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"abstract": "Mesh surfaces with planar hexagonal faces, what we refer to as PH meshes, offer an elegant way of paneling freeform architectural surfaces due to their node simplicity (i.e., valence-3 nodes) and naturally appealing layout. We investigate PH meshes to understand how the shape, size, and pattern of PH faces are constrained by surface geometry. This understanding enables us to develop an effective method for paneling freeform architectural surfaces with PH meshes. Our method first constructs an ideal triangulation of a given smooth surface, guided by surface geometry. We show that such an ideal triangulation leads to a Dupin-regular PH mesh via tangent duality on the surface. We have developed several novel and effective techniques for improving undesirable mesh layouts caused by singular behaviors of surface curvature. We compute support structures associated with PH meshes, including exact vertex offsets and approximate edge offsets, as demanded in panel manufacturing. The efficacy of our method is validated by a number of architectural examples.",
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"abstract": "Movement data sets collected using today’s advanced tracking devices consist of complex trajectories in terms of length, shape, and number of recorded positions. Multiple additional attributes characterizing the movement and its environment are often also included making the level of complexity even higher. Simplification of trajectories can improve the visibility of relevant information by reducing less relevant details while maintaining important movement patterns. We propose a systematic stepwise methodology for simplifying and thematically enhancing trajectories in order to support their visual analysis. The methodology is applied iteratively and is composed of: (a) a simplification step applied to reduce the morphological complexity of the trajectories, (b) a thematic enhancement step which aims at accentuating patterns of movement, and (c) the representation and interactive exploration of the results in order to make interpretations of the findings and further refinement to the simplification and enhancement process. We illustrate our methodology through an analysis example of two different types of tracks, aircraft and pedestrian movement.",
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"abstract": "We propose a method to calibrate viewpoint-dependent, channel-wise image blur of near-eye displays, especially of Optical See-Through Head-Mounted Displays (OST-HMDs). Imperfections in HMD optics cause channel-wise image shift and blur that degrade the image quality of the display at a user's viewpoint. If we can estimate such characteristics perfectly, we could mitigate the effect by applying correction techniques from the computational photography in computer vision as analogous to cameras. Unfortunately, directly applying existing calibration techniques of cameras to OST-HMDs is not a straightforward task. Unlike ordinary imaging systems, image blur in OST-HMDs is viewpoint-dependent, i.e., the optical characteristic of a display dynamically changes depending on the current viewpoint of the user. This constraint makes the problem challenging since we must measure image blur of an HMD, ideally, over the entire 3D eyebox in which a user can see an image. To overcome this problem, we model the viewpoint-dependent blur as a Gaussian Light Field (GLF) that stores spatial information of the display screen as a (4D) light field with depth information and the blur as point-spread functions in the form of Gaussian kernels, respectively. We first describe both our GLF model and a calibration procedure to learn a GLF for a given OST-HMD. We then apply our calibration method to two HMDs that use different optics: a cubic prism or holographic gratings. The results show that our method achieves significantly better accuracy in Point-Spread Function (PSF) estimations with an accuracy about 2 to 7 dB in Peak SNR.",
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"abstract": "Galvanoscopic scanning laser projectors are powerful vector graphic devices offering a tremendous local brightness advantage compared to standard video projection systems. However, such devices have inherent problems, such as temporal flicker and spatially inaccurate rendering. We propose a method to generate an accurate point-based projection with such devices. To overcome the mentioned problems, we present a camera-based method to automatically analyze the laser projector's motion behavior. With this information, a model database is generated that is used to optimize the scanning path of projected point sequences. The optimization considers the overall path length, its angular shape, acceleration behavior, and the spatio-temporal point neighborhood. The method minimizes perceived visual flickering while guaranteeing an accurate spatial point projection at the same time. Comparisons and timing measurements prove the effectiveness of our method. An informal user evaluation shows substantial visual quality improvement as well.",
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"abstract": "Abstract—This paper investigates the set of all selectively refined meshes that can be obtained from a progressive mesh. We call the set the transitive mesh space of a progressive mesh and present a theoretical analysis of the space. We define selective edge collapse and vertex split transformations, which we use to traverse all selectively refined meshes in the transitive mesh space. We propose a complete selective refinement scheme for a progressive mesh based on the transformations and compare the scheme with previous selective refinement schemes in both theoretical and experimental ways. In our comparison, we show that the complete scheme always generates selectively refined meshes with smaller numbers of vertices and faces than previous schemes for a given refinement criterion. The concept of dual pieces of the vertices in the vertex hierarchy plays a central role in the analysis of the transitive mesh space and the design of selective edge collapse and vertex split transformations.",
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"abstract": "Abstract—Consistent transition algorithms preserve salient source motion features by establishing feature-based correspondence between motions and accordingly warping them before interpolation. These processes are commonly dubbed as preprocessing in motion transition literature. Current transition methods suffer from a lack of economical and generic preprocessing algorithms. Classical computer vision methods for human motion classification and correspondence are too computationally intensive for computer animation. This paper proposes an analytical framework that combines low-level kinematics analysis and high-level knowledge-based analysis to create states that provide coherent snapshots of body-parts active during the motion. These states are then corresponded via a globally optimal search tree algorithm. The framework proposed here is intuitive, controllable, and delivers results in near real-time. The validity and performance of the proposed system are tangibly proven with extensive experiments.",
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"abstract": "Abstract—This paper presents an algorithm for material interface reconstruction for data sets where fractional material information is given as a percentage for each element of the underlying grid. The reconstruction problem is transformed to a problem that analyzes a dual grid, where each vertex in the dual grid has an associated barycentric coordinate tuple that represents the fraction of each material present. Material boundaries are constructed by analyzing the barycentric coordinate tuples of a tetrahedron in material space and calculating intersections with Voronoi cells that represent the regions where one material dominates. These intersections are used to calculate intersections in the Euclidean coordinates of the tetrahedron. By triangulating these intersection points, one creates the material boundary. The algorithm can treat data sets containing any number of materials. The algorithm can also create nonmanifold boundary surfaces if necessary. By clipping the generated material boundaries against the original cells, one can examine the error in the algorithm. Error analysis shows that the algorithm preserves volume fractions within an error range of 0.5 percent per material.",
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"abstract": "Abstract—Mass-spring and particle systems have been widely employed in computer graphics to model deformable objects because they allow fast numerical solutions. In this work, we establish a link between these discrete models and classical mathematical elasticity. It turns out that discrete systems can be derived from a continuum model by a finite difference formulation and approximate classical continuum models unless the deformations are large. In this work, we present the derivation of a particle system from a continuum model, compare it to the models of classical elasticity theory, and assess its accuracy. In this way, we gain insight into the way discrete systems work and we are able to specify the correct scaling when the discretization is changed. Physical material parameters that describe materials in continuum mechanics are also used in the derived particle system.",
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