Volume 35 (2016)

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BubbleNet: A Cyber Security Dashboard for Visualizing Patterns
(The Eurographics Association and John Wiley & Sons Ltd., 2016) McKenna, Sean; Staheli, Diane; Fulcher, Cody; Meyer, Miriah; Kwan-Liu Ma and Giuseppe Santucci and Jarke van Wijk
The field of cyber security is faced with ever-expanding amounts of data and a constant barrage of cyber attacks. Within this space, we have designed BubbleNet as a cyber security dashboard to help network analysts identify and summarize patterns within the data. This design study faced a range of interesting constraints from limited time with various expert users and working with users beyond the network analyst, such as network managers. To overcome these constraints, the design study employed a user-centered design process and a variety of methods to incorporate user feedback throughout the design of BubbleNet. This approach resulted in a successfully evaluated dashboard with users and further deployments of these ideas in both research and operational environments. By explaining these methods and the process, it can benefit future visualization designers to help overcome similar challenges in cyber security or alternative domains.
Non-Local Sparse and Low-Rank Regularization for Structure-Preserving Image Smoothing
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Zhu, Lei; Fu, Chi-Wing; Jin, Yueming; Wei, Mingqiang; Qin, Jing; Heng, Pheng-Ann; Eitan Grinspun and Bernd Bickel and Yoshinori Dobashi
This paper presents a new image smoothing method that better preserves prominent structures. Our method is inspired by the recent non-local image processing techniques on the patch grouping and filtering. Overall, it has three major contributions over previous works. First, we employ the diffusion map as the guidance image to improve the accuracy of patch similarity estimation using the region covariance descriptor. Second, we model structure-preserving image smoothing as a low-rank matrix recovery problem, aiming at effectively filtering the texture information in similar patches. Lastly, we devise an objective function, namely the weighted robust principle component analysis (WRPCA), by regularizing the low rank with the weighted nuclear norm and sparsity pursuit with L1 norm, and solve this non-convex WRPCA optimization problem by adopting the alternative direction method of multipliers (ADMM) technique. We experiment our method with a wide variety of images and compare it against several state-of-the-art methods. The results show that our method achieves better structure preservation and texture suppression as compared to other methods. We also show the applicability of our method on several image processing tasks such as edge detection, texture enhancement and seam carving.
Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Manak, Martin; Maks Ovsjanikov and Daniele Panozzo
Properties of granular materials or molecular structures are often studied on a simple geometric model - a set of 3D balls. If the balls simultaneously change in size by a constant speed, topological properties of the empty space outside all these balls may also change. Capturing the changes and their subsequent classification may reveal useful information about the model. This has already been solved for balls of the same size, but only an approximate solution has been reported for balls of different sizes. These solutions work on simplicial complexes derived from the dual structure of the ordinary Voronoi diagram of ball centers and use the mathematical concept of simplicial homology groups. If the balls have different radii, it is more appropriate to use the additively weighted Voronoi diagram (also known as the Apollonius diagram) instead of the ordinary diagram, but the dual structure is no longer a simplicial complex, so the previous approaches cannot be used directly. In this paper, a method is proposed to overcome this problem. The method works with Voronoi edges and vertices instead of the dual structure. Additional bridge edges are introduced to overcome disconnected cases. The output is a tree graph of events where cavities are created or merged during a simulated shrinking of the balls. This graph is then reorganized and filtered according to some criteria to get a more concise information about the development of the empty space in the model.
Composite Flow Maps
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Cornel, Daniel; Konev, Artem; Sadransky, Bernhard; Horváth, Zsolt; Brambilla, Andrea; Viola, Ivan; Waser, Jürgen; Kwan-Liu Ma and Giuseppe Santucci and Jarke van Wijk
Flow maps are widely used to provide an overview of geospatial transportation data. Existing solutions lack the support for the interactive exploration of multiple flow components at once. Flow components are given by different materials being transported, different flow directions, or by the need for comparing alternative scenarios. In this paper, we combine flows as individual ribbons in one composite flow map. The presented approach can handle an arbitrary number of sources and sinks. To avoid visual clutter, we simplify our flow maps based on a force-driven algorithm, accounting for restrictions with respect to application semantics. The goal is to preserve important characteristics of the geospatial context. This feature also enables us to highlight relevant spatial information on top of the flow map such as traffic conditions or accessibility. The flow map is computed on the basis of flows between zones. We describe a method for auto-deriving zones from geospatial data according to application requirements. We demonstrate the method in real-world applications, including transportation logistics, evacuation procedures, and water simulation. Our results are evaluated with experts from corresponding fields.
Symmetry and Orbit Detection via Lie-Algebra Voting
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Shi, Zeyun; Alliez, Pierre; Desbrun, Mathieu; Bao, Hujun; Huang, Jin; Maks Ovsjanikov and Daniele Panozzo
In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting-based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence unifying and extending many existing mappings in a single Lie-algebra voting formulation. Compared to previous work, our resulting method offers significantly improved robustness as it guarantees that our symmetry detection of an input model is frame, scale, and reflection invariant. As a consequence, we demonstrate that our approach efficiently and reliably discovers symmetries and orbits of geometric datasets without requiring heavy parameter tuning.
Curve Reconstruction with Many Fewer Samples
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Ohrhallinger, Stefan; Mitchell, Scott A.; Wimmer, Michael; Maks Ovsjanikov and Daniele Panozzo
We consider the problem of sampling points from a collection of smooth curves in the plane, such that the CRUST family of proximity-based reconstruction algorithms can rebuild the curves. Reconstruction requires a dense sampling of local features, i.e., parts of the curve that are close in Euclidean distance but far apart geodesically. We show that e < 0:47-sampling is sufficient for our proposed HNN-CRUST variant, improving upon the state-of-the-art requirement of e < 13 -sampling. Thus we may reconstruct curves with many fewer samples. We also present a new sampling scheme that reduces the required density even further than e < 0:47-sampling. We achieve this by better controlling the spacing between geodesically consecutive points. Our novel sampling condition is based on the reach, the minimum local feature size along intervals between samples. This is mathematically closer to the reconstruction density requirements, particularly near sharp-angled features. We prove lower and upper bounds on reach r-sampling density in terms of lfs e-sampling and demonstrate that we typically reduce the required number of samples for reconstruction by more than half.
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Biasotti, S.; Cerri, A.; Bronstein, A.; Bronstein, M.; Chen, Min and Zhang, Hao (Richard)
The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences. After presenting in detail the theoretical foundations underlying these approaches, we classify them by looking at their most salient features, including the kind of structure and invariance properties they capture, as well as the distances and the output modalities according to which the similarity between shapes is assessed and returned. We also review the usage of these methods in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Finally, the most promising directions for future research developments are discussed.The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences.
TSS BVHs: Tetrahedron Swept Sphere BVHs for Ray Tracing Subdivision Surfaces
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Du, Peng; Kim, Yong-Jun; Yoon, Sung Eui; Eitan Grinspun and Bernd Bickel and Yoshinori Dobashi
We present a novel, compact bounding volume hierarchy, TSS BVH, for ray tracing subdivision surfaces computed by the Catmull-Clark scheme. We use Tetrahedron Swept Sphere (TSS) as a bounding volume to tightly bound limit surfaces of such subdivision surfaces given a user tolerance. Geometric coordinates defining our TSS bounding volumes are implicitly computed from the subdivided mesh via a simple vertex ordering method, and each level of our TSS BVH is associated with a single distance bound, utilizing the Catmull-Clark scheme. These features result in a linear space complexity as a function of the tree depth, while many prior BVHs have exponential space complexity. We have tested our method against different benchmarks with path tracing and photon mapping. We found that our method achieves up to two orders of magnitude of memory reduction with a high culling ratio over the prior AABB BVH methods, when we represent models with two to four subdivision levels. Overall, our method achieves three times performance improvement thanks to these results. These results are acquired by our theorem that rigorously computes our TSS bounding volumes.
Buoyancy Optimization for Computational Fabrication
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Wang, Lingfeng; Whiting, Emily; Joaquim Jorge and Ming Lin
This paper introduces a design and fabrication pipeline for creating floating forms. Our method optimizes for buoyant equilibrium and stability of complex 3D shapes, applying a voxel-carving technique to control the mass distribution. The resulting objects achieve a desired floating pose defined by a user-specified waterline height and orientation. In order to enlarge the feasible design space, we explore novel ways to load the interior of a design using prefabricated components and casting techniques. 3D printing is employed for high-precision fabrication. For larger scale designs we introduce a method for stacking lasercut planar pieces to create 3D objects in a quick and economic manner. We demonstrate fabricated designs of complex shape in a variety of floating poses.
Image Recoloring with Valence-Arousal Emotion Model
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Kim, Hye-Rin; Kang, Henry; Lee, In-Kwon; Eitan Grinspun and Bernd Bickel and Yoshinori Dobashi
We introduce an affective image recoloring method for changing the overall mood in the image in a numerically measurable way. Given a semantically segmented source image and a target emotion, our system finds reference image segments from the collection of images that have been tagged via crowdsourcing with numerically measured emotion labels. We then recolorize the source segments using colors from the selected target segments while preserving the gradient of the source image to generate a seamless and natural result. User study confirms the effectiveness of our method in accomplishing the stated goal of altering the mood of the image to match the target emotion level.
Environmental Objects for Authoring Procedural Scenes
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Grosbellet, Francois; Peytavie, Adrien; Guérin, Éric; Galin, Éric; Mérillou, Stéphane; Benes, Bedrich; Chen, Min and Zhang, Hao (Richard)
We propose a novel approach for authoring large scenes with automatic enhancement of objects to create geometric decoration details such as snow cover, icicles, fallen leaves, grass tufts or even trash. We introduce environmental objects that extend an input object geometry with a set of procedural effects that defines how the object reacts to the environment, and by a set of scalar fields that defines the influence of the object over of the environment. The user controls the scene by modifying environmental variables, such as temperature or humidity fields. The scene definition is hierarchical: objects can be grouped and their behaviours can be set at each level of the hierarchy. Our per object definition allows us to optimize and accelerate the effects computation, which also enables us to generate large scenes with many geometric details at a very high level of detail. In our implementation, a complex urban scene of 10 000 m, represented with details of less than 1 cm, can be locally modified and entirely regenerated in a few seconds.We propose a novel approach for authoring large scenes with automatic enhancement of objects to create geometric decoration details such as snow cover, icicles, fallen leaves, grass tufts or even trash. We introduce environmental objects that extend an input object geometry with a set of procedural effects that defines how the object reacts to the environment, and by a set of scalar fields that defines the influence of the object over of the environment. The user controls the scene by modifying environmental variables, such as temperature or humidity fields.
Visual Analysis of Governing Topological Structures in Excitable Network Dynamics
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Ngo, Quynh Quang; Hütt, Marc-Thorsten; Linsen, Lars; Kwan-Liu Ma and Giuseppe Santucci and Jarke van Wijk
To understand how topology shapes the dynamics in excitable networks is one of the fundamental problems in network science when applied to computational systems biology and neuroscience. Recent advances in the field discovered the influential role of two macroscopic topological structures, namely hubs and modules. We propose a visual analytics approach that allows for a systematic exploration of the role of those macroscopic topological structures on the dynamics in excitable networks. Dynamical patterns are discovered using the dynamical features of excitation ratio and co-activation. Our approach is based on the interactive analysis of the correlation of topological and dynamical features using coordinated views. We designed suitable visual encodings for both the topological and the dynamical features. A degree map and an adjacency matrix visualization allow for the interaction with hubs and modules, respectively. A barycentric-coordinates layout and a multi-dimensional scaling approach allow for the analysis of excitation ratio and co-activation, respectively. We demonstrate how the interplay of the visual encodings allows us to quickly reconstruct recent findings in the field within an interactive analysis and even discovered new patterns. We apply our approach to network models of commonly investigated topologies as well as to the structural networks representing the connectomes of different species. We evaluate our approach with domain experts in terms of its intuitiveness, expressiveness, and usefulness.
Visual Analysis of Tumor Control Models for Prediction of Radiotherapy Response
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Raidou, Renata Georgia; Casares-Magaz, Oscar; Muren, Ludvig Paul; Heide, Uulke A. van der; Rørvik, Jarle; Breeuwer, Marcel; Vilanova, Anna; Kwan-Liu Ma and Giuseppe Santucci and Jarke van Wijk
In radiotherapy, tumors are irradiated with a high dose, while surrounding healthy tissues are spared. To quantify the probability that a tumor is effectively treated with a given dose, statistical models were built and employed in clinical research. These are called tumor control probability (TCP) models. Recently, TCP models started incorporating additional information from imaging modalities. In this way, patient-specific properties of tumor tissues are included, improving the radiobiological accuracy of models. Yet, the employed imaging modalities are subject to uncertainties with significant impact on the modeling outcome, while the models are sensitive to a number of parameter assumptions. Currently, uncertainty and parameter sensitivity are not incorporated in the analysis, due to time and resource constraints. To this end, we propose a visual tool that enables clinical researchers working on TCP modeling, to explore the information provided by their models, to discover new knowledge and to confirm or generate hypotheses within their data. Our approach incorporates the following four main components: (1) It supports the exploration of uncertainty and its effect on TCP models; (2) It facilitates parameter sensitivity analysis to common assumptions; (3) It enables the identification of inter-patient response variability; (4) It allows starting the analysis from the desired treatment outcome, to identify treatment strategies that achieve it. We conducted an evaluation with nine clinical researchers. All participants agreed that the proposed visual tool provides better understanding and new opportunities for the exploration and analysis of TCP modeling.
Autocorrelation Descriptor for Efficient Co‐Alignment of 3D Shape Collections
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Averkiou, Melinos; Kim, Vladimir G.; Mitra, Niloy J.; Chen, Min and Zhang, Hao (Richard)
Co‐aligning a collection of shapes to a consistent pose is a common problem in shape analysis with applications in shape matching, retrieval and visualization. We observe that resolving among some orientations is easier than Others, for example, a common mistake for bicycles is to align front‐to‐back, while even the simplest algorithm would not erroneously pick orthogonal alignment. The key idea of our work is to analyse rotational autocorrelations of shapes to facilitate shape co‐alignment. In particular, we use such an autocorrelation measure of individual shapes to decide which shape pairs might have well‐matching orientations; and, if so, which configurations are likely to produce better alignments. This significantly prunes the number of alignments to be examined, and leads to an efficient, scalable algorithm that performs comparably to state‐of‐the‐art techniques on benchmark data sets, but requires significantly fewer computations, resulting in 2–16× speed improvement in our tests.Co‐aligning a collection of shapes to a consistent pose is a common problem in shape analysis with applications in shape matching, retrieval and visualization. We observe that resolving among some orientations is easier than Others, for example, a common mistake for bicycles is to align front‐to‐back, while even the simplest algorithm would not erroneously pick orthogonal alignment. The key idea of our work is to analyse rotational autocorrelations of shapes to facilitate shape co‐alignment. In particular, we use such an autocorrelation measure of individual shapes to decide which shape pairs might have well‐matching orientations; and, if so, which configurations are likely to produce better alignments. This significantly prunes the number of alignments to be examined, and leads to an efficient, scalable algorithm that performs comparably to state‐of‐the‐art techniques on benchmark data sets, but requires significantly fewer computations, resulting in 2‐16x speed improvement in our tests.
Fast ANN for High‐Quality Collaborative Filtering
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Tsai, Yun‐Ta; Steinberger, Markus; Pająk, Dawid; Pulli, Kari; Chen, Min and Zhang, Hao (Richard)
Collaborative filtering collects similar patches, jointly filters them and scatters the output back to input patches; each pixel gets a contribution from each patch that overlaps with it, allowing signal reconstruction from highly corrupted data. Exploiting self‐similarity, however, requires finding matching image patches, which is an expensive operation. We propose a GPU‐friendly approximated‐nearest‐neighbour(ANN) algorithm that produces high‐quality results for any type of collaborative filter. We evaluate our ANN search against state‐of‐the‐art ANN algorithms in several application domains. Our method is orders of magnitudes faster, yet provides similar or higher quality results than the previous work.Collaborative filtering is a powerful, yet computationally demanding denoising approach. (a) Relying on self‐similarity in the input data, collaborative filtering requires the search for patches which are similar to a reference patch (red). Filtering the patches, either by averaging the pixels or modifying the coefficients after a wavelet or Other transformation, removes unwanted noise, and each output pixel is collaboratively filtered using all the denoised image patches that overlap the pixel. Our method accelerates the process of searching for similar patches and facilitates high‐quality collaborative filtering even on mobile devices. Application examples for collaborative filtering include (left: our output; right: noisy input) (b) denoising an image burst, (c) filtering the samples for global illumination and (d) geometry reconstruction.
A Hierarchical Approach for Regular Centroidal Voronoi Tessellations
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Wang, L.; Hétroy‐Wheeler, F.; Boyer, E.; Chen, Min and Zhang, Hao (Richard)
In this paper, we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modelling and analysis. While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers. This criterion allows us to compare CVTs on a common basis. It builds on earlier theoretical work showing that second moments of cells converge to a lower bound when optimizing CVTs. In addition to proposing a regularity criterion, this paper also considers computational strategies to determine regular CVTs. We introduce a hierarchical framework that propagates regularity over decomposition levels and hence provides CVTs with provably better regularities than existing methods. We illustrate these principles with a wide range of experiments on synthetic and real models.In this paper, we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modelling and analysis.While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers.
Data-Driven Bending Elasticity Design by Shell Thickness
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Zhang, Xiaoting; Le, Xinyi; Wu, Zihao; Whiting, Emily; Wang, Charlie C. L.; Maks Ovsjanikov and Daniele Panozzo
We present a method to design the deformation behavior of 3D printed models by an interactive tool, where the variation of bending elasticity at different regions of a model is realized by a change in shell thickness. Given a soft material to be used in 3D printing, we propose an experimental setup to acquire the bending behavior of this material on tubes with different diameters and thicknesses. The relationship between shell thickness and bending elasticity is stored in an echo state network using the acquired dataset. With the help of the network, an interactive design tool is developed to generate non-uniformly hollowed models to achieve desired bending behaviors. The effectiveness of this method is verified on models fabricated by different 3D printers by studying whether their physical deformation can match the designed target shape.
Variational Image Fusion with Optimal Local Contrast
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Hafner, David; Weickert, Joachim; Chen, Min and Zhang, Hao (Richard)
In this paper, we present a general variational method for image fusion. In particular, we combine different images of the same subject to a single composite that offers optimal exposedness, saturation and local contrast. Previous research approaches this task by first pre‐computing application‐specific weights based on the input, and then combining these weights with the images to the final composite later on. In contrast, we design our model assumptions directly on the fusion result. To this end, we formulate the output image as a convex combination of the input and incorporate concepts from perceptually inspired contrast enhancement such as a local and non‐linear response. This output‐driven approach is the key to the versatility of our general image fusion model. In this regard, we demonstrate the performance of our fusion scheme with several applications such as exposure fusion, multispectral imaging and decolourization. For all application domains, we conduct thorough validations that illustrate the improvements compared to state‐of‐the‐art approaches that are tailored to the individual tasks. In this paper, we present a general variational method for image fusion. In particular, we combine different images of the same subject to a single composite that offers optimal exposedness, saturation and local contrast. Previous research approaches this task by first pre‐computing application‐specific weights based on the input, and then combining these weights with the images to the final composite later on. In contrast, we design our model assumptions directly on the fusion result. To this end, we formulate the output image as a convex combination of the input and incorporate concepts from perceptually inspired contrast enhancement such as a local and non‐linear response. This output‐driven approach is the key to the versatility of our general image fusion model. In this regard, we demonstrate the performance of our fusion scheme with several applications such as exposure fusion, multispectral imaging and decolourization.
Real‐Time Rendering Techniques with Hardware Tessellation
(Copyright © 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Nießner, M.; Keinert, B.; Fisher, M.; Stamminger, M.; Loop, C.; Schäfer, H.; Chen, Min and Zhang, Hao (Richard)
Graphics hardware has progressively been optimized to render more triangles with increasingly flexible shading. For highly detailed geometry, interactive applications restricted themselves to performing transforms on fixed geometry, since they could not incur the cost required to generate and transfer smooth or displaced geometry to the GPU at render time. As a result of recent advances in graphics hardware, in particular the GPU tessellation unit, complex geometry can now be generated on the fly within the GPU's rendering pipeline. This has enabled the generation and displacement of smooth parametric surfaces in real‐time applications. However, many well‐established approaches in offline rendering are not directly transferable due to the limited tessellation patterns or the parallel execution model of the tessellation stage. In this survey, we provide an overview of recent work and challenges in this topic by summarizing, discussing, and comparing methods for the rendering of smooth and highly detailed surfaces in real time.Graphics hardware has progressively been optimized to render more triangles with increasingly flexible shading. For highly detailed geometry, interactive applications restricted themselves to performing transforms on fixed geometry, since they could not incur the cost required to generate and transfer smooth or displaced geometry to the GPU at render time. As a result of recent advances in graphics hardware, in particular the GPU tessellation unit, complex geometry can now be generated on the fly within the GPU's rendering pipeline. This has enabled the generation and displacement of smooth parametric surfaces in real‐time applications. However, many well‐established approaches in offline rendering are not directly transferable due to the limited tessellation patterns or the parallel execution model of the tessellation stage.
Skeleton-driven Adaptive Hexahedral Meshing of Tubular Shapes
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Livesu, Marco; Muntoni, Alessandro; Puppo, Enrico; Scateni, Riccardo; Eitan Grinspun and Bernd Bickel and Yoshinori Dobashi
We propose a novel method for the automatic generation of structured hexahedral meshes of articulated 3D shapes. We recast the complex problem of generating the connectivity of a hexahedral mesh of a general shape into the simpler problem of generating the connectivity of a tubular structure derived from its curve-skeleton. We also provide volumetric subdivision schemes to nicely adapt the topology of the mesh to the local thickness of tubes, while regularizing per-element size. Our method is fast, one-click, easy to reproduce, and it generates structured meshes that better align to the branching structure of the input shape if compared to previous methods for hexa mesh generation.

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