Extraction of coherent and smooth feature lines from meshes with fine details

Feature lines such as ridge-valley lines can be defined as the loci of points which maximize a certain geometric property (e.g. the principal curvature) along the corresponding critical directions (e.g. the principal direction of curvature). Such extrema over mesh edges are often determined by zero-crossings of directional derivatives. As a result, lines generated by existing algorithms suffer frequently from fragmentation (gaps on lines) and fluctuation (lack of smoothness). As such, we propose a novel method for tracing such lines. Points on feature lines, i.e. extrema over mesh edges, are detected and located by interpolating extrema in the vicinity of mesh vertices, which effectively reduces fragmentation and fluctuation of lines. Meanwhile, the majority of the existing algorithms for feature lines extraction employ high-order derivatives of the underlying surfaces for estimating both the geometric property and the critical direction. Estimation of differential invariants including curvature typically requires at least 2-ring neighborhoods of mesh vertices, making such quantities intrinsically incapable of capturing local features. By leveraging integral invariants, which can be defined over an appropriately small neighborhood, we are able to extract features of small scales when compared to that of mesh elements. In this paper, we demonstrate the effectiveness of our proposed method in generating coherent and smooth feature lines while providing more desirable details. (C) 2019 Elsevier Ltd. All rights reserved.