Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

Abstract

Abstract-The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error δ, minimal interior angle θ and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound δ as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. Our optimization framework greedily searches for the coarsest mesh with minimal interior angle above θ and approximation error bounded by δ. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Index Terms-surface remeshing, error-bounded, feature preserving, minimal angle improvement, feature intensity.

A Constrained Resampling Strategy for Mesh Improvement

“…Unlike the majority of remeshing algorithms that assume features are specified in advance, e.g., [GYJZ15], our constraints implicitly preserve features up to a smoothness parameter, which makes it closer to the approach in [LT98]. The recent work in [HYB*16] is similar to ours as they consider multiple objectives, i.e., angle bounds and the Hausdorff error, along with reducing the vertex count. Although their approach can be superior in Hausdorff error, our approach is simpler and more versatile.…”

“…While this approach does not guarantee a bound on Hausdorff errors, which is a crucial measure in several applications, our results show that the resulting meshes are reasonably close although other methods can be superior in terms of Hausdorff errors. It is possible, however, to incorporate a suitable overestimator of the Hausdorff error committed by each potential update and reject the update if the error exceeds a given threshold as in [HYB*16]. One caveat is that bounding dihedral angles does not prevent the creation of needle‐like features.…”

Surface remeshing with robust user-guided segmentation

“…However, this scheme cannot be applied naturally to free-form objects. Various solutions (e.g., feature-sensitive remeshing [29], implicit feature preservation [4,5]) have been proposed to preserve features for general objects, especially for models with thin and sharp features. However, these solutions do not always successfully handle thin and sharp features, such as the ear of the Elk model.…”

“…In each local region, the bad triangle is treated with edge-based operations [5], while the vertices in the local regions are also relocated for quality improvement. We calculate the new position p i as the Laplacian center c i of the one ring around v i when relocating a vertex v i .…”

“…In many remeshing algorithms, a user-given feature skeleton is required as an input for use in feature preservation [2,3]. Several approaches include efficient feature functions for implicit feature preservation [4,5]. These approaches can efficiently handle models, such as CAD models and man-made objects with clearly defined features, or models without minimal local features.…”