10,659 research outputs found
The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements
For both the Poisson model problem and the Stokes problem in any dimension,
this paper proves that the enriched Crouzeix-Raviart elements are actually
identical to the first order Raviart-Thomas elements in the sense that they
produce the same discrete stresses. This result improves the previous result in
literature which, for two dimensions, states that the piecewise constant
projection of the stress by the first order Raviart-Thomas element is equal to
that by the Crouzeix-Raviart element. For the eigenvalue problem of Laplace
operator, this paper proves that the error of the enriched Crouzeix-Raviart
element is equivalent to that of the Raviart-Thomas element up to higher order
terms
Optimized Data Representation for Interactive Multiview Navigation
In contrary to traditional media streaming services where a unique media
content is delivered to different users, interactive multiview navigation
applications enable users to choose their own viewpoints and freely navigate in
a 3-D scene. The interactivity brings new challenges in addition to the
classical rate-distortion trade-off, which considers only the compression
performance and viewing quality. On the one hand, interactivity necessitates
sufficient viewpoints for richer navigation; on the other hand, it requires to
provide low bandwidth and delay costs for smooth navigation during view
transitions. In this paper, we formally describe the novel trade-offs posed by
the navigation interactivity and classical rate-distortion criterion. Based on
an original formulation, we look for the optimal design of the data
representation by introducing novel rate and distortion models and practical
solving algorithms. Experiments show that the proposed data representation
method outperforms the baseline solution by providing lower resource
consumptions and higher visual quality in all navigation configurations, which
certainly confirms the potential of the proposed data representation in
practical interactive navigation systems
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