SGP: Eurographics Symposium on Geometry Processing

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https://diglib.eg.org/handle/10.2312/434

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Browsing SGP: Eurographics Symposium on Geometry Processing by Subject "Animation"

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    As-Killing-As-Possible Vector Fields for Planar Deformation
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Solomon, Justin; Ben-Chen, Mirela; Butscher, Adrian; Guibas, Leonidas; Mario Botsch and Scott Schaefer
    Cartoon animation, image warping, and several other tasks in two-dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, and its quality is determined by the type of distortion it introduces. In many applications, a desirable map is as isometric as possible. Finding such deformations, however, is a nonlinear problem, and most of the existing solutions approach it by minimizing a nonlinear energy. Such methods are not guaranteed to converge to a global optimum and often suffer from robustness issues. We propose a new approach based on approximate Killing vector fields (AKVFs), first introduced in shape processing. AKVFs generate near-isometric deformations, which can be motivated as direction fields minimizing an as-rigid-as-possible (ARAP) energy to first order. We first solve for an AKVF on the domain given user constraints via a linear optimization problem and then use this AKVF as the initial velocity field of the deformation. In this way, we transfer the inherent nonlinearity of the deformation problem to finding trajectories for each point of the domain having the given initial velocities. We show that a specific class of trajectories - the set of logarithmic spirals - is especially suited for this task both in practice and through its relationship to linear holomorphic vector fields. We demonstrate the effectiveness of our method for planar deformation by comparing it with existing state-of-the-art deformation methods.
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    Optimising Perceived Distortion in Lossy Encoding of Dynamic Meshes
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Vá a, L.; Petrík, O.; Mario Botsch and Scott Schaefer
    Development of geometry data compression techniques in the past years has been limited by the lack of a metric with proven correlation with human perception of mesh distortion. Many algorithms have been proposed, but usually the aim has been to minimise mean squared error, or some of its derivatives. In the field of dynamic mesh compression, the situation has changed with the recent proposal of the STED metric, which has been shown to capture the human perception of mesh distortion much better than previous metrics. In this paper we show how existing algorithms can be steered to provide optimal results with respect to this metric, and we propose a novel dynamic mesh compression algorithm, based on trajectory space PCA and Laplacian coordinates, specifically designed to minimise the newly proposed STED error. Our experiments show that using the proposed algorithm, we were able to reduce the required data rate by up to 50% while preserving the introduced STED error.