Adapting Feature Curve Networks to a Prescribed Scale

• Published in: Computer graphics forum Vol. 35; no. 2; pp. 319 - 330
• Main Authors: Gehre, Anne, Lim, Isaak, Kobbelt, Leif
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2016
• Subjects: Algorithms; Analysis; and Level Of Detail Algorithms-Feature Curve Networks; Anisotropy; Approximation; Categories and Subject Descriptors (according to ACM CCS); Compatibility; Computer graphics; Digital Geometry Processing; I.3.3 [Computer Graphics]: Computational Geometry; I.3.3 [Computer Graphics]: Computational Geometry, Digital Geometry Processing, and Level Of Detail Algorithms—Feature Curve Networks; Mathematical analysis; Networks; Optimization; Optimization algorithms; Segments; Studies; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12834

Feature curves on surface meshes are usually defined solely based on local shape properties such as dihedral angles and principal curvatures. From the application perspective, however, the meaningfulness of a network of feature curves also depends on a global scale parameter that takes the distance between feature curves into account, i.e., on a coarse scale, nearby feature curves should be merged or suppressed if the surface region between them is not representable at the given scale/resolution. In this paper, we propose a computational approach to the intuitive notion of scale conforming feature curve networks where the density of feature curves on the surface adapts to a global scale parameter. We present a constrained global optimization algorithm that computes scale conforming feature curve networks by eliminating curve segments that represent surface features, which are not compatible to the prescribed scale. To demonstrate the usefulness of our approach we apply isotropic and anisotropic remeshing schemes that take our feature curve networks as input. For a number of example meshes, we thus generate high quality shape approximations at various levels of detail.