Publications
SGLDBench
A Benchmark Suite for Stress-Guided Lightweight 3D Designs IEEE TVCG 2025
, DOI:
10.1109/TVCG.2025.3573774
PDF
🏆 CGF Cover
Code
@Article{wang2025sgldbench,
author = {Wang, Junpeng and Bukenberger, Dennis R. and Niedermayr, Simon and Neuhauser, Christoph and Wu, Jun and Westermann, Rüdiger},
journal = {IEEE Transactions on Visualization and Computer Graphics},
title = {{SGLDBench: A Benchmark Suite for Stress-Guided Lightweight 3D Designs}},
year = {2025},
pages = {1-13},
doi = {10.1109/TVCG.2025.3573774},
}
We introduce the Stress-Guided Lightweight Design Benchmark (SGLDBench), a comprehensive benchmark suite to apply and evaluate material layout strategies for generating stiff lightweight designs in 3D domains.
SGLDBench provides a seamlessly integrated simulation and analysis framework, providing six reference strategies accompanied by a scalable multigrid elasticity solver to efficiently execute these strategies and validate the stiffness of their results.
This facilitates systematic analysis and comparison of design strategies regarding the mechanical properties they achieve. SGLDBench enables the evaluation of diverse settings of load conditions and, through the tight integration of the solver, enables support for high-resolution designs and stiffness analysis.
Moreover, SGLDBench emphasizes visual analysis to explore relations between the geometric structure of a design and the distribution of stresses, providing insights into the specific properties and behaviors of different design strategies.
SGLDBenchs' specific features are highlighted in several experiments, by comparing the results of reference strategies with respect to geometric and mechanical properties.
Stress-Aligned Hexahedral Lattice Structures
CGF 2024, DOI:
10.1111/cgf.15265
PDF
Code
@HexaLab
@Article{bukenberger2024stress,
author = {Bukenberger, Dennis R. and Wang, Junpeng and Wu, Jun and Westermann, Rüdiger},
journal = {Computer Graphics Forum},
title = {{Stress-Aligned Hexahedral Lattice Structures}},
year = {2024},
issn = {1467-8659},
pages = {e15265},
volume = {44.1},
doi = {10.1111/cgf.15265},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
}
Maintaining the maximum stiffness of components with as little material as possible is an overarching objective in computational design and engineering.
It is well-established that in stiffness-optimal designs, material is aligned with orthogonal principal stress directions.
In the limit of material volume, this alignment forms micro-structures resembling quads or hexahedra.
Achieving a globally consistent layout of such orthogonal micro-structures presents a significant challenge, particularly in three-dimensional settings.
In this paper, we propose a novel geometric algorithm for compiling stress-aligned hexahedral lattice structures.
Our method involves deforming an input mesh under load to align the resulting stress field along an orthogonal basis.
The deformed object is filled with a hexahedral grid, and the deformation is reverted to recover the original shape.
The resulting stress-aligned mesh is used as basis for a final hollowing procedure, generating a volume-reduced stiff infill composed of hexahedral micro-structures.
We perform quantitative comparisons with structural optimization and hexahedral meshing approaches and demonstrate the superior mechanical performance of our designs with finite element simulation experiments.
Our work extends common pixelization techniques, enabling novel geometric pop-art stylization.
We employ dedicated feature analysis to autonomously extract facial features, ensuring the best recognizability of persons and facial expressions in portraits.
Additionally, our method includes automated content-related detail level extraction for scenic image content.
Based on these detail levels, a hierarchical structure sets the basis for non-uniform pixelization.
A joint optimization routine computes a reduced color palette alongside the coarse superpixel segmentation.
We propose an adapted modification to common superpixel methods to handle non-uniform sized cells, maintaining a comparable level of detail while allowing for a coarser, more pixelated look.
Additionally, this intermediate result serves as the basis for our geometric abstraction by eventually clustering polygonal shapes based on the pixelization.
We document the theoretical details of our method, discuss and elaborate the possible extensions.
Provided results of the intermediate pixelization are compared qualitatively to related methods.
Compared to other stylization methods, our resulting geometric abstractions are generated automatically, preserving a high level of relevant details from the source image.
Unlike simple filtering techniques or learning-based stylization methods, our approach allows for the incorporation of user input to highlight features.
Furthermore, our method stays true to the original image and results in scale-independent vector graphics, rendering it a valuable tool for artists and graphic designers.
Discrete Laplacians are the basis for various tasks in geometry processing.
While the most desirable properties of the discretization invariably lead to the so-called cotangent Laplacian for triangle meshes, applying the same principles to polygon Laplacians leaves degrees of freedom in their construction.
From linear finite elements, it is well-known how the shape of triangles affects both the error and the operator's condition.
We notice that shape quality can be encapsulated as the trace of the Laplacian and suggest that trace minimization is a helpful tool to improve numerical behavior.
We apply this observation for the polygon Laplacian constructed from a virtual triangulation (Bunge et al. 2020) to derive optimal parameters per polygon.
Moreover, we devise a smoothing approach for the vertices of a polygon mesh to minimize the trace.
We analyze the properties of the optimized discrete operators and show their superiority over generic parameter selection in theory and through various experiments.
Constructing L∞ Voronoi Diagrams in 2D and 3D
SGP 2022, DOI:
10.1111/cgf.14609
PDF
Code
@Article{bukenberger2022constructing,
author = {Bukenberger, Dennis R. and Buchin, Kevin and Botsch, Mario},
journal = {Computer Graphics Forum},
title = {{Constructing $L_\infty$ Voronoi Diagrams in 2D and 3D}},
year = {2022},
issn = {1467-8659},
pages = {135--147},
volume = {41.5},
doi = {10.1111/cgf.14609},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
}
Voronoi diagrams and their computation are well known in the Euclidean L2 space.
They are easy to sample and render in generalized Lp spaces but nontrivial to construct geometrically.
Especially the limit of this norm with p → ∞ 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∞ 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∞ 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∞ Voronoi criterion, leaving only the non-convex cell geometry.
Eventually we discuss the algorithms complexity, numerical precision and analyze the applicability of our generalized L∞ diagrams for the construction of Centroidal Voronoi Tessellations (CVT) using Lloyd’s algorithm.
The digital representation of real-world objects is a classical challenge in computer graphics, most commonly approached with either modeling or, in the focus of the thesis, reconstructing the object from a scan.
The information collected during a non-intrusive 3D scan of an object is usually stored in the form of a point cloud.
This loose set of three-dimensional positions only implies the geometry of the sampled surface.
There is an established collection of different techniques and approaches to actually recover a closed hull from this kind of information.
However, many of those methods still struggle under certain circumstances, produce artifacts, lack detail, or come with other drawbacks.
The goal of this research was to explore this challenge in novel and unconventional ways rather than increment on existing methods.
The thesis is based on four main contributions, each presenting valuable additions to the state-of-the-art in their individual fields.
The first surface meshing procedure is able to produce pure quad-meshes with adaptive resolution and feature-aligned structures.
In contrast to other standard methods, it does not require frame-fields, parameterization, or even normal information; a simple unoriented point cloud is already sufficient as input.
A hierarchical space partitioning structure is utilized to cluster meaningful neighborhoods of the point cloud and interconnect them with quadrangular tiles, using a bottom-up algorithm.
Volume meshing procedures usually require at least a surface and some kind of auxiliary input like framefields, parameterized mappings, sometimes even handcrafted split planes, singularity graphs, or annotated feature edges.
The proposed hex-meshing pipeline is able to skip the surface precomputation step and reconstruct hex-dominant volume meshes directly from point clouds, and naturally also from surfaces if given.
Furthermore, the procedure introduces a novel generalized mesh class, called at-most-hexa meshes: It constrains the meshes to only feature hexahedral or smaller primitives but no general, larger, and arbitrarily shaped polyhedra as it is common in other hex-dominant meshes.
A fundamental part of this volume meshing procedure is properly arranging hexahedral cells within the given volume, which is realized using a Lloyd relaxation with a modified L∞ norm.
The third contribution allows to analytically approach the L∞ energy within a cell of the before mentioned relaxation procedure, using tetrahedral geometry extended with a density domain.
Moreover, various other application scenarios of tetrahedral meshes under linearly varying density are proposed; like analyzing, optimizing, and even 3D printing such geometry with altered mass properties.
The fourth contribution introduces another installment of a meshing technique in a rather classical sense, focused on accurate surface reconstructions with fine details, sharp features, and an overall high mesh uniformity.
This is realized using a growing mesh complex: Starting from a small trivial initialization mesh or a rough approximation of the target, the mesh progressively assimilates towards the target hull, which can be given as a volumetric function, mesh or point cloud.
Furthermore, it is shown how this method can be adapted to improve the reconstruction accuracy of other meshing pipelines, exemplarily demonstrated on the aforementioned quad- and hex-meshed results.
Due to the common origin and related fields of research, links between the individually proposed contributions are drawn in introductory background sections.
Each technique is described and discussed in a dedicated chapter but eventually concluded with a joint discussion on future improvements and achieved results.
Volumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations.
Still, their construction bears several additional challenges compared to boundary-based representations.
Tetrahedral meshes and (pure) hex-meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages.
Hex-meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements.
Hex-dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult.
In this work, we introduce a strict subset of general hex-dominant meshes, which we term ‘at-most-hexa meshes’, in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides.
We exemplify the ease of construction of at-most-hexa meshes by proposing a frugal and straightforward method to generate high-quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan.
In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre-computations and can start directly from surfaces or samples.
We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the L∞ norm for cubical cells.
The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces.
We introduce specialized operations on the three-dimensional graph structure to enforce consistency during the relaxation.
The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes.
Inspired by the ability of water to assimilate any shape, if being poured into it, regardless if flat, round, sharp, or pointy we present a novel, high-quality meshing method.
Our algorithm creates a triangulated mesh, which automatically refines where necessary and accurately aligns to any target, given as mesh, point cloud, or volumetric function.
Our core optimization iterates over steps for mesh uniformity, point cloud projection, and mesh topology corrections, always guaranteeing mesh integrity and ε-close surface reconstructions.
In contrast to similar approaches, our simple algorithm operates on an individual vertex basis.
This allows for automated and seamless transitions between the optimization phases for rough shape approximation and fine detail reconstruction.
Therefore, our proposed algorithm equals established techniques in terms of accuracy and robustness but supersedes them in terms of simplicity and better feature reconstruction, all controlled by a single parameter, the intended edgelength.
Due to the overall increased versatility of input scenarios and robustness of the assimilation, our technique furthermore generalizes multiple established approaches such as ballooning or shrink wrapping.
We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities.
For objects given as 3D triangle meshes the method is analytically accurate and at the same time faster than any established approximation method.
Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation.
The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh.
Involved integrals are formulated in closed-form and can be evaluated by simple, easily parallelized, vector-matrix multiplications.
The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia.
In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve L2|∞ Lloyd relaxations by exact integration of the Chebyshev norm.
In the context of additive manufacturing research, objects of varying density are a prominent topic.
However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects.
Many existing frameworks will benefit by replacing approximations with fast and exact calculations.
In this paper we present a novel method to reconstruct watertight quad meshes on scanned 3D geometry.
There exist many different approaches to acquire 3D information from real world objects and sceneries.
Resulting point clouds depict scanned surfaces as sparse sets of positional information.
A common downside is the lack of normals, connectivity or topological adjacency data which makes it difficult to actually recover a meaningful surface.
The concept described in this paper is designed to reconstruct a surface mesh despite all this missing information.
Even when facing varying sample density, our algorithm is still guaranteed to produce watertight manifold meshes featuring quad faces only.
The topology can be set-up to follow superimposed regular structures or align naturally to the point cloud’s shape.
Our proposed approach is based on an initial divide and conquer subsampling procedure: Surface samples are clustered in meaningful neighborhoods as leafs of a kd-tree.
A representative sample of the surface neighborhood is determined for each leaf using a spherical surface approximation.
The hierarchical structure of the binary tree is utilized to construct a basic set of loose tiles and to interconnect them.
As a final step, missing parts of the now coherent tile structure are filled up with an incremental algorithm for locally optimal gap closure.
Disfigured or concave faces in the resulting mesh can be removed with a constrained smoothing operator.
Notebook scribbles, art or technical illustrations - line drawings are a simplistic method to visually communicate information.
Automated line drawings often originate from virtual 3D models, but one cannot trivially experience their three-dimensionality.
This paper introduces a novel concept to produce stereo-consistent line drawings of virtual 3D objects.
Some contour lines do not only depend on an objects geometry but also on the position of the observer.
To accomplish consistency between multiple view positions, our approach exploits geometrical characteristics of 3D surfaces in object space.
Established techniques for stereo-consistent line drawings operate on rendered pixel images.
In contrast, our pipeline operates in object space yielding many advantages: The position of the final viewpoint(s) is flexible within a certain window even after the contour generation, e.g., a stereoscopic image pair is only one possible application.
Such windows can be concatenated to simulate contours observed from an arbitrary camera path.
Various types of popular contour generators can be handled equivalently, occlusions are natively supported and stylization based on geometry characteristics is also easily possible.
Creating an animation based on video footage (rotoscoping) often requires significant manual work.
For monoscopic videos diverse publications already feature (semi-)automatic techniques to apply non-photorealistic image abstraction (NPR) to videos.
This paper addresses abstraction of 3D stereo content minimizing stereoscopic discomfort in images and videos.
We introduce a completely autonomous framework that enhances stereo and temporal consistency.
Stereoscopic coherence with consistent textures for both eyes is produced by warping the left and right images into a central disparity domain followed by mapping them back to the left and right view.
Smooth movements with reduced flickering are achieved by considering optical flow in the propagation of abstract features between frames.
The results show significant improvements of stereo consistency without discomforting artifacts in the depth perception.
We extend existing stroke based rendering (SBR) for higher accuracy at strong image gradients.
Furthermore, we demonstrate that our stereo framework is easily applicable to other point-based abstraction styles.
Finally, we evaluate the stereo consistency of our results in a small user study and show that the comfort of the visual appearance is maintained.
Experiments involving eye-tracking usually require analysis of large data.
While there is a rich landscape of tools to extract information about fixations and saccades from such data, the analysis at a higher level of abstraction (e.g., comparison of visual scanpaths between subjects) is still performed manually.
Especially, the comparison of scanpaths derived from dynamic scenarios, where the observer is in permanent interaction with her environment, is highly challenging.
In this work we (i) introduce a new work-flow for automated scanpath comparison in dynamic environments, which combines image processing, object tracking, and sequence comparison algorithms, and (ii) provide a new data set for performance evaluation of scanpath comparison methods that was extracted from eye-tracking data during an interactive tea-cooking task, referring to the experiments by Land et al..
Furthermore, to showcase the applicability of our work-flow, we applied our method to the above data set to find differences in visual behavior between several runs for the tea-cooking task.