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  • 1
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    On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces (2005)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in Euclidian $3$-space. The notion of totally normal convergence is shown to be equivalent to the convergence of either one of the following: surface area, intrinsic metric, and Laplace-Beltrami operators. We further s how that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justification for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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  • 2
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    Anisotropic Filtering of Non-Linear Surface Features (2004)
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    Publikationsdatum: 2014-02-26
    Beschreibung: A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non-linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well-known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non-linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 3
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    Evolution of 3d Curves under Strict Spatial Constraints (2005)
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    Publikationsdatum: 2014-02-26
    Beschreibung: We present a new algorithm for fairing of space curves with respect spatial constraints based on a vector valued curvature function. Smoothing with the vector valued curvature function is superior to standard Frenet techniques since the individual scalar components can be modeled similar to curvature-based curve smoothing techniques in 2d. This paper describes a curve smoothing flow that satisfies strict spatial constraints and allows simultaneous control of both curvature functions.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 4
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    Eigenmodes of Surface Energies for Shape Analysis (2010)
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    Publikationsdatum: 2022-07-19
    Beschreibung: In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Furthermore, we design a quadratic energy, such that the eigenmodes of the Hessian of this energy are sensitive to the extrinsic curvature of the surface. Based on these spectra and eigenmodes, we derive two shape signatures. One that measures the similarity of points on a surface, and another that can be used to identify features of the surface. In addition, we discuss a spectral quadrangulation scheme for surfaces.
    Sprache: Englisch
    Materialart: incollection , doc-type:Other
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  • 5
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    Geometry processing (2014)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
    Materialart: bookpart , doc-type:bookPart
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  • 6
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    Animating articulated characters using wiggly splines (2015)
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    Publikationsdatum: 2022-07-19
    Beschreibung: We propose a new framework for spacetime optimization that can generate artistic motion with a long planning horizon for complex virtual characters. The scheme can be used for generating general types of motion and neither requires motion capture data nor an initial motion that satisfies the constraints. Our modeling of the spacetime optimization combines linearized dynamics and a novel warping scheme for articulated characters. We show that the optimal motions can be described using a combination of vibration modes, wiggly splines, and our warping scheme. This enables us to restrict the optimization to low-dimensional spaces of explicitly parametrized motions. Thereby the computation of an optimal motion is reduced to a low-dimensional non-linear least squares problem, which can be solved with standard solvers. We show examples of motions created by specifying only a few constraints for positions and velocities.
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 7
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    Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects (2016)
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    Publikationsdatum: 2022-07-19
    Beschreibung: We introduce techniques for the processing of motion and animations of non-rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in Rn to the processing of motion of non-rigid shapes. Following this principle, we introduce a discrete geometric flow for curves in shape space. The flow iteratively replaces every shape with a weighted average shape of a local neighborhood and thereby globally decreases an energy whose minimizers are discrete geodesics in shape space. Based on the flow, we devise a novel smoothing filter for motions and animations of deformable shapes. By shortening the length in shape space of an animation, it systematically regularizes the deformations between consecutive frames of the animation. The scheme can be used for smoothing and noise removal, e.g., for reducing jittering artifacts in motion capture data. We introduce a reduced-order method for the computation of the flow. In addition to being efficient for the smoothing of curves, it is a novel scheme for computing geodesics in shape space. We use the scheme to construct non-linear Bézier curves by executing de Casteljau's algorithm in shape space.
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 8
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    Anisotropic filtering of non-linear surface features (2004)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 9
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    Evolution of 3D curves under strict spatial constraints (2005)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 10
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    Smooth feature lines on surface meshes (2005)
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    Publikationsdatum: 2022-07-19
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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