Modeling dynamic developable meshes by the Hamilton principle

Liu, Yong-Jin; Tang, Kai; Joneja, Ajay

doi:10.1016/j.cad.2007.02.013

Cited by 20 publications

(15 citation statements)

References 16 publications

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“…Most existing methods for this kind of simulations are physically based (cf., [26], [27], [28], [29], [30], [31], and [32]), which usually require extremely long computing time and in most cases are not capable of maintaining developability on the cloth since the cloth is always assumed to be elastic (extensible). In their recent impressive work [33], Goldenthal et al improved it by forbidding the extensibility in two mutually orthogonal directions, warp and weft, on the cloth; nevertheless, the developability is neither explicitly addressed nor analyzed in [33].…”

Section: Resultsmentioning

confidence: 99%

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

Tang

Chen

2009

IEEE Trans. Visual. Comput. Graphics

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Abstract-We present a new algorithm for finding a most "developable" smooth mesh surface to interpolate a given set of arbitrary points or space curves. Inspired by the recent progress in mesh editing that employs the concepts of preserving the Laplacian coordinates and handle-based shape editing, we formulate the interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, such as a planar figure, to a final mesh surface that interpolates the given points and/or curves. During the deformation, the developability of the intermediate mesh is maintained by means of preserving the zero-valued Gaussian curvature on the mesh. To treat the high nonlinearity of the geometric constrains owing to the preservation of Gaussian curvature, we linearize those nonlinear constraints using Taylor expansion and eventually construct a sparse and overdetermined linear system that is subsequently solved by a robust least squares solution. By iteratively performing this procedure, the initial mesh is gradually and smoothly "dragged" to the given points and/or curves. The initial experimental tests have shown some promising aspects of the proposed algorithm as a general quasi-developable surface interpolation tool.

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Section: Resultsmentioning

confidence: 99%

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

Tang

Chen

2009

IEEE Trans. Visual. Comput. Graphics

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“…Bergou et al [2006] introduced the nonconforming elements we use in the context of deriving a compact stencil for bending forces on conforming meshes; our work generalizes this to use them for in-plane dynamics to solve locking. Liu et al [2007] imposed developability as a constraint on conforming triangle meshes, proving that n triangles give you O( √ n) degrees of freedom. Unfortunately, those degrees of freedom suffer from mesh-dependent artifacts which do not vanish under refinement: this is the clearest illustration in the literature of the locking problem we face, and motivates why we need a new method.…”

Section: Previous Workmentioning

confidence: 99%

Animating developable surfaces using nonconforming elements

English¹,

Bridson²

2008

ACM SIGGRAPH 2008 Papers

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We present a new discretization for the physics-based animation of developable surfaces. Constrained to not deform at all in-plane but free to bend out-of-plane, these are an excellent approximation for many materials, including most cloth, paper, and stiffer materials. Unfortunately the conforming (geometrically continuous) discretizations used in graphics break down in this limit. Our nonconforming approach solves this problem, allowing us to simulate surfaces with zero in-plane deformation as a hard constraint. However, it produces discontinuous meshes, so we further couple this with a "ghost" conforming mesh for collision processing and rendering. We also propose a new second order accurate constrained mechanics time integration method that greatly reduces the numerical damping present in the usual first order methods used in graphics, for virtually no extra cost and sometimes significant speed-up.

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“…Structural elegance, these and many other contributions are in contrast to recent free-form architecture. Applied mathematics and in particular geometry have initiated the implementation of comprehensive frameworks for modeling and mastering the complexity of today's architectural needs shapes in an optimal sense by ruled surfaces, (CARMO, 1976;LIUA et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

<b>New type surfaces in terms of B-Smarandache Curves in Sol<sup>3

Körpınar

2015

Acta Sci. Technol.

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ABSTRACT. In this work, new type ruled surfaces in terms of B-Smarandache TM 1 curves of biharmonic B-slant helices in the SOL 3 are studied. We characterize the B-Smarandache TM 1 curves in terms of their Bishop curvatures. Additionally, we express some interesting relations.Keywords: bienergy, B-slant helix, sol space, curvature, ruled surface. Novos tipos de superfícies conforme as Curvas de B-Smarandache em Sol 3RESUMO. Analisa-se novos tipos de superfícies conforme as curvas B-Smarandache TM 1 das hélices com inclinação B bi-harmonica. Caracterizam-se as curvas B-Smarandache TM 1 conforme as curvaturas de Bishop, acresentando outras relações interessantes.

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Modeling dynamic developable meshes by the Hamilton principle

Cited by 20 publications

References 16 publications

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

Animating developable surfaces using nonconforming elements

<b>New type surfaces in terms of B-Smarandache Curves in Sol<sup>3

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