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COMPUTER GRAPHICS FORUM 2022年第5期41卷 125-134页

作者： Beaufort, P-A Reberol, M. Kalmykov, D. Liu, H. Ledoux, F. Bommes, D. Univ Bern Bern Switzerland Catholic Univ Louvain Louvain Belgium CEA Paris France Univ Paris Saclay Paris France

HexMe consists of 189 tetrahedral meshes with tagged features and a workflow to generate them. The primary purpose of HexMe meshes is to enable consistent and practically meaningful evaluation of hexahedral meshing algorithms and related techniques, specifically regarding the correct meshing of specified feature points, curves, and surfaces. The tetrahedral meshes have been generated with Gmsh, starting from 63 computer-aided design (CAD) models from various databases. To highlight and label the diverse and challenging aspects of hexahedral mesh generation, the CAD models are classified into three categories: simple, nasty, and industrial. For each CAD model, we provide three kinds of tetrahedral meshes (uniform, curvature-adapted, and box-embedded). The mesh generation pipeline is defined with the help of Snakemake, a modern workflow management system, which allows us to specify a fully automated, extensible, and sustainable workflow. It is possible to download the whole dataset or select individual meshes by browsing the online catalog. The HexMe dataset is built with evolution in mind and prepared for future developments. A public GitHub repository hosts the HexMe workflow, where external contributions and future releases are possible and encouraged. We demonstrate the value of HexMe by exploring the robustness limitations of state-of-the-art frame-field-based hexahedral meshing algorithm. Only for 19 of 189 tagged tetrahedral inputs all feature entities are meshed correctly, while the average success rates are 70.9% / 48.5% / 34.6% for feature points/curves/surfaces.

关键词： CCS Concepts • General and reference → Evaluation • computing methodologies → mesh geometry models • Information systems → Test collections

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Constructing L∞ Voronoi Diagrams in 2D and 3D

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COMPUTER GRAPHICS FORUM 2022年第5期41卷 135-147页

作者： Bukenberger, D. R. Buchin, K. Botsch, M. TU Dortmund Univ Dortmund Germany

Voronoi diagrams and their computation are well known in the Euclidean L-2 space. They are easy to sample and render in generalized L-p spaces but nontrivial to construct geometrically. Especially the limit of this norm with p -> infinity lends itself to many quad- and hex-meshing related applications as the level-set in this space is a hypercube. Many application scenarios circumvent the actual computation of L-infinity diagrams altogether as known concepts for these diagrams are limited to 2D, uniformly weighted and axis-aligned sites. Our novel algorithm allows for the construction of generalized L-infinity Voronoi diagrams. Although parts of the developed concept theoretically extend to higher dimensions it is herein presented and evaluated for the 2D and 3D case. It further supports individually oriented sites and allows for generating weighted diagrams with anisotropic weight vectors for individual sites. The algorithm is designed around individual sites, and initializes their cells with a simple meshed representation of a site's level-set. Hyperplanes between adjacent cells cut the initialization geometry into convex polyhedra. Non-cell geometry is filtered out based on the L-infinity Voronoi criterion, leaving only the non-convex cell geometry. Eventually we conclude with discussions on the algorithms complexity, numerical precision and analyze the applicability of our generalized L-infinity diagrams for the construction of Centroidal Voronoi Tessellations (CVT) using Lloyd's algorithm.

关键词： CCS Concepts • computing methodologies → mesh geometry models mesh models Volumetric models

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Occluder Generation for Buildings in Digital Games

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COMPUTER GRAPHICS FORUM 2022年第7期41卷 205-214页

作者： Wu, Kui He, Xu Pan, Zherong Gao, Xifeng Tencent LightSpeed Studios Shenzhen Guangdong Peoples R China

Occlusion culling has become a prevalent method in modern game engines. It can significantly reduce the rendering cost by using an approximate coarse mesh (occluder) for culling hidden objects. An ideal occluder should use as few faces as possible to represent the high-resolution input mesh with a high culling accuracy. We address the open problem of automatic occluder generation for 3D building models with complex topology and interior structures. Our method first generates two coarse sets of faces via patch-based and voxel-based mesh simplification techniques. A metric-guided selection algorithm chooses the best subset of faces to form the occluder, achieving a high occlusion rate and accuracy. Over an evaluation of 77 building models, our method compares favorably against state-of-the-arts in terms of occlusion accuracy, occlusion rate, and face number.

关键词： CCS Concepts • computing methodologies → mesh geometry models

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Interactive Sculpting of Digital Faces Using an Anatomical Modeling Paradigm

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COMPUTER GRAPHICS FORUM 2020年第5期39卷 93-102页

作者： Gruber, A. Fratarcangeli, M. Zoss, G. Cattaneo, R. Beeler, T. Gross, M. Bradley, D. DisneyRes Studios Los Angeles CA 90065 USA Swiss Fed Inst Technol Zurich Switzerland Chalmers Univ Technol Gothenburg Sweden

Digitally sculpting 3D human faces is a very challenging task. It typically requires either 1) highly-skilled artists using complex software packages for high quality results, or 2) highly-constrained simple interfaces for consumer-level avatar creation, such as in game engines. We propose a novel interactive method for the creation of digital faces that is simple and intuitive to use, even for novice users, while consistently producing plausible 3D face geometry, and allowing editing freedom beyond traditional video game avatar creation. At the core of our system lies a specialized anatomical local face model (ALM), which is constructed from a dataset of several hundred 3D face scans. User edits are propagated to constraints for an optimization of our data-driven ALM model, ensuring the resulting face remains plausible even for simple edits like clicking and dragging surface points. We show how several natural interaction methods can be implemented in our framework, including direct control of the surface, indirect control of semantic features like age, ethnicity, gender, and BMI, as well as indirect control through manipulating the underlying bony structures. The result is a simple new method for creating digital human faces, for artists and novice users alike. Our method is attractive for low-budget VFX and animation productions, and our anatomical modeling paradigm can complement traditional game engine avatar design packages.

关键词： CCS Concepts • computing methodologies → mesh geometry models

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Properties of Laplace Operators for Tetrahedral meshes

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COMPUTER GRAPHICS FORUM 2020年第5期39卷 55-68页

作者： Alexa, Marc Herholz, Philipp Kohlbrenner, Maximilian Sorkine-Hornung, Olga TU Berlin Berlin Germany Swiss Fed Inst Technol Zurich Switzerland

Discrete Laplacians for triangle meshes are a fundamental tool in geometry processing. The so-called cotan Laplacian is widely used since it preserves several important properties of its smooth counterpart. It can be derived from different principles: either considering the piecewise linear nature of the primal elements or associating values to the dual vertices. Both approaches lead to the same operator in the two-dimensional setting. In contrast, for tetrahedral meshes, only the primal construction is reminiscent of the cotan weights, involving dihedral angles. We provide explicit formulas for the lesser-known dual construction. In both cases, the weights can be computed by adding the contributions of individual tetrahedra to an edge. The resulting two different discrete Laplacians for tetrahedral meshes only retain some of the properties of their two-dimensional counterpart. In particular, while both constructions have linear precision, only the primal construction is positive semi-definite and only the dual construction generates positive weights and provides a maximum principle for Delaunay meshes. We perform a range of numerical experiments that highlight the benefits and limitations of the two constructions for different problems and meshes.

关键词： CCS Concepts • Mathematics of computing → mesh generation Discrete optimization • computing methodologies → mesh geometry models • Theory of computation → Computational geometry

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Compacting Voxelized Polyhedra via Tree Stacking

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COMPUTER GRAPHICS FORUM 2019年第7期38卷 323-333页

作者： Hao, Yue Lien, Jyh-Ming George Mason Univ Fairfax VA 22030 USA

Volume compaction is a geometric problem that aims to reduce the volume of a polyhedron via shape transform. Compactable structures are easier to transport and in some cases easier to manufacture, therefore, they are commonly found in our daily life (e.g. collapsible containers) and advanced technology industries (e.g., the recent launch of 60 Starlink satellites compacted in a single rocket by SpaceX). It is known in the literature that finding a universal solution to compact an arbitrary 3D shape is computationally challenging. Previous approaches showed that stripifying mesh surface can lead to optimal compaction, but the resulting structures were often impractical. In this paper, we propose an algorithm that cuts the 3D orthogonal polyhedron, tessellated by thick square panels, into a tree structure that can be transformed into compact piles by folding and stacking. We call this process tree stacking. Our research found that it is possible to decompose the problem into a pipeline of several solvable local optimizations. We also provide an efficient algorithm to check if the solution exists by avoiding the computational bottleneck of the pipeline. Our results show that tree stacking can efficiently generate stackable structures that have better folding accuracy and similar compactness comparing to the most compact stacking using strips.

关键词： CCS Concepts • General and reference → Design • computing methodologies → mesh geometry models Volumetric models

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Local Editing of Procedural models

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COMPUTER GRAPHICS FORUM 2019年第2期38卷 13-25页

作者： Lipp, M. Specht, M. Lau, C. Wonka, P. Mueller, P. Esri R&D Ctr Zurich Zurich Switzerland KAUST Thuwal Saudi Arabia

Procedural modeling is used across many industries for rapid 3D content creation. However, professional procedural tools often lack artistic control, requiring manual edits on baked results, diminishing the advantages of a procedural modeling pipeline. Previous approaches to enable local artistic control require special annotations of the procedural system and manual exploration of potential edit locations. Therefore, we propose a novel approach to discover meaningful and non-redundant good edit locations (GELs). We introduce a bottom-up algorithm for finding GELs directly from the attributes in procedural models, without special annotations. To make attribute edits at GELs persistent, we analyze their local spatial context and construct a meta-locator to uniquely specify their structure. Meta-locators are calculated independently per attribute, making them robust against changes in the procedural system. Functions on meta-locators enable intuitive and robust multi-selections. Finally, we introduce an algorithm to transfer meta-locators to a different procedural model. We show that our approach greatly simplifies the exploration of the local edit space, and we demonstrate its usefulness in a user study and multiple real-world examples.

关键词： CCS Concepts • computing methodologies → mesh geometry models

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Surface Fairing towards Regular Principal Curvature Line Networks

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COMPUTER GRAPHICS FORUM 2019年第7期38卷 115-125页

作者： Chu, Lei Bo, Pengbo Liu, Yang Wang, Wenping Univ Hong Kong Hong Kong Peoples R China Harbin Inst Technol Weihai Peoples R China Microsoft Res Asia Beijing Peoples R China

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high-frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high-quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.

关键词： CCS Concepts • computing methodologies → mesh geometry models Parametric curve and surface models Shape analysis

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