Robust Inside-Outside Segmentation Using Generalized Winding Numbers

Solid shapes in computer graphics are often represented with boundary descriptions, e.g. triangle meshes, but animation, physicallybased simulation, and geometry processing are more realistic and accurate when explicit volume representations are available. Tetrahedral meshes which exactly contain (interpolate) the input boundary description are desirable but difficult to construct for a large class of input meshes. Character meshes and CAD models are often composed of many connected components with numerous selfintersections, non-manifold pieces, and open boundaries, precluding existing meshing algorithms. We propose an automatic algorithm handling all of these issues, resulting in a compact discretization of the input’s inner volume. We only require reasonably consistent orientation of the input triangle mesh. By generalizing the winding number for arbitrary triangle meshes, we define a function that is a perfect segmentation for watertight input and is well-behaved otherwise. This function guides a graphcut segmentation of a constrained Delaunay tessellation (CDT), providing a minimal description that meets the boundary exactly and may be fed as input to existing tools to achieve element quality. We highlight our robustness on a number of examples and show applications of solving PDEs, volumetric texturing and elastic simulation

Methodology for automatic recovering of 3D partitions from unstitched faces of non-manifold CAD models

Data exchanges between different software are currently used in industry to speed up the preparation of digital prototypes for Finite Element Analysis (FEA). Unfortunately, due to data loss, the yield of the transfer of manifold models rarely reaches 1. In the case of non-manifold models, the transfer results are even less satisfactory. This is particularly true for partitioned 3D models: during the data transfer based on the well-known exchange formats, all 3D partitions are generally lost. Partitions are mainly used for preparing mesh models required for advanced FEA: mapped meshing, material separation, definition of specific boundary conditions, etc. This paper sets up a methodology to automatically recover 3D partitions from exported non-manifold CAD models in order to increase the yield of the data exchange. Our fully automatic approach is based on three steps. First, starting from a set of potentially disconnected faces, the CAD model is stitched. Then, the shells used to create the 3D partitions are recovered using an iterative propagation strategy which starts from the so-called manifold vertices. Finally, using the identified closed shells, the 3D partitions can be reconstructed. The proposed methodology has been validated on academic as well as industrial examples.This work has been carried out under a research contract between the Research and Development Direction of the EDF Group and the Arts et Métiers ParisTech Aix-en-Provence

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

A comparison of hole-filling methods in 3D

This paper presents a review of the most relevant current techniques that deal with hole-filling in 3D models. Contrary to earlier reports, which approach mesh repairing in a sparse and global manner, the objective of this review is twofold. First, a specific and comprehensive review of hole-filling techniques (as a relevant part in the field of mesh repairing) is carried out. We present a brief summary of each technique with attention paid to its algorithmic essence, main contributions and limitations. Second, a solid comparison between 34 methods is established. To do this, we define 19 possible meaningful features and properties that can be found in a generic hole-filling process. Then, we use these features to assess the virtues and deficiencies of the method and to build comparative tables. The purpose of this review is to make a comparative hole-filling state-of-the-art available to researchers, showing pros and cons in a common framework.• Ministerio de Economía y Competitividad: Proyecto DPI2013-43344-R (I+D+i) • Gobierno de Castilla-La Mancha: Proyecto PEII-2014-017-PpeerReviewe

Heritage Reproduction in the Age of High-Resolution Scanning:A Critical Evaluation of Digital Infilling Methods for Historic Preservation

High-definition digital scanning has established itself as a useful tool for documenting cultural heritage in the twenty-first century. Proponents of surveying technology are hailing the use of digital fact-based 3D models as valuable tools for recording, analyzing and safeguarding items of cultural importance. Methods for digitally filling holes have not yet been considered through the lens of historic preservation. No modeling technique is error-free and understanding how heritage professionals are addressing lacunae is vital for understanding digital heritage objects resulting from 3D scanning hardware. Frameworks exist for working with scanned data, but they define general principles for a broad range of applications and do not provide any guidelines or strategies of how to comply with them practically. This thesis is a comparative evaluation of current practices of in-filling digital lacunae that attempts to establish which methods are best suited to the following historic preservation practices: documentation, Interpretation graphics, Long-term monitoring, digital restoration, physical fabrication

Watertight and 2-Manifold Surface Meshes Using Dual Contouring With Tetrahedral Decomposition of Grid Cubes

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. The advantage of DC is that it can reproduce sharp features by inserting vertices anywhere inside the grid cube, as opposed to the Marching Cubes (MC) algorithm that can insert vertices only on the grid edges. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. Our method decomposes an ambiguous grid cube into a maximum of twelve tetrahedral cells; we introduce novel polygon generation rules that produce 2-manifold and watertight surface meshes. We have applied our proposed method on realistic data, and a comparison of the results of our proposed method with results from traditional DC shows the effectiveness of our method