Mean value coordinates in 3D

Floater, Michael S.; Kós, Géza; Reimers, Martin

doi:10.1016/j.cagd.2005.06.004

Cited by 230 publications

(182 citation statements)

References 4 publications

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“…Examples of generalized barycentric coordinates are Wachspress coordinates [42], mean value coordinates [12,13,18,43], Laplace interpolants [17], harmonic coordinates [21,25], and maximum entropy coordinates [31,19].…”

Section: Introductionmentioning

confidence: 99%

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Sieger

Alliez

Botsch

2010

Proceedings of the 19th International Meshing Roundtable

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Summary. We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities-short edges in the Voronoi diagram. We evaluate our method on a 2D Poisson problem and demonstrate that our simple but effective optimization achieves a significant improvement of the stiffness matrix condition number.

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Section: Introductionmentioning

confidence: 99%

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Sieger

Alliez

Botsch

2010

Proceedings of the 19th International Meshing Roundtable

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“…MVCs for polygons were initially 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 introduced in two dimensions as a means to achieve smooth information interpolations in generic polygons. Later, in [15], the method was extended by applying it to 3D triangular meshes. In [16], Laplace equations called harmonic coordinates (HC) were used to define the displacement of an object's vertices based on the deformation of the surrounding cage.…”

Section: B) Cage-basedmentioning

confidence: 99%

A new methodological approach for shoe sole design and validation

Davia-Aracil

Jimeno-Morenilla

Salas

2016

Int J Adv Manuf Technol

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Abstract. Shoe soles are extremely complex to design and manufacture due to their organically shaped but technically precise nature and their manufacturing constraints. Consequently, there is a need for the increased design process flexibility offered by the use of specific CAD methodologies and techniques, to facilitate the work of expert designers and permit effective construction of the three-dimensional elements comprising the complete structure. Recent advances in additive manufacturing systems have extended the possibilities of shoe sole design. These systems can be used to create the final mould and to incorporate dynamic elements that are of particular value in sports footwear. In this article, we present a new methodology for the design and validation of shoe soles. The methodology assists designers in the design concept process and in transfer of the design to manufacturing. The model incorporates both a structural and a functional approach. To this end, a set of specific tools have been developed that can be used to quantify design quality. For example, the model calculates the coefficient of friction, or slip resistance, necessary to comply with international standards concerning safety footwear.Keywords: shoe sole design, additive manufacturing, rapid prototyping, parametric design, shoe slip resistance. Highlights  This paper presents a new methodological techniqueto design complex footwear soles.  It shows how to specific CAD/CAE tools can improve footwear sole 2D/3D design shorting time and validating final model for manufacturing.  It also shows how to additive manufacturing can be used in footwear industry for shoe sole mould production.  A full practical case of shoe sole design is presented.

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“…Initially, Floater introduced the MVCs for two-dimensional polygons as a way to achieve smooth information interpolations in polygons. Later, in [52] the method was expanded, applying it to three-dimensional triangle meshes. Other works appear in the area of automatic deformation control mesh creation: in [53] the semi-automatic creation of skinning templates is proposed for use through these deformation techniques.…”

Section: Bio-deformable Foot Modelmentioning

confidence: 99%

Footwear bio-modelling: An industrial approach

Davia

Jimeno-Morenilla

Salas

2013

Computer-Aided Design

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There is a growing need within the footwear sector to customise the design of the last from which a specific footwear style is to be produced. This customisation is necessary for user comfort and health reasons, as the user needs to wear a suitable shoe. For this purpose, a relationship must be established between the user foot and the last with which the style will be made; up until now, no model has existed that integrates both elements. On the one hand, traditional customised footwear manufacturing techniques are based on purely artisanal procedures which make the process arduous and complex; on the other hand, geometric models proposed by different authors present the impossibility of implementing them in an industrial environment with limited resources for the acquisition of morphometric and structural data for the foot, apart from the fact that they do not prove to be sufficiently accurate given the non similarity of the foot and last. In this paper, two interrelated geometric models are defined, the first, a bio-deformable foot model and the second, a deformable last model. The experiments completed show the goodness of the model, with it obtaining satisfactory results in terms of comfort, efficiency and precision, which make it viable for use in the sector. Footwear Bio-modelling: An industrial approachAbstract. There is a growing need within the footwear sector to customise the design of the last from which a specific footwear style is to be produced. This customisation is necessary for user comfort and health reasons, as the user needs to wear a suitable shoe. For this purpose, a relationship must be established between the user foot and the last with which the style will be made; up until now, no model has existed that integrates both elements. On the one hand, traditional customised footwear manufacturing techniques are based on purely artisanal procedures which make the process arduous and complex; on the other hand, geometric models proposed by different authors present the impossibility of implementing them in an industrial environment with limited resources for the acquisition of morphometric and structural data for the foot, apart from the fact that they do not prove to be sufficiently accurate given the non similarity of the foot and last. In this paper, two interrelated geometric models are defined, the first, a bio-deformable foot model and the second, a deformable last model. The experiments completed show the goodness of the model, with it obtaining satisfactory results in terms of comfort, efficiency and precision, which make it viable for use in the sector. -There are many different possibilities to adapt the foot surface to the last pitch (heel height). Cage-based methods (exoskeletons) perform better than others when it comes to the deformation of the surface, in that the cage can be better controlled and adapted to the foot morphology, allowing bending areas to be more accurately defined according to the characteristic curves of the foot. The paper rules out Free Form Deforma...

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Mean value coordinates in 3D

Cited by 230 publications

References 4 publications

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

A new methodological approach for shoe sole design and validation

Footwear bio-modelling: An industrial approach

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