Differentiation Under the Integral Sign

Flanders, Harley

doi:10.2307/2319163

Cited by 153 publications

(54 citation statements)

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“…Let n be the outward unit normal vector of ∂D t . Then for a smooth function g(x, t), x ∈ D t , the general Leibniz rule [10] states…”

Section: Weighted Odtmentioning

confidence: 99%

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Chen¹,

Wang²,

Lévy³

et al. 2014

SIAM J. Sci. Comput.

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Abstract. This paper proposes a new algorithm to generate a graded three-dimensional tetrahedral mesh. It revisits the class of methods based on optimal Delaunay triangulation (ODT) and proposes a proper way of injecting a background density function into the objective function minimized by ODT. This continuous/analytic point of view leads to an objective function that is continuous and Delaunay consistent, in contrast with the discrete/geometrical point of view developed in previous work. To optimize the objective function, this paper proposes a hybrid algorithm that combines a local search (quasi-Newton) with a global optimization (simulated annealing). The benefits of the method are both improved performances and an improved quality of the result in terms of dihedral angles. This results from the combination of two effects. First, the local search has a faster speed of convergence than previous work due to the better behavior of the objective function, and second, the algorithm avoids getting stuck in a poor local minimum. Experimental results are evaluated and compared using standard metrics.

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“…Let n be the outward unit normal vector of ∂D t . Then for a smooth function g(x, t), x ∈ D t , the general Leibniz rule [10] states…”

Section: Weighted Odtmentioning

confidence: 99%

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Chen¹,

Wang²,

Lévy³

et al. 2014

SIAM J. Sci. Comput.

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show abstract

“…First, we introduce the generalized Leibniz rule [43], also called the LeibnizReynolds transport theorem, concerning the differentiation under the integral sign. CapCVT method using different λ's, the CVT method (which is equivalent to our method with λ = 0), the retiling method [42], and Bowers et al's method [28].…”

Section: Properties Of the Capcvt Energymentioning

confidence: 99%

Variational Blue Noise Sampling

Chen

Yuan

Choi

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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Abstract-Blue noise point sampling is one of the core algorithms in computer graphics. In this paper we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including non-photorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces.

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“…Not only the Jacobiandeterminant contribution makes their difference (Ruiz-Montero, Frenkel et al 1997;Heńin, Fiorin et al 2010), but also in a forthcoming paper, we will show that actually change of domains with respect to the coordinate of interest can also contribute to the free-energy profile, i.e., the Leibnizian contribution (Flanders 1973). …”

Section: Classical Free-energy Profile Vs Classical Potential Of Meanmentioning

confidence: 70%

Developing a Systematic Approach for Ab Initio Path-Integral Simulations

Wong¹

2012

Molecular Dynamics - Theoretical Developments and Applications in Nanotechnology and Energy

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Differentiation Under the Integral Sign

Cited by 153 publications

References 0 publications

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Variational Blue Noise Sampling

Developing a Systematic Approach for Ab Initio Path-Integral Simulations

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