Mesh Fairing Research Articles

Smooth operator: The effects of different 3D mesh retriangulation protocols on the computation of Dirichlet normal energy.

Dirichlet normal energy (DNE) is a metric of surface topography that has been used to evaluate the relationship between the surface complexity of primate cheek teeth and dietary categories. This study examines the effects of different 3D mesh retriangulation protocols on DNE. We examine how different protocols influence the DNE of a simple geometric shape-a hemisphere-to gain a more thorough understanding than can be achieved by investigating a complex biological surface such as a tooth crown. We calculate DNE on 3D surface meshes of hemispheres and on primate molars subjected to various retriangulation protocols, including smoothing algorithms, smoothing amounts, target face counts, and criteria for boundary face exclusion. Software used includes R, MorphoTester, Avizo, and MeshLab. DNE was calculated using the R package "molaR." In all cases, smoothing as performed in Avizo sharply decreases DNE initially, after which DNE becomes stable. Using a broader boundary exclusion criterion or performing additional smoothing (using "mesh fairing" methods) further decreases DNE. Increasing the mesh face count also results in increased DNE on tooth surfaces. Different retriangulation protocols yield different DNE values for the same surfaces, and should not be combined in meta-analyses. Increasing face count will capture surface microfeatures, but at the expense of computational speed. More aggressive smoothing is more likely to alter the essential geometry of the surface. A protocol is proposed that limits potential artifacts created during surface production while preserving pertinent features on the occlusal surface.

An efficient and collision-free hole-filling algorithm for orthodontics

Hole filling of teeth and gums is an essential stage in orthodontics after segmentation. The patching mesh should keep the morphological features of generic teeth and gums while avoiding collision between two adjacent teeth. This paper presents an efficient hole-filling algorithm to reconstruct the missing part of teeth and gums. Our proposed method involves four necessary steps: boundary construction and projection, hole triangulation in 2D, back projection of vertices to 3D, and mesh fairing. By combining constrained Delaunay triangulation in 2D with back projection of vertices to 3D using mean value coordinates, we achieve high robustness of hole triangulation and a high-quality initial patching mesh. In addition, we propose an automatic method to control the deformation degree to avoid collision. Our experiments demonstrate that the proposed method can achieve satisfactory results, not only in morphology, but also in efficiency. The results are very similar to real teeth and gums and can meet the requirements of orthodontics in medicine.

Calculation of Velocity on an Implicit Surface by Curvature Invariance

This paper presents an accurate method for computing the surface velocity which is used to advect the vertex in mesh-based surface tracking. We propose a curvature invariance condition that accurately captures the move- ment of a surface, especially in the case of rotating objects. The method uses the least-squares method and mesh fairing to solve the problem that the surface velocity would not be calculated when the implicit function defining the surface does not change. We show that the method works well in scenes including rotation and deformation.

Geometric characterization of nanoporous metals

Nanoporous metals made by dealloying possess significant geometric complexity—they are random, bicontinuous structures that also possess bubbles within ligaments, regions of very high negative, positive, and saddlepoint curvature, and significant polyfaceting. Here we introduce methods to geometrically quantify the structure of nanoporous metals employing simulated model nanoporous metals generated via large-scale kinetic Monte Carlo simulations as the basis of discussion. A method is introduced to transform these simulated structures into smooth triangulated meshes using new mesh-smoothing algorithms that hybridize mean curvature flow and signal processing approaches to mesh fairing. The technique is assessed by comparing the exact genus of high-genus meshes with the genus calculated via the Gauss–Bonnet formula, and works well to find the local curvature at all points of simulated surfaces of high topological genus. Specific geometric quantification of nanoporous metals is discussed for two quantities: (i) the relative surface area fraction of different crystal facets, which is important for catalysis; and (ii) the curvature distribution on the surface of porous metals, important for applications in which high curvature features are active (e.g. optical sensing).

Digital Differential Geometry Processing

The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.

Triangular surface mesh fairing via Gaussian curvature flow

Surface mesh fairing by the mean curvature flow and its various modifications have become a popular topic. However, very few researches have been attempted on using the Gaussian curvature flow in surface fairing. The aim of this paper is to investigate such a problem. We find that Gaussian curvature flow can only be used to smooth convex meshes. Hence, it cannot be used to smooth noisy surface meshes because a noisy surface mesh is not convex. To overcome this difficulty, we design a new diffusion equation whose evolution direction depends on the mean curvature normal and the magnitude is a properly defined function of the Gaussian curvature. Experimental results show that the designed fairing scheme can effectively remove the noise and simultaneously preserve the sharp features, such as corners and edges.

Smooth surface meshing for automated finite element model generation from 3D image data

Finite element (FE) modelling based on data from three-dimensional high-resolution computed tomography (CT) imaging systems provides a non-invasive method to assess structural mechanics. Automated mesh generation from these voxel based image data can be achieved by direct conversion to hexahedron elements, however these model representations have jagged edges. This paper proposes an automated method to generate smoothed FE meshes from voxel-based image data. Mesh fairing processes are utilized that allow constraints that control the smoothing process, and are computationally efficient. Surfaces of the mesh on the exterior, as well as interfaces between two tissues, can be smoothed by varying fairing parameters and constraint criteria. The method was tested on a variety of real and simulated three-dimensional data sets, resulting in both hexahedron and tetrahedron meshes. It was shown that the fairing process is linearly related to the number of smoothing iterations, and that peak stresses are reduced in FE simulations of the smoothed models. Although developed for micro-CT data sets, this fast and reliable mesh smoothing method could be applied to any three-dimensional image data where node and element connectivity have been defined.

Mesh fairing based on an intrinsic PDE approach

In this paper, we propose to create fair surfaces satisfying prescribed G 1 boundary constraints, based on solving a partial differential equation (PDE) that is intrinsic. The PDE is simple and leads to surfaces that have no local mean curvature extrema in the interior. It enables the reproduction of the important class of surfaces with constant mean curvature, containing spheres, cylinders and minimal surfaces. As an application, we present an algorithm that creates fair meshes with a semi-regular structure. The construction scheme is designed to produce meshes that are partitioned into regular domains. Using this domain knowledge in advance, we can develop a fast iterative algorithm that produces surfaces of high aesthetic quality.

A Fast Surface-Based Procedure for Object Reconstruction from 3D Scattered Points

In this paper, a new fast three-phase method for object reconstruction from 3D scattered points is presented. The first phase is founded on a novel fast triangulation algorithm, which generates a base approximation of the object surface. By inserting bridges, the triangulation algorithm also handles surfaces with genus greater than zero and determines the genus of the reconstructed surface. From results of the first phase, the object surface features, such as sharp edges, silhouette polylines, and corners, are extracted in the next phase. Sharp edges and corners are used as constraints for triangular mesh fairing later in the final phase, where a new improved decimation and a novel mesh refinement procedure are introduced, while silhouette polylines can be applied for generation of a wire-frame model of the reconstructed object. The overall object reconstruction procedure has a tested linear time complexity.

Curve mesh fairing and $GC^2$ surface interpolation

Curve mesh fairing and $GC^2$ surface interpolation