A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

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 Unified Surface Geometric Framework for Feature-Aware Denoising, Hole Filling and Context-Aware Completion

Technologies for 3D data acquisition and 3D printing have enormously developed in the past few years, and, consequently, the demand for 3D virtual twins of the original scanned objects has increased. In this context, feature-aware denoising, hole filling and context-aware completion are three essential (but far from trivial) tasks. In this work, they are integrated within a geometric framework and realized through a unified variational model aiming at recovering triangulated surfaces from scanned, damaged and possibly incomplete noisy observations. The underlying non-convex optimization problem incorporates two regularisation terms: a discrete approximation of the Willmore energy forcing local sphericity and suited for the recovery of rounded features, and an approximation of the l(0) pseudo-norm penalty favouring sparsity in the normal variation. The proposed numerical method solving the model is parameterization-free, avoids expensive implicit volumebased computations and based on the efficient use of the Alternating Direction Method of Multipliers. Experiments show how the proposed framework can provide a robust and elegant solution suited for accurate restorations even in the presence of severe random noise and large damaged areas

From 3D Models to 3D Prints: an Overview of the Processing Pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens of methods that prepare the 3D model for fabrication, while analysing and optimizing geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and Innovation action; Grant agreement N. 68044

Plane-Based Optimization of Geometry and Texture for RGB-D Reconstruction of Indoor Scenes

We present a novel approach to reconstruct RGB-D indoor scene with plane primitives. Our approach takes as input a RGB-D sequence and a dense coarse mesh reconstructed by some 3D reconstruction method on the sequence, and generate a lightweight, low-polygonal mesh with clear face textures and sharp features without losing geometry details from the original scene. To achieve this, we firstly partition the input mesh with plane primitives, simplify it into a lightweight mesh next, then optimize plane parameters, camera poses and texture colors to maximize the photometric consistency across frames, and finally optimize mesh geometry to maximize consistency between geometry and planes. Compared to existing planar reconstruction methods which only cover large planar regions in the scene, our method builds the entire scene by adaptive planes without losing geometry details and preserves sharp features in the final mesh. We demonstrate the effectiveness of our approach by applying it onto several RGB-D scans and comparing it to other state-of-the-art reconstruction methods.Comment: in International Conference on 3D Vision 2018; Models and Code: see https://github.com/chaowang15/plane-opt-rgbd. arXiv admin note: text overlap with arXiv:1905.0885

Connectivity Control for Quad-Dominant Meshes

abstract: Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh. Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.Dissertation/ThesisDoctoral Dissertation Computer Science 201

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

Geometry considerations for high-order finite-volume methods on structured grids with adaptive mesh refinement

2022 Summer.Includes bibliographical references.Computational fluid dynamics (CFD) is an invaluable tool for engineering design. Meshing complex geometries with accuracy and efficiency is vital to a CFD simulation. In particular, using structured grids with adaptive mesh refinement (AMR) will be invaluable to engineering optimization where automation is critical. For high-order (fourth-order and above) finite volume methods (FVMs), discrete representation of complex geometries adds extra challenges. High-order methods are not trivially extended to complex geometries of engineering interest. To accommodate geometric complexity with structured AMR in the context of high-order FVMs, this work aims to develop three new methods. First, a robust method is developed for bounding high-order interpolations between grid levels when using AMR. High-order interpolation is prone to numerical oscillations which can result in unphysical solutions. To overcome this, localized interpolation bounds are enforced while maintaining solution conservation. This method provides great flexibility in how refinement may be used in engineering applications. Second, a mapped multi-block technique is developed, capable of representing moderately complex geometries with structured grids. This method works with high-order FVMs while still enabling AMR and retaining strict solution conservation. This method interfaces with well-established engineering work flows for grid generation and interpolates generalized curvilinear coordinate transformations for each block. Solutions between blocks are then communicated by a generalized interpolation strategy while maintaining a single-valued flux. Finally, an embedded-boundary technique is developed for high-order FVMs. This method is particularly attractive since it automates mesh generation of any complex geometry. However, the algorithms on the resulting meshes require extra attention to achieve both stable and accurate results near boundaries. This is achieved by performing solution reconstructions using a weighted form of high-order interpolation that accounts for boundary geometry. These methods are verified, validated, and tested by complex configurations such as reacting flows in a bluff-body combustor and Stokes flows with complicated geometries. Results demonstrate the new algorithms are effective for solving complex geometries at high-order accuracy with AMR. This study contributes to advance the geometric capability in CFD for efficient and effective engineering applications