VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base Domains

Correspondences between geometric domains (mappings) are ubiquitous in computer graphics and engineering, both for a variety of downstream applications and as core building blocks for higher level algorithms. In particular, mapping a shape to a convex or star-shaped domain with simple geometry is a fundamental module in existing pipelines for mesh generation, solid texturing, generation of shape correspondences, advanced manufacturing etc. For the case of surfaces, computing such a mapping with guarantees of injectivity is a solved problem. Conversely, robust algorithms for the generation of injective volume mappings to simple polytopes are yet to be found, making this a fundamental open problem in volume mesh processing. VOLMAP is a large scale benchmark aimed to support ongoing research in volume mapping algorithms. The dataset contains 4.7K tetrahedral meshes, whose boundary vertices are mapped to a variety of simple domains, either convex or star-shaped. This data constitutes the input for candidate algorithms, which are then required to position interior vertices in the domain to obtain a volume map. Overall, this yields more than 22K alternative test cases. VOLMAP also comprises tools to process this data, analyze the resulting maps, and extend the dataset with new meshes, boundary maps and base domains. This article provides a brief overview of the field, discussing its importance and the lack of effective techniques. We then introduce both the dataset and its major features. An example of comparative analysis between two existing methods is also present

Deterministic Linear Time Constrained Triangulation using Simplified Earcut

Triangulation algorithms that conform to a set of non-intersecting input segments typically proceed in an incremental fashion, by inserting points first, and then segments. Inserting a segment amounts to: (1) deleting all the triangles it intersects; (2) filling the so generated hole with two polygons that have the wanted segment as shared edge; (3) triangulate each polygon separately. In this paper we prove that these polygons are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear. The fact that any simple polygon contains at least three convex vertices guarantees the existence of a valid ear to cut, ensuring convergence. Not only this translates to an optimal deterministic linear time triangulation algorithm, but such algorithm is also trivial to implement. We formally prove the correctness of our approach, also validating it in practical applications and comparing it with prior art

HexaLab

HexaLab is a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. This visualization tool targets both users and scholars. Practitioners who employ hexmeshes for Finite Element Analysis, can readily check mesh quality and assess its usability for simulation. Researchers involved in mesh generation may use HexaLab to perform a detailed analysis of the mesh structure, isolating weak points and testing new solutions to improve on the state of the art and generate high quality images. To this end, we support a wide variety of visualization and volume inspection tools. The system also offers immediate access to a repository containing all the publicly available meshes produced with the most recent techniques for hex mesh generation. We believe HexaLab, providing a common tool for visualizing, assessing and distributing results, will push forward the recent strive for replicability in our scientific community. The system supports hexahedral models in the popular .mesh and .vtk ASCII formats. HexaLab aims also to easily present the results of recent papers on hex meshing by directly including them in its own repository when provided by the authors. The datasets presented are copyrighted by the respective paper authors. Look in the datasets folder for more info

HexaLab.net: An online viewer for hexahedral meshes

© 2018 Elsevier Ltd We introduce HexaLab: a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. Our visualization tool targets both users and scholars. Practitioners who employ hexmeshes for Finite Element Analysis, can readily check mesh quality and assess its usability for simulation. Researchers involved in mesh generation may use HexaLab to perform a detailed analysis of the mesh structure, isolating weak points and testing new solutions to improve on the state of the art and generate high quality images. To this end, we support a wide variety of visualization and volume inspection tools. Our system offers also immediate access to a repository containing all the publicly available meshes produced with the most recent techniques for hexmesh generation. We believe HexaLab, providing a common tool for visualizing, assessing and distributing results, will push forward the recent strive for replicability in our scientific community

HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid- based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques

Loopy Cuts: Surface-Field Aware Block Decomposition for Hex-Meshing.

We present a new fully automatic block-decomposition hexahedral meshing algorithm capable of producing high quality meshes that strictly preserve feature curve networks on the input surface and align with an input surface cross-field. We produce all-hex meshes on the vast majority of inputs, and introduce localized non-hex elements only when the surface feature network necessitates those. The input to our framework is a closed surface with a collection of geometric or user-demarcated feature curves and a feature-aligned surface cross-field. Its output is a compact set of blocks whose edges interpolate these features and are loosely aligned with this cross-field. We obtain this block decomposition by cutting the input model using a collection of simple cutting surfaces bounded by closed surface loops. The set of cutting loops spans the input feature curves, ensuring feature preservation, and is obtained using a field-space sampling process. The computed loops are uniformly distributed across the surface, cross orthogonally, and are loosely aligned with the cross-field directions, inducing the desired block decomposition. We validate our method by applying it to a large range of complex inputs and comparing our results to those produced by state-of-the-art alternatives. Contrary to prior approaches, our framework consistently produces high-quality field aligned meshes while strictly preserving geometric or user-specified surface features

Skeleton based cage generation guided by harmonic fields

International audienceWe propose a novel user-assisted cage generation tool. We start from a digital character and its skeleton, and create a coarse control cage for its animation. Our method requires minimal interaction to select bending points on the skeleton, and computes the corresponding cage automatically. The key contribution is a volumetric field defined in the interior of the character and embedding the skeleton. The integral lines of such field are used to propagate cutting surfaces from the interior of the character to its skin, and allow us to robustly trace non-planar cross sections that adapt to the local shape of the character. Our method overcomes previous approaches that rely on the popular (but tedious and limiting) cutting planes. We validated our software on a variety of digital characters. Our final cages are coarse yet entirely compliant with the structure induced by the underlying skeleton, enriched with the semantics provided by the bending points selected by the user. Automatic placement of bending nodes for a fully automatic caging pipeline is also supported

Improving additive manufacturing performance by build orientation optimization

Additive manufacturing (AM) is an emerging type of production technology to create three-dimensional objects layer-by-layer directly from a 3D CAD model. AM is being extensively used in several areas by engineers and designers. Build orientation is a critical issue in AM since it is associated with the part accuracy, the number of supports required and the processing time to produce the object. This paper presents an optimization approach to solve the part build orientation problem taking into account some characteristics or measures that can affect the accuracy of the part, namely the volumetric error, the support area, the staircase effect, the build time, the surface roughness and the surface quality. A global optimization method, the Electromagnetism-like algorithm, is used to solve the part build orientation problem.The authors are grateful to the anonymous referees for their fruitfulcomments and suggestions. This work has been supported and developed under the FIBR3Dproject - Hybrid processes based on additive manufacturing of composites with long or shortfibers reinforced thermoplastic matrix (POCI-01-0145-FEDER-016414), supported by theLisbon Regional Operational Programme 2020, under the PORTUGAL 2020 PartnershipAgreement, through the European Regional Development Fund (ERDF). This work hasbeen also supported by national funds through FCT - Funda ̧c ̃ao para a Ciˆencia e Tecnologiawithin the Project Scope: UID/CEC/00319/201

A comparison of methods for gradient field estimation on simplicial meshes

The estimation of the differential properties of a function sampled at the vertices of a discrete domain is at the basis of many applied sciences. In this paper, we focus on the computation of function gradients on triangle and tetrahedral meshes. We study one cell-based method (the standard the facto), plus three vertex-based methods. Comparisons regard accuracy, ability to perform on different domain discretizations, and efficiency. We performed extensive tests and provide an in-depth analysis of our results. Besides some common behaviour, we found that some methods perform better than others, considering both accuracy and efficiency. This directly translates to useful suggestions for the implementation of gradient estimators in research and industrial code