In data analysis, scatterplots serve as an initial tool for exploring the relationships between two or three attributes. While scatterplot matrices (SPLOMs) display every attribute combination through numerous 2D scatterplots to show a concise overview of a multivariate dataset, this approach is not directly suitable for 3D scatterplots due to visual clutter. Since research has shown that immersive virtual environments can enhance data analysis compared to traditional 2D desktop setups – especially for spatial analysis tasks – we propose an interactive system, called SPLOCIS, that makes use of virtual reality to enable users to interactively filter and select 3D scatter-plots from all possible attribute combinations. Our user study, combining both qualitative and quantitative results, demonstrates that SPLOCIS is a particularly novel and stimulating approach to work with multivariate data in immersive environments. It enables solving classic data exploration tasks in an efficient and accurate way, while not imposing unexpectedly high task loads. Moreover, our findings provide promising suggestions for further developments.

Abstract Most real‐time animation techniques for digital humans are limited to deforming the outer skin surface. Geometric skinning methods are highly efficient but struggle with artifacts such as collapsing joints or self‐intersections when animating inner anatomy along with the outer skin. Volumetric physics‐based simulations, on the other hand, naturally resolve these issues by coordinating bones, muscles, and skin, but are far too slow for interactive use. We solve this problem by training a neural network to predict deformation gradients. Learning deformation gradients instead of vertex displacements makes our method naturally robust to artifacts such as element inversion or volume deviation. Our model, trained on high‐quality finite element simulations, generalizes well across diverse body shapes and poses. This enables anatomically consistent and physically grounded animation of bones, muscles, and skin at interactive frame rates.

This paper presents the first systematic investigation of how congruence in visual self-representation influences self-perception and behavior. We span a continuum from the physical self through avatars with graded self-similarity to clearly dissimilar avatars in virtual reality (VR). In a 1 ×4 within-user study, participants completed movement and quiz tasks in either physical reality or a digital twin environment in VR, where they embodied one of three avatars: a photorealistic self-similar avatar, a dissimilar same-gender avatar, or a dissimilar opposite-gender avatar. Subjective measures included presence, sense of embodiment, self-identification, and perceived change, and were complemented by an objective movement metric of behavioral change. Compared to physical reality, VR, even with a self-similar avatar, produced lower presence, a weaker sense of embodiment, and reduced self-identification, revealing a persistent gap in visual congruence. Within VR, self-similar avatars enhanced body ownership, self-location, and self-identification relative to dissimilar avatars. Conversely, dissimilar avatars produced measurable behavioral changes compared with self-similar ones. Gender cues, however, had little impact in gender-neutral tasks. Overall, the findings show that photorealistic self-similar avatars reinforce embodiment and self-identification. However, VR still falls short of achieving congruence with physical reality, underscoring key challenges for avatar realism and ecological validity.

Recent developments in smartphone-based avatar reconstruction have made the creation of personalized and realistic avatars significantly more accessible. However, relying on one smartphone camera leads to capturing images sequentially, which introduces new challenges; particularly longer capture times increase the susceptibility to subject motion, which results in degraded reconstructions.

Abstract Due to the increasing use of virtual avatars, the animation of head‐hand interactions has recently gained attention. To this end, we present a novel volumetric and physics‐based interaction simulation. In contrast to previous work, our simulation incorporates temporal effects such as collision paths, respects anatomical constraints, and can detect and simulate skin pulling. As a result, we can achieve more natural‐looking interaction animations and take a step towards greater realism. However, like most complex and computationally expensive simulations, ours is not real‐time capable even on high‐end machines. Therefore, we train small and efficient neural networks as accurate approximations that achieve about 200 FPS on consumer GPUs, about 50 FPS on CPUs, and are learned in less than four hours for one person. In general, our focus is not to generalize the approximation networks to low‐resolution head models but to adapt them to more detailed personalized avatars. Nevertheless, we show that these networks can learn to approximate our head‐hand interaction model for multiple identities while maintaining computational efficiency. Since the quality of the simulations can only be judged subjectively, we conducted a comprehensive user study which confirms the improved realism of our approach. In addition, we provide extensive visual results and inspect the neural approximations quantitatively. All data used in this work has been recorded with a multi–view camera rig. Code and data are available at https://gitlab.cs.hs‐rm.de/cvmr_releases/HeadHand .

Working with scatterplots is a classic everyday task for data analysts, which gets increasingly complex the more plots are required to form an understanding of the underlying data. To help analysts retrieve relevant plots more quickly when they are needed, immersive virtual environments (iVEs) provide them with the option to freely arrange scatterplots in the 3D space around them. In this paper, we investigate the impact of different virtual environments on the users' ability to quickly find and retrieve individual scatterplots from a larger collection. We tested three different scenarios, all having in common that users were able to position the plots freely in space according to their own needs, but each providing them with varying numbers of landmarks serving as visual cues: an Empty scene as a baseline condition, a single landmark condition with one prominent visual cue being a Desk, and a multiple landmarks condition being a virtual Office. Results from a between-subject investigation with 45 participants indicate that the time and effort users invest in arranging their plots within an iVE had a greater impact on memory performance than the design of the iVE itself. We report on the individual arrangement strategies that participants used to solve the task effectively and underline the importance of an active arrangement phase for supporting the spatial memorization of scatterplots in iVEs.

This paper investigates if and how self-similarity and having motor control impact sense of embodiment, self-identification, and body weight perception in Augmented Reality (AR). We conducted a 2x2 mixed design experiment involving 60 participants who interacted with either synchronously moving virtual humans or independently moving ones, each with self-similar or generic appearances, across two consecutive AR sessions. Participants evaluated their sense of embodiment, self-identification, and body weight perception of the virtual human. Our results show that self-similarity significantly enhanced sense of embodiment, self-identification, and the accuracy of body weight estimates with the virtual human. However, the effects of having motor control over the virtual human movements were notably weaker in these measures than in similar VR studies. Further analysis indicated that not only the virtual human itself but also the participants' body weight, self-esteem, and body shape concerns predict body weight estimates across all conditions. Our work advances the understanding of virtual human body weight perception in AR systems, emphasizing the importance of factors such as coherence with the real-world environment.

Facial expressions are crucial for many eXtended Reality (XR) use cases, from mirrored self exposures to social XR, where users interact via their avatars as digital alter egos. However, current XR devices differ in sensor coverage of the face region. Hence, a faithful reconstruction of facial expressions either has to exclude these areas or synthesize missing animation data with model-based approaches, potentially leading to perceivable mismatches between executed and perceived expression. This paper investigates potential effects of the coverage of facial animations (none, partial, or whole) on important factors of self-perception. We exposed 83 participants to their mirrored personalized avatar. They were shown their mirrored avatar face with upper and lower face animation, upper face animation only, lower face animation only, or no face animation. Whole animations were rated higher in virtual embodiment and slightly lower in uncanniness. Missing animations did not differ from partial ones in terms of virtual embodiment. Contrasts showed significantly lower humanness, lower eeriness, and lower attractiveness for the partial conditions. For questions related to self-identification, effects were mixed. We discuss participants' shift in body part attention across conditions. Qualitative results show participants perceived their virtual representation as fascinating yet uncanny.

Virtual reality (VR) offers various opportunities for innovative therapeutic approaches, especially regarding self-related mind-body interventions. We introduce a VR body swap system enabling multiple users to swap their perspectives and appearances and evaluate its effects on virtual sense of embodiment (SoE) and perception- and cognition-based self-related processes. In a self-compassion-framed scenario, twenty participants embodied their personalized, photorealistic avatar, swapped bodies with an unfamiliar peer, and reported their SoE, interoceptive awareness (perception), and self-compassion (cognition). Participants’ experiences differed between bottom-up and top-down processes. Regarding SoE, their agency and self-location shifted to the swap avatar, while their top-down self-identification remained with their personalized avatar. Further, the experience positively affected interoceptive awareness but not self-compassion. Our outcomes offer novel insights into the SoE in a multiple-embodiment scenario and highlight the need to differentiate between the different processes in intervention design. They raise concerns and requirements for future research on avatar-based mind-body interventions.

Facial animation on computationally limited systems still heavily relies on linear blendshape models. Nonetheless, these models exhibit common issues like volume loss, self-collisions, and inaccuracies in soft tissue elasticity. Furthermore, personalizing blendshapes models demands significant effort, but there are limited options for simulating or manipulating physical and anatomical characteristics afterwards. Also, second-order dynamics can only be partially represented. For many years, physics-based facial simulations have been explored as an alternative to linear blendshapes, however, those remain cumbersome to implement and result in a high computational burden. We present a novel deep learning approach that offers the advantages of physics-based facial animations while being effortless and fast to use on top of linear blendshapes. For this, we design an innovative hypernetwork that efficiently approximates a physics-based facial simulation while generalizing over the extensive DECA model of human identities, facial expressions, and a wide range of material properties that can be locally adjusted without re-training. In addition to our previous work, we also demonstrate how the hypernetwork can be applied to facial animation from a sparse set of tracked landmarks. Unlike before, we no longer require linear blendshapes as the foundation of our system but directly operate on neutral head representations. This application is also used to complement an existing framework for commodity smartphones that already implements high resolution scanning of neutral faces and expression tracking.

Offline facial retargeting, i.e., transferring facial expressions from a source to a target character, is a common production task that still regularly leads to considerable algorithmic challenges. This task can be roughly dissected into the transfer of sequential facial animations and non-sequential blendshape personalization. Both problems are typically solved by data-driven methods that require an extensive corpus of costly target examples. Other than that, geometrically motivated approaches do not require intensive data collection but cannot account for character-specific deformations and are known to cause manifold visual artifacts. We present AnaConDaR, a novel method for offline facial retargeting, as a hybrid of data-driven and geometry-driven methods that incorporates anatomical constraints through a physics-based simulation. As a result, our approach combines the advantages of both paradigms while balancing out the respective disadvantages. In contrast to other recent concepts, AnaConDaR achieves substantially individualized results even when only a handful of target examples are available. At the same time, we do not make the common assumption that for each target example a matching source expression must be known. Instead, AnaConDaR establishes correspondences between the source and the target character by a data-driven embedding of the target examples in the source domain. We evaluate our offline facial retargeting algorithm visually, quantitatively, and in two user studies.

Abstract 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 fortrianglemeshes, applying the same principles topolygonLaplacians 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 to the polygon Laplacian constructed from a virtual triangulation [BHKB20] 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.

Abstract Human shape spaces have been extensively studied, as they are a core element of human shape and pose inference tasks. Classic methods for creating a human shape model register a surface template mesh to a database of 3D scans and use dimensionality reduction techniques, such as Principal Component Analysis, to learn a compact representation. While these shape models enable global shape modifications by correlating anthropometric measurements with the learned subspace, they only provide limitedlocalizedshape control. We instead register a volumetric anatomical template, consisting of skeleton bones and soft tissue, to the surface scans of the CAESAR database. We further enlarge our training data to the full Cartesian product of all skeletons and all soft tissues using physically plausible volumetric deformation transfer. This data is then used to learn an anatomically constrained volumetric human shape model in a self‐supervised fashion. The resultingTailorMemodel enables shape sampling, localized shape manipulation, and fast inference from given surface scans.

Sphere tracing is a fast and high-quality method for visualizing surfaces encoded by signed distance functions (SDFs). We introduce a similar method for a completely different class of surfaces encoded by harmonic functions , opening up rich new possibilities for visual computing. Our starting point is similar in spirit to sphere tracing: using conservative Harnack bounds on the growth of harmonic functions, we develop a Harnack tracing algorithm for visualizing level sets of harmonic functions, including those that are angle-valued and exhibit singularities. The method takes much larger steps than naïve ray marching, avoids numerical issues common to generic root finding methods and, like sphere tracing, needs only perform pointwise evaluation of the function at each step. For many use cases, the method is fast enough to run real time in a shader program. We use it to visualize smooth surfaces directly from point clouds (via Poisson surface reconstruction) or polygon soup (via generalized winding numbers) without linear solves or mesh extraction. We also use it to visualize nonplanar polygons (possibly with holes), surfaces from architectural geometry, mesh "exoskeletons", and key mathematical objects including knots, links, spherical harmonics, and Riemann surfaces. Finally we show that, at least in theory, Harnack tracing provides an alternative mechanism for visualizing arbitrary implicit surfaces.

Our work investigates the influence of self-related cues in the design of virtual humans on body perception in virtual reality. In a $2\times 2$ mixed design, 64 participants faced photorealistic virtual humans either as a motion-synchronized embodied avatar or as an autonomous moving agent, appearing subsequently with a personalized and generic texture. Our results unveil that self-related cues through embodiment and personalization yield an individual and complemented increase in participants' sense of embodiment and self-identification towards the virtual human. Different body weight modification and estimation tasks further showed an impact of both factors on participants' body weight perception. Additional analyses revealed that the participant's body mass index predicted body weight estimations in all conditions and that participants' self-esteem and body shape concerns correlated with different body weight perception results. Hence, we have demonstrated the occurrence of double standards through induced self-related cues in virtual human perception, especially through embodiment.

Virtual Reality (VR) allows us to replace our visible body with a virtual self-representation (avatar) and to explore its effects on our body perception. While the feeling of owning and controlling a virtual body is widely researched, how VR affects the awareness of internal body signals (body awareness) remains open. Forty participants performed moving meditation tasks in reality and VR, either facing their mirror image or not. Both the virtual environment and avatars photorealistically matched their real counterparts. We found a negative effect of VR on body awareness, mediated by feeling embodied in and changed by the avatar. Further, we revealed a negative effect of a mirror on body awareness. Our results indicate that assessing body awareness should be essential in evaluating VR designs and avatar embodiment aiming at mental health, as even a scenario as close to reality as possible can distract users from their internal body signals.

Traditional digital tools for exploring historical data mostly rely on conventional 2D visualizations, which often cannot reveal all relevant interrelationships between historical fragments (e.g., persons or events). In this paper, we present a novel interactive exploration tool for historical data in VR, which represents fragments as spheres in a 3D environment and arranges them around the user based on their temporal, geo, categorical and semantic similarity. Quantitative and qualitative results from a user study with 29 participants revealed that most participants considered the virtual space and the abstract fragment representation well-suited to explore historical data and to discover complex interrelationships. These results were particularly underlined by high usability scores in terms of attractiveness, stimulation, and novelty, while researching historical facts with our system did not impose unexpectedly high task loads. Additionally, the insights from our post-study interviews provided valuable suggestions for future developments to further expand the possibilities of our system.

Body awareness is relevant for the efficacy of psychotherapy. However, previous work on virtual reality (VR) and avatar-assisted therapy has often overlooked it. We investigated the effect of avatar individualization on body awareness in the context of VR-specific user experience, including sense of embodiment (SoE), plausibility, and sense of presence (SoP). In a between-subject design, 86 participants embodied three avatar types and engaged in VR movement exercises. The avatars were (1) generic and gender-matched, (2) customized from a set of pre-existing options, or (3) personalized photorealistic scans. Compared to the other conditions, participants with personalized avatars reported increased SoE, yet higher eeriness and reduced body awareness. Further, SoE and SoP positively correlated with body awareness across conditions. Our results indicate that VR user experience and body awareness do not always dovetail and do not necessarily predict each other. Future research should work towards a balance between body awareness and SoE.

Facial animation on computationally weak systems is still mostly dependent on linear blendshape models. However, these models suffer from typical artifacts such as loss of volume, self-collisions, or erroneous soft tissue elasticity. In addition, while extensive effort is required to personalize blendshapes, there are limited options to simulate or manipulate physical and anatomical properties once a model has been crafted. Finally, second-order dynamics can only be represented to a limited extent.

The Laplace-Beltrami operator is one of the essential tools in geometric processing. It allows us to solve numerous partial differential equations on discrete surface and volume meshes, which is a fundamental building block in many computer graphics applications. Discrete Laplacians are typically limited to standard elements like triangles or quadrilaterals, which severely constrains the tessellation of the mesh. But in recent years, several approaches were able to generalize the Laplace Beltrami and its closely related gradient and divergence operators to more general meshes. This allows artists and engineers to work with a wider range of elements which are sometimes required and beneficial in their field. This course, which extends the state-of-the-art report by Bunge and Botsch [2023], discusses the different constructions of these three ubiquitous differential operators on arbitrary polygons and polyhedra and analyzes their individual advantages and properties in common computer graphics applications.

Abstract The Laplace Beltrami operator is one of the essential tools in geometric processing. It allows us to solve numerous partial differential equations on discrete surface meshes, which is a fundamental building block in many computer graphics applications. Discrete Laplacians are typically limited to standard elements like triangles or quadrilaterals, which severely constrains the tessellation of the mesh. But in recent years, several approaches were able to generalize the Laplace Beltrami and its closely related gradient and divergence operators to more general meshes. This allows artists and engineers to work with a wider range of elements which are sometimes required and beneficial in their field. This paper discusses the different constructions of these three ubiquitous differential operators on arbitrary polygons and analyzes their individual advantages and properties in common computer graphics applications.

This article investigates the effects of different XR displays on the perception and plausibility of personalized virtual humans. We compared immersive virtual reality (VR), video see-through augmented reality (VST AR), and optical see-through AR (OST AR). The personalized virtual alter egos were generated by state-of-the-art photogrammetry methods. 42 participants were repeatedly exposed to animated versions of their 3D-reconstructed virtual alter egos in each of the three XR display conditions. The reconstructed virtual alter egos were additionally modified in body weight for each repetition. We show that the display types lead to different degrees of incongruence between the renderings of the virtual humans and the presentation of the respective environmental backgrounds, leading to significant effects of perceived mismatches as part of a plausibility measurement. The device-related effects were further partly confirmed by subjective misestimations of the modified body weight and the measured spatial presence. Here, the exceedingly incongruent OST AR condition leads to the significantly highest weight misestimations as well as to the lowest perceived spatial presence. However, similar effects could not be confirmed for the affective appraisal (i.e., humanness, eeriness, or attractiveness) of the virtual humans, giving rise to the assumption that these factors might be unrelated to each other.

Digital reconstruction of humans has various interesting use-cases. Animated virtual humans, avatars and agents alike, are the central entities in virtual embodied human-computer and human-human encounters in social XR. Here, a faithful reconstruction of facial expressions becomes paramount due to their prominent role in non-verbal behavior and social interaction. Current XR-platforms, like Unity 3D or the Unreal Engine, integrate recent smartphone technologies to animate faces of virtual humans by facial motion capturing. Using the same technology, this article presents an optimization-based approach to generate personalized blendshapes as animation targets for facial expressions. The proposed method combines a position-based optimization with a seamless partial deformation transfer, necessary for a faithful reconstruction. Our method is fully automated and considerably outperforms existing solutions based on example-based facial rigging or deformation transfer, and overall results in a much lower reconstruction error. It also neatly integrates with recent smartphone-based reconstruction pipelines for mesh generation and automated rigging, further paving the way to a widespread application of human-like and personalized avatars and agents in various use-cases.

Abstract 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 conclude with discussions on 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.

Solving partial differential equations (PDEs) on geometric domains is an important component of computer graphics, geometry processing, and many other fields. Typically, the given discrete mesh is the geometric representation and should not be altered for simulation purposes. Hence, accurately solving PDEs on general meshes is a central goal and has been considered for various differential operators over the last years. While it is known that using higher-order basis functions on simplicial meshes can substantially improve accuracy and convergence, extending these benefits to general surface or volume tessellations in an efficient fashion remains an open problem. Our work proposes variationally optimized piecewise quadratic shape functions for polygons and polyhedra, which generalize quadratic P 2 elements, exactly reproduce them on simplices, and inherit their beneficial numerical properties. To mitigate the associated cost of increased computation time, particularly for volumetric meshes, we introduce a custom two-level multigrid solver which significantly improves computational performance.

Embodiment and body perception have become important research topics in the field of virtual reality (VR). VR is considered a particularly promising tool to support research and therapy in regard to distorted body weight perception. However, the influence of embodiment on body weight perception has yet to be clarified. To address this gap, we compared body weight perception of 56 female participants of normal weight using a VR application. They either (a) self-embodied a photorealistic, non-personalized virtual human and performed body movements in front of a virtual mirror or (b) only observed the virtual human as other's avatar (or agent) performing the same movements in front of them. Afterward, participants had to estimate the virtual human's body weight. Additionally, we considered the influence of the participants' body mass index (BMI) on the estimations and captured the participants' feelings of presence and embodiment. Participants estimated the body weight of the virtual human as their embodied self-avatars significantly lower compared to participants rating the virtual human as other's avatar. Furthermore, the estimations of body weight were significantly predicted by the participant's BMI with embodiment, but not without. Our results clearly highlight embodiment as an important factor influencing the perception of virtual humans' body weights in VR.

The appearance of avatars can potentially alter changes in their users’ perception and behavior. Based on this finding, approaches to support the therapy of body perception disturbances in eating or body weight disorders by mixed reality (MR) systems gain in importance. However, the methodological heterogeneity of previous research has made it difficult to assess the suitability of different MR systems for therapeutic use in these areas. The effects of MR system properties and related psychometric factors on body-related perceptions have so far remained unclear. We developed an interactive virtual mirror embodiment application to investigate the differences between an augmented reality see-through head-mounted-display (HMD) and a virtual reality HMD on the before-mentioned factors. Additionally, we considered the influence of the participant’s body-mass-index (BMI) and the BMI difference between participants and their avatars on the estimations. The 54 normal-weight female participants significantly underestimated the weight of their photorealistic, generic avatar in both conditions. Body weight estimations were significantly predicted by the participants’ BMI and the BMI difference. We also observed partially significant differences in presence and tendencies for differences in virtual body ownership between the systems. Our results offer new insights into the relationships of body weight perception in different MR environments and provide new perspectives for the development of therapeutic applications.

This paper introduces an automated 3D-reconstruction method for generating high-quality virtual humans from monocular smartphone cameras. The input of our approach are two video clips, one capturing the whole body and the other providing detailed close-ups of head and face. Optical flow analysis and sharpness estimation select individual frames, from which two dense point clouds for the body and head are computed using multi-view reconstruction. Automatically detected landmarks guide the fitting of a virtual human body template to these point clouds, thereby reconstructing the geometry. A graph-cut stitching approach reconstructs a detailed texture. Our results are compared to existing low-cost monocular approaches as well as to expensive multi-camera scan rigs. We achieve visually convincing reconstructions that are almost on par with complex camera rigs while surpassing similar low-cost approaches. The generated high-quality avatars are ready to be processed, animated, and rendered by standard XR simulation and game engines such as Unreal or Unity.

Abstract The discrete Laplace‐Beltrami operator for surface meshes is a fundamental building block for many (if not most) geometry processing algorithms. While Laplacians on triangle meshes have been researched intensively, yielding the cotangent discretization as the de‐facto standard, the case of general polygon meshes has received much less attention. We present a discretization of the Laplace operator which is consistent with its expression as the composition of divergence and gradient operators, and is applicable to general polygon meshes, including meshes with non‐convex, and even non‐planar, faces. Byvirtuallyinserting a carefully placed point we implicitly refine each polygon into a triangle fan, but then hide the refinement within the matrix assembly. The resulting operator generalizes the cotangent Laplacian, inherits its advantages, and is empirically shown to be on par or even better than the recent polygon Laplacian of Alexa and Wardetzky [AW11] — while being simpler to compute.

We present a novel physics-based character skinning approach that improves the recent Projective Skinning in terms of animation quality and computational performance. Our method provides physically plausible animations, dynamic secondary motion effects, and global collision handling in a real-time skinning simulation. We achieve this through a custom-tailored GPU implementation of the underlying projective dynamics simulation and a high-quality upsampling from the simulation mesh to the high-resolution visualization mesh based on quadratic moving least squares.

We introduce an integrated meshing and finite-element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order bases on its elements, combining triquadratic B-splines, triquadratic hexahedra, and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson’s equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.

This article investigates performance and user experience in Social Virtual Reality (SVR) targeting distributed, embodied, and immersive, face-to-face encounters. We demonstrate the close relationship between scalability, reproduction accuracy, and the resulting performance characteristics, as well as the impact of these characteristics on users co-located with larger groups of embodied virtual others. System scalability provides a variable number of co-located avatars and Al-controlled agents with a variety of different appearances, including realistic-looking virtual humans generated from photogrammetry scans. The article reports on how to meet the requirements of embodied SVR with today's technical off-the-shelf solutions and what to expect regarding features, performance, and potential limitations. Special care has been taken to achieve low latencies and sufficient frame rates necessary for reliable communication of embodied social signals. We propose a hybrid evaluation approach which coherently relates results from technical benchmarks to subjective ratings and which confirms required performance characteristics for the target scenario of larger distributed groups. A user-study reveals positive effects of an increasing number of co-located social companions on the quality of experience of virtual worlds, i.e., on presence, possibility of interaction, and co-presence. It also shows that variety in avatar/agent appearance might increase eeriness but might also stimulate an increased interest of participants about the environment.

Real-world evolutionary design optimizations of complex shapes can efficiently be solved using linear deformation representations, but the optimization performance crucially depends on the initial deformation setup. For instance, when modeling the deformation by radial basis functions (RBF) the convergence speed depends on the condition number of the involved kernel matrix, which previous work therefore tried to optimize through careful placement of RBF kernels. We show that such representation-specific techniques are inherently limited and propose a generic, representation-agnostic optimization based on orthogonalization of the deformation matrix. This straightforward black-box optimization projects any given linear deformation setup to optimal condition number without changing its design space, which, as we show through extensive numerical experiments, can boost the convergence speed of evolutionary optimizations by up to an order of magnitude.

Abstract We present a method for automatically generating reduced marker layouts for marker‐based optical motion capture of human hands. The employed motion reconstruction method is based on subspace‐constrained inverse kinematics, which allows for the recovery of realistic hand movements even from sparse input data. We additionally present a user‐specific hand model calibration procedure that fits an articulated hand model to point cloud data of the user's hand. Our marker layout optimization is sensitive to the kinematic structure and the subspace representations of hand articulations utilized in the reconstruction method, in order to generate sparse marker configurations that are optimal for solving the constrained inverse kinematics problem. We propose specific quality criteria for reduced marker sets that combine numerical stability with geometric feasibility of the resulting layout. These criteria are combined in an objective function that is minimized using a specialized surface‐constrained particle swarm optimization scheme, which generates marker layouts bound to the surface of an animated hand model. Our method provides a principled way for determining reduced marker layouts based on subspace representations of hand articulations. We demonstrate the effectiveness of our motion reconstruction and model calibration methods in a thorough evaluation.

This article reports the impact of the degree of personalization and individualization of users' avatars as well as the impact of the degree of immersion on typical psychophysical factors in embodied Virtual Environments. We investigated if and how virtual body ownership (including agency), presence, and emotional response are influenced depending on the specific look of users' avatars, which varied between (1) a generic hand-modeled version, (2) a generic scanned version, and (3) an individualized scanned version. The latter two were created using a state-of-the-art photogrammetry method providing a fast 3D-scan and post-process workflow. Users encountered their avatars in a virtual mirror metaphor using two VR setups that provided a varying degree of immersion, (a) a large screen surround projection (L-shape part of a CAVE) and (b) a head-mounted display (HMD). We found several significant as well as a number of notable effects. First, personalized avatars significantly increase body ownership, presence, and dominance compared to their generic counterparts, even if the latter were generated by the same photogrammetry process and hence could be valued as equal in terms of the degree of realism and graphical quality. Second, the degree of immersion significantly increases the body ownership, agency, as well as the feeling of presence. These results substantiate the value of personalized avatars resembling users' real-world appearances as well as the value of the deployed scanning process to generate avatars for VR-setups where the effect strength might be substantial, e.g., in social Virtual Reality (VR) or in medical VR-based therapies relying on embodied interfaces. Additionally, our results also strengthen the value of fully immersive setups which, today, are accessible for a variety of applications due to the widely available consumer HMDs.

A dynamic industrial design optimization requires high-quality optimization algorithms as well as adaptive representations to find the global solution for a given problem. For adapting the representation to changing environments or to new input we utilize the concept of evolvability, which in our interpretation consists of three criteria: variability, regularity, and improvement potential, where regularity and improvement potential characterize conflicting goals between exploration and exploitation. Our goal is the efficient adaptation of the representation according to a given preference weight between regularity and improvement potential. We propose a combination of two heuristics, Lloyd sampling and orthogonal least squares sampling, to initialize the adaptation process for a given preference weight. We show that this initialization improves the convergence speed of the adaptation process as well as the resulting fitness. We then realize a stepwise design optimization procedure by alternating the adaptation of the representation with optimization of the design. During the design optimization process we extract information which we exploit in the next adaptation phase. We show that an intermediate preference weight, balancing between regularity and improvement potential, allows to exploit this information and is robust to erroneous initial information. Thereby, we increase the performance of the whole design optimization process.

Many approaches for motion processing or motion analysis employ Dynamic Time Warping (DTW) for temporally aligning an input movement with a reference movement. DTW, however, does not work online since it requires the complete input trajectory. Its online extension Open-End DTW can lead to poor alignments. In this paper we propose Weight-Optimized Open-End DTW, which combines path-length weighting and joint weights optimized from training data. We demonstrate our method to work online and to outperform Open-End DTW in terms of alignment quality.

In this paper we present a complete pipeline to create ready-to-animate virtual humans by fitting a template character to a point set obtained by scanning a real person using multi-view stereo reconstruction. Our virtual humans are built upon a holistic character model and feature a detailed skeleton, fingers, eyes, teeth, and a rich set of facial blendshapes. Furthermore, due to the careful selection of techniques and technology, our reconstructed humans are quite realistic in terms of both geometry and texture. Since we represent our models as single-layer triangle meshes and animate them through standard skeleton-based skinning and facial blendshapes, our characters can be used in standard VR engines out of the box. By optimizing for computation time and minimizing manual intervention, our reconstruction pipeline is capable of processing whole characters in less than ten minutes.

This paper investigates the effect of avatar realism on embodiment and social interactions in Virtual Reality (VR). We compared abstract avatar representations based on a wooden mannequin with high fidelity avatars generated from photogrammetry 3D scan methods. Both avatar representations were alternately applied to participating users and to the virtual counterpart in dyadic social encounters to examine the impact of avatar realism on self-embodiment and social interaction quality. Users were immersed in a virtual room via a head mounted display (HMD). Their full-body movements were tracked and mapped to respective movements of their avatars. Embodiment was induced by presenting the users' avatars to themselves in a virtual mirror. Afterwards they had to react to a non-verbal behavior of a virtual interaction partner they encountered in the virtual space. Several measures were taken to analyze the effect of the appearance of the users' avatars as well as the effect of the appearance of the others' avatars on the users. The realistic avatars were rated significantly more human-like when used as avatars for the others and evoked a stronger acceptance in terms of virtual body ownership (VBO). There also was some indication of a potential uncanny valley. Additionally, there was an indication that the appearance of the others' avatars impacts the self-perception of the users.

While facial capturing focuses on accurate reconstruction of an actor's performance, facial animation retargeting has the goal to transfer the animation to another character, such that the semantic meaning of the animation remains. Because of the popularity of blendshape animation, this effectively means to compute suitable blendshape weights for the given target character. Current methods either require manually created examples of matching expressions of actor and target character, or are limited to characters with similar facial proportions (i.e., realistic models). In contrast, our approach can automatically retarget facial animations from a real actor to stylized characters. We formulate the problem of transferring the blendshapes of a facial rig to an actor as a special case of manifold alignment, by exploring the similarities of the motion spaces defined by the blendshapes and by an expressive training sequence of the actor. In addition, we incorporate a simple, yet elegant facial prior based on discrete differential properties to guarantee smooth mesh deformation. Our method requires only sparse correspondences between characters and is thus suitable for retargeting marker-less and marker-based motion capture as well as animation transfer between virtual characters.

Point sets generated by image-based 3D reconstruction techniques are often much noisier than those obtained using active techniques like laser scanning. Therefore, they pose greater challenges to the subsequent surface reconstruction (meshing) stage. We present a simple and effective method for removing noise and outliers from such point sets. Our algorithm uses the input images and corresponding depth maps to remove pixels which are geometrically or photometrically inconsistent with the colored surface implied by the input. This allows standard surface reconstruction methods (such as Poisson surface reconstruction) to perform less smoothing and thus achieve higher quality surfaces with more features. Our algorithm is efficient, easy to implement, and robust to varying amounts of noise. We demonstrate the benefits of our algorithm in combination with a variety of state-of-the-art depth and surface reconstruction methods.

Industrial product design is characterized by increasing complexity due to the high number of involved parameters, objectives, and boundary conditions, all typically changing over time. Population-based evolutionary design optimization targets to solve these kinds of application problems, offering efficient algorithms striving for high-quality solutions. An important factor in the optimization setup is the representation, which defines the encoding of the design and the mapping from parameter space to design space. Being able to numerically quantify the quality of different representation settings would strengthen the optimal choice of encoding. Motivated by the biological concept of evolvability, we propose three criteria, namely variability, regularity, and improvement potential, to evaluate linear deformation representations for their use in shape optimization problems. The first aspect characterizes the exploration potential of the design space, the second measures the expected convergence speed, and the third determines the expected improvement of the quality of a design. We propose and experimentally analyze mathematical definitions for each of the three criteria. We demonstrate the successful application of our model to two evolutionary optimization scenarios: fitting of 1D height fields and fitting of 3D face scans, both based on RBF deformations. Due to the general character of our definition we expect the transferability of our concepts to alternative deformation methods.

Latency between a user's movement and visual feedback is inevitable in every Virtual Reality application, as signal transmission and processing take time. Unfortunately, a high end-to-end latency impairs perception and motor performance. While it is possible to reduce feedback delay to tens of milliseconds, these delays will never completely vanish. Currently, there is a gap in literature regarding the impact of feedback delays on perception and motor performance as well as on their interplay in virtual environments employing full-body avatars. With the present study at hand, we address this gap by performing a systematic investigation of different levels of delay across a variety of perceptual and motor tasks during full-body action inside a Cave Automatic Virtual Environment. We presented participants with their virtual mirror image, which responded to their actions with feedback delays ranging from 45 to 350 ms. We measured the impact of these delays on motor performance, sense of agency, sense of body ownership and simultaneity perception by means of psychophysical procedures. Furthermore, we looked at interaction effects between these aspects to identify possible dependencies. The results show that motor performance and simultaneity perception are affected by latencies above 75 ms. Although sense of agency and body ownership only decline at a latency higher than 125 ms, and deteriorate for a latency greater than 300 ms, they do not break down completely even at the highest tested delay. Interestingly, participants perceptually infer the presence of delays more from their motor error in the task than from the actual level of delay. Whether or not participants notice a delay in a virtual environment might therefore depend on the motor task and their performance rather than on the actual delay.

A successful design optimization crucially depends on the underlying representation, which has to adapt to a variety of demands and changing boundary conditions. Complex system engineering addresses these challenges through key features like self-organization, modularity, locality, or evolution. The representation covers the parameter setup (location and quantity) and the mapping between parameter space (genotype) and design space (phenotype), and should allow for both adaptation and specialization of a design. To quantify the potential of a representation, suitable quality criteria are needed. Evolvability is such a criterion, which has been derived from biological analysis. However, many biological and technical studies propose different definitions of evolvability. We analyze, interpret, and extend them in order to derive an evolvability criterion suitable for complex system engineering. This can be used as a basis for future design optimization problems.

We present a multimodal coaching system that supports online motor skill learning. In this domain, closed-loop interaction between the movements of the user and the action instructions by the system is an essential requirement. To achieve this, the actions of the user need to be measured and evaluated and the system must be able to give corrective instructions on the ongoing performance. Timely delivery of these instructions, particularly during execution of the motor skill by the user, is thus of the highest importance. Based on the results of an empirical study on motor skill coaching, we analyze the requirements for an interactive coaching system and present an architecture that combines motion analysis, dialogue management, and virtual human animation in a motion tracking and 3D virtual reality hardware setup. In a preliminary study we demonstrate that the current system is capable of delivering the closed-loop interaction that is required in the motor skill learning domain.

We present a method for automatically generating reduced marker layouts for marker-based optical motion capture of human hand motions. Reducing the number of markers on the hand is important to ensure the generated motions are performed in a natural way and indeed a reduced marker set might be a technical requirement should simultaneous body motion capture also have to be carried out. The employed motion reconstruction method is based on subspace-constrained inverse kinematics, which allows for the recovery of realistic hand movements even from sparse input data. Our marker layout optimization is sensitive to the kinematic structure and the subspace representations of hand articulations utilized in the reconstruction method in order to generate sparse marker configurations that are optimal for solving the constrained inverse kinematics problem. We propose specific quality criteria for reduced marker sets that combine numerical stability with geometric feasibility of the resulting layout. These criteria are combined in an objective function that is minimized using a specialized surface-constrained particle swarm optimization scheme. Our method provides a principled way for determining reduced marker layouts based on subspace representations of hand articulations.

Virtual Reality (VR) has the potential to support motor learning in ways exceeding beyond the possibilities provided by real world environments. New feedback mechanisms can be implemented that support motor learning during the performance of the trainee and afterwards as a performance review. As a consequence, VR environments excel in controlled evaluations, which has been proven in many other application scenarios.

Abstract We present a robust method for capturing articulated hand motions in realtime using a single depth camera. Our system is based on a realtime registration process that accurately reconstructs hand poses by fitting a 3D articulated hand model to depth images. We register the hand model using depth, silhouette, and temporal information. To effectively map low‐quality depth maps to realistic hand poses, we regularize the registration with kinematic and temporal priors, as well as a data‐driven prior built from a database of realistic hand poses. We present a principled way of integrating such priors into our registration optimization to enable robust tracking without severely restricting the freedom of motion. A core technical contribution is a new method for computing tracking correspondences that directly models occlusions typical of single‐camera setups. To ensure reproducibility of our results and facilitate future research, we fully disclose the source code of our implementation.

Virtual characters contribute strongly to the entire visuals of 3D animated films. However, designing believable characters remains a challenging task. Artists rely on stylization to increase appeal or expressivity, exaggerating or softening specific features. In this paper we analyze two of the most influential factors that define how a character looks: shape and material. With the help of artists, we design a set of carefully crafted stimuli consisting of different stylization levels for both parameters, and analyze how different combinations affect the perceived realism, appeal, eeriness, and familiarity of the characters. Moreover, we additionally investigate how this affects the perceived intensity of different facial expressions (sadness, anger, happiness, and surprise). Our experiments reveal that shape is the dominant factor when rating realism and expression intensity, while material is the key component for appeal. Furthermore our results show that realism alone is a bad predictor for appeal, eeriness, or attractiveness.

We present a method for real-time bare hand tracking that utilizes natural hand synergies to reduce the complexity and improve the plausibility of the hand posture estimation. The hand pose and posture are estimated by fitting a virtual hand model to the 3D point cloud obtained from a Kinect camera using an inverse kinematics approach. We use real human hand movements captured with a Vicon motion tracking system as the ground truth for deriving natural hand synergies based on principal component analysis. These synergies are integrated in the tracking scheme by optimizing the posture in a reduced parameter space. Tracking in this reduced space combined with joint limit avoidance constrains the posture estimation to natural hand articulations. The information loss associated with dimension reduction can be dealt with by employing a hierarchical optimization scheme. We show that our synergistic hand tracking approach improves runtime performance and increases the quality of the posture estimation.

Abstract Despite the huge progress made in interactive physics‐based mesh deformation, manipulating a geometrically complex mesh or posing a detailed character is still a tedious and time‐consuming task. Example‐driven methods significantly simplify the modelling process by incorporating structural or anatomical knowledge learned from example poses. However, these approaches yield counter‐intuitive, non‐physical results as soon as the shape space spanned by the example poses is left. In this paper, we propose a modelling framework that is both example‐driven and physics‐based and thereby overcomes the limitations of both approaches. Based on an extension of the discrete shell energy we derive mesh deformation and mesh interpolation techniques that can be seamlessly combined into a simple and flexible mesh‐based inverse kinematics system.

We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston , measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.

We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by customdesigned basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures , which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C 1 continuous basis functions and thus allows for simpler, C 0 continuous XFEM enrichment functions.

Abstract The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.

Abstract Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.

This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed high-resolution meshes, like those produced by scanning real-world objects. The challenge of manipulating such complex surfaces is three-fold: the deformation technique has to be sufficiently fast, robust, and intuitive and easy to control to be useful for interactive applications. An intuitive, and thus predictable, deformation tool should provide physically plausible and aesthetically pleasing surface deformations, which in particular requires its geometric details to be preserved. The methods we survey generally formulate surface deformation as a global variational optimization problem that addresses the differential properties of the edited surface. Efficiency and robustness are achieved by linearizing the underlying objective functional, such that the global optimization amounts to solving a sparse linear system of equations. We review the different deformation energies and detail preservation techniques that were proposed in the recent years, together with the various techniques to rectify the linearization artifacts. Our goal is to provide the reader with a systematic classification and comparative description of the different techniques, revealing the strengths and weaknesses of each approach in common editing scenarios.

Abstract We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical solver for the resulting nonlinear optimization problem. Scalability is achieved using an adaptive spatial discretization that is decoupled from the resolution of the embedded object. Our approach is versatile and easy to implement, supports thin‐shell and solid deformations of 2D and 3D objects, and is applicable to arbitrary sample‐based representations, such as meshes, triangle soups, or point clouds.

Abstract We present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping. This more flexible discretization is particularly useful for simulations that involve topological changes, such as cutting or fracture. Since splitting convex elements along a plane produces convex elements, remeshing or subdivision schemes used in simulations based on tetrahedra are not necessary, leading to less elements after such operations. We propose various operators for cutting the polyhedral discretization. Our method can handle arbitrary cut trajectories, and there is no limit on how often elements can be split.

We present a novel multi-scale representation and acquisition method for the animation of high-resolution facial geometry and wrinkles. We first acquire a static scan of the face including reflectance data at the highest possible quality. We then augment a traditional marker-based facial motion-capture system by two synchronized video cameras to track expression wrinkles. The resulting model consists of high-resolution geometry, motion-capture data, and expression wrinkles in 2D parametric form. This combination represents the facial shape and its salient features at multiple scales. During motion synthesis the motion-capture data deforms the high-resolution geometry using a linear shell-based mesh-deformation method. The wrinkle geometry is added to the facial base mesh using nonlinear energy optimization. We present the results of our approach for performance replay as well as for wrinkle editing.

We present a novel architecture for hardware-accelerated rendering of point primitives. Our pipeline implements a refined version of EWA splatting, a high quality method for antialiased rendering of point sampled representations. A central feature of our design is the seamless integration of the architecture into conventional, OpenGL-like graphics pipelines so as to complement triangle-based rendering. The specific properties of the EWA algorithm required a variety of novel design concepts including a ternary depth test and using an on-chip pipelined heap data structure for making the memory accesses of splat primitives more coherent. In addition, we developed a computationally stable evaluation scheme for perspectively corrected splats. We implemented our architecture both on reconfigurable FPGA boards and as an ASIC prototype, and we integrated it into an OpenGL-like software implementation. Our evaluation comprises a detailed performance analysis using scenes of varying complexity.

Current surface-based methods for interactive freeform editing of high resolution 3D models are very powerful, but at the same time require a certain minimum tessellation or sampling quality in order to guarantee sufficient robustness. In contrast to this, space deformation techniques do not depend on the underlying surface representation and hence are affected neither by its complexity nor by its quality aspects. However, while analogously to surfacebased methods high quality deformations can be derived from variational optimization, the major drawback lies in the computation and evaluation, which is considerably more expensive for volumetric space deformations. In this paper we present techniques which allow us to use triharmonic radial basis functions for real-time freeform shape editing. An incremental least-squares method enables us to approximately solve the involved linear systems in a robust and efficient manner and by precomputing a special set of deformation basis functions we are able to significantly reduce the per-frame costs. Moreover, evaluating these linear basis functions on the GPU finally allows us to deform highly complex polygon meshes or point-based models at a rate of 30M vertices or 13M splats per second, respectively. 1.

In an increasing number of applications triangle meshes represent a flexible and efficient alternative to traditional NURBS-based surface representations. Especially in engineering applications it is crucial to guarantee that a prescribed approximation tolerance to a given reference geometry is respected for any combination of geometric algorithms that are applied when processing a triangle mesh. We propose a simple and generic method for computing the distance of a given polygonal mesh to the reference surface, based on a linear approximation of its signed distance field. Exploiting the hardware acceleration of modern GPUs allows us to perform up to 3M triangle checks per second, enabling real-time distance evaluations even for complex geometries. An additional feature of our approach is the accurate high-quality distance visualization of dynamically changing meshes at a rate of 15M triangles per second. Due to its generality, the presented approach can be used to enhance any mesh processing method by global error control, guaranteeing the resulting mesh to stay within a prescribed error tolerance. The application examples that we present include mesh decimation, mesh smoothing and freeform mesh deformation.

We present a freeform modeling framework for unstructured triangle meshes which is based on constraint shape optimization. The goal is to simplify the user interaction even for quite complex freeform or multiresolution modifications. The user first sets various boundary constraints to define a custom tailored (abstract) basis function which is adjusted to a given design task. The actual modification is then controlled by moving one single 9-dof manipulator object. The technique can handle arbitrary support regions and piecewise boundary conditions with smoothness ranging continuously from C 0 to C 2 . To more naturally adapt the modification to the shape of the support region, the deformed surface can be tuned to bend with anisotropic stiffness. We are able to achieve real-time response in an interactive design session even for complex meshes by precomputing a set of scalar-valued basis functions that correspond to the degrees of freedom of the manipulator by which the user controls the modification.

In the last years, point-based rendering has been shown to offer the potential to outperform traditional triangle based rendering both in speed and visual quality when it comes to processing highly complex models. Existing surface splatting techniques achieve superior visual quality by proper filtering but they are still limited in rendering speed. On the other hand the increasing availability and programmability of graphics hardware lead to the development of very efficient hardware-accelerated rendering methods. However, since no filtered splats are used, these approaches trade visual quality for rendering speed. In this paper, we propose a rendering framework for point-based geometry providing high visual quality as well as efficient rendering. Our approach is based on a two-pass splatting technique with Gaussian filtering, resulting in a visual quality comparable to existing software rendering systems. Using programmable graphics hardware we delegate all expensive rendering tasks to the GPU, thereby minimizing data transfer and saving CPU resources. The proposed system renders up to 28M mid-quality or up to 10M high-quality surface splats per second on the latest graphics hardware.

The most important concepts for the handling and storage of freeform shapes in geometry processing applications are parametric representation and volumetric representations. Both have their specific advantages and drawbacks. While the algebraic complexity of volumetric representations S = {(x,y,z) | f(x,y,z) = 0} is independent from the shape complexity, the domain /spl Omega/ of a parametric representation f : /spl Omega/ /spl rarr/ S usually has to have the same structure as the surface S itself (which sometimes makes it necessary to update the domain when the surface is modified. On the other hand, the topology of a parametrically defined surface can be controlled explicitly while in a volumetric representation, the surface topology can change accidentally during deformation. A volumetric representation reduces distance queries or inside/outside tests to mere function evaluations but the geodesic neighborhood relation between surface points is difficult to resolve. As a consequence, it seems promising to combine parametric and volumetric representations to effectively exploit both advantages. A number of applications are presented and discussed where such a combination leads to efficient and numerically stable algorithms for the solution of various geometry processing tasks. These applications include: surface remeshing, mesh fairing, global error control for mesh decimation and smoothing, and topology control for level-set surfaces.

Abstract We propose a new representation for multiresolution models which uses volume elements enclosed between thedifferent resolution levels to encode the detail information. Keeping these displacement volumes locally constantduring a deformation of the base surface leads to a natural behaviour of the detail features. The correspondingreconstruction operator can be implemented efficiently by a hierarchical iterative relaxation scheme, providingclose to interactive response times for moderately complex models. Based on this representation we implement a multiresolution editing tool for irregular polygon meshes that allowsthe designer to freely edit the base surface of a multiresolution model without having to care about self‐intersectionsin the respective detailed surface. We demonstrate the effectiveness and robustness of the reconstructionby several examples with real‐world data.

Figure 1: We present a new technique to extract high quality triangle meshes from volume representations of geometric objects.The two main contributions are an enhanced distance field representation and an extended Marching Cubes algorithm.The above figures show reconstructions of the well-known "fandisk" dataset from its distance field representation.The distance field has been sampled on a uniform 65×65×65 grid.The far left image shows the standard Marching Cubes reconstruction, center left is the reconstruction by the same algorithm but applied to the enhanced distance field with the same resolution.Center right shows the result of our new extended Marching Cubes algorithm applied to the original volume data, and finally on the far right we show the reconstruction by our new algorithm applied to the enhanced distance field.The approximation error to the original polygonal model is below 0.25 %.

Efficient surface reconstruction and reverse engineering techniques are usually based on a polygonal mesh representation of the geometry: the resulting models emerge from piecewise linear interpolation of a set of sample points. The quality of the reconstruction not only depends on the number and density of the sample points but also on their alignment to sharp and rounded features of the original geometry. Bad alignment can lead to severe alias artifacts. In this paper we present a sampling pattern for feature and blend regions which minimizes these alias errors. We show how to improve the quality of a given polygonal mesh model by resampling its feature and blend regions within an interactive framework. We further demonstrate sophisticated modeling operations that can be implemented based on this resampling technique.

We present an interactive system for the generation of high quality triangle meshes that allows us to handle hybrid geometry (point clouds, polygons,. . .) as input data. In order to be able to robustly process huge data sets, we exploit graphics hardware features like the raster manager and the z‐buffer for specific sub‐tasks in the overall procedure. By this we significantly accelerate the stitching of mesh patches and obtain an algorithm for sub‐sampling the data points in linear time. The target resolution and the triangle alignment in sub‐regions of the resulting mesh can be controlled by adjusting the screen resolution and viewing transformation. An intuitive user interface provides a flexible tool for application dependent optimization of the mesh.