introduce a novel method for accurate androbust reconstructions of piecewise smooth surfaces from a triangulatedsurface. Our proposed method extends the Continuous Moving Frames (CMF) and theWeighted Averaging of Local Fittings (WALF) methods (Engrg. Comput. 28 (2012))in two main aspects. First, it utilizes a Hermite-style least squaresapproximation to achieve fourth and higher-order accuracy with compact support,even if the input mesh is relatively coarse. Second, it introduces an iterativefeature-aware parameterization to ensure high-order accurate, G0 continuousreconstructions near sharp features. We present the theoretical framework ofthe method and compare it against CMF and WALF in terms of accuracy andstability. We also demonstrate that the use of the Hermite-style reconstructionin the solutions of PDEs using finite element methods (FEM), and show thatquartic and sextic FEMs using the high-order reconstructed surfaces producenearly identical results as using exact geometry while providing additionalflexibility.

Compact Feature-Aware Hermite-Style High-Order Surface Reconstruction