An optimization method for elastic shape matching

Buhan, Maya de; Dapogny, Charles; Frey, Pascal; Nardoni, Chiara

doi:10.1016/j.crma.2016.05.007

Cited by 7 publications

(11 citation statements)

References 11 publications

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“…They do not allow for general deformations of source vertices onto the target surface, and the approach is quite heavy computationally due to the use of the product manifold. The elastic matching of volumetric shapes from the perspective of shape optimization has been investigated by Buhan et al [dBDFN16]. Finally, Iglesias et al [IRS18] have applied elastic energies for computing correspondences between level‐set surfaces.…”

Section: Related Workmentioning

confidence: 99%

Elastic Correspondence between Triangle Meshes

Ezuz

Heeren

Azencot

et al. 2019

Computer Graphics Forum

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We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes.

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Section: Related Workmentioning

confidence: 99%

Elastic Correspondence between Triangle Meshes

Ezuz

Heeren

Azencot

et al. 2019

Computer Graphics Forum

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“…• Functionals of the form (19), based on the signed distance function have already been used in [28] (or prior in [11]) in the contexts of shape morphing and shape registration. • Different functionals P (Ω) from (19) could be devised for the same shape matching purpose; for instance, one may imagine using a least-square functional of the form:…”

Section: 1mentioning

confidence: 99%

“…In a first experiment, we seek to minimize the compliance of the considered structures, under a volume constraint, namely: (28) min…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The compliance of Ω T is very high (C(Ω T ) = 48693), and we would like to improve its structural performance, that is to optimize the shape Ω in view of its compliance so that it has the same material volume |Ω|= V T , while staying 'close' to Ω T . Unfortunately, solving (28) with Ω T as an initial guess gives no guarantee that the resulting optimized shape will retain any resemblance with Ω T , as evidenced in Figure 10 In order to incorporate the desired aesthetic information, we trade (28) for the new optimization problem (29), (29) min…”

Section: Numerical Examplesmentioning

confidence: 99%

“…At first, a simple minimization of the compliance C(Ω) of the bridge under the volume constraint Vol(Ω) = V T is performed -i.e. (28) is solved -where the target volume is the fraction V T = 0.1|D| of that of the working domain D, and D acts as an initial shape. One can see that the resulting optimized shape Ω * contains regions with large thickness in the (yz)-plane, although its isotropic maximum thickness is low.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Geometric constraints for shape and topology optimization in architectural design

et al. 2017

Self Cite

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To cite this version:Charles Dapogny, Alexis Faure, Georgios Michailidis, Grégoire Allaire, Agnes Couvelas, et al.. Geometric constraints for shape and topology optimization in architectural design.Abstract. This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.

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A level set shape metamorphosis with mechanical constraints for geometrically graded microstructures

Zhou

Kim

2019

Struct Multidisc Optim

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Functional performance benefits brought by graded materials or a variation of microstructures have been established. However, the challenge of connecting the adjacent microstructures remains open. Without connected microstructures, the design is only theoretical and cannot be realized in practice. This paper presents a shape metamorphosis approach to address this challenge. The approach formulates an optimization problem to minimize the difference between two shapes, where the shapes generated during the optimization iterations form the graded microstructures. A stiffness-based constraint is proposed to eliminate potential breakage or shrinkages in generating the intermediate shapes, which are used to build a transition zone for the two shapes to be connected. This also ensures that the optimal functionality is not compromised significantly. A series of numerical studies demonstrate that the proposed approach is capable of producing smoothly connected microstructures for multiscale optimization.

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An optimization method for elastic shape matching

Cited by 7 publications

References 11 publications

Elastic Correspondence between Triangle Meshes

Elastic Correspondence between Triangle Meshes

Geometric constraints for shape and topology optimization in architectural design

A level set shape metamorphosis with mechanical constraints for geometrically graded microstructures

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