Shape Tuning in Fully Free-Form Deformation Features

[+] Author and Article Information
J-P. Pernot

 Laboratory 3S - Integrated Design Project, Domaine Universitaire, Grenoble, France  Istituto di Matematical Applicata e Tecnologie, Informatiche - CNR, Via de Marini, Genova, Italypernot@hmg.inpg.fr

S. Guillet

 Laboratory 3S - Integrated Design Project Domaine Universitaire, Grenoble (France)guillet@hmg.inpg.fr

J-C. Léon

 Laboratory 3S - Integrated Design Project Domaine Universitaire, Grenoble (France)leon@hmg.inpg.fr

B. Falcidieno

 Istituto di Matematica Applicata e Tecnologie Informatiche - CNR Via de Marini, Genova (Italy)falcidieno@ge.imati.cnr.it

F. Giannini

 Istituto di Matematica Applicata e Tecnologie Informatiche - CNR Via de Marini, Genova (Italy)giannini@ge.imati.cnr.it

J. Comput. Inf. Sci. Eng 5(2), 95-103 (Feb 04, 2005) (9 pages) doi:10.1115/1.1884146 History: Received September 21, 2004; Revised February 04, 2005

In this paper, an approach for shape tuning and predictable surface deformation is proposed. It pertains to the development of Fully Free Form Deformation Features (δF4) which have been proposed to avoid low-level manipulations of free form surfaces. In our approach, δF4 are applied through the specification of higher level parameters and constraints such as curves and points to be interpolated by the resulting surfaces. From the system perspective, the deformation is performed through the modification of the static equilibrium of bar networks coupled to the control polyhedra of the trimmed patches composing the free form surfaces on which the δF4 are defined. The equations system coming from the constraints specification is often underconstrained, the selection of one among the whole set of possible solutions requires the definition of an optimization problem where an objective function has to be minimized. In this paper we propose a formulation of this optimization problem where the objective function can be defined as a multiple combination of various local quantities related either to the geometry of the bar network (e.g., the length of a bar or the displacement of a node), or to its mechanical characteristics (e.g. the external force applied at a node or a bar deformation energy). Different types of combinations are also proposed and analyzed according to the induced shape behaviors. In this way the shape of a δF4 can be controlled globally, with a unique minimization, or locally with different minimizations applied to subdomains of the surface.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Feature classification based on the level of freedom the user has on the resulting surface

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Figure 2

A dimensionally parameterized δ‐F4

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Figure 3

The various phases of the adopted free form surface deformation process

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Figure 4

Decomposition of the bar network connectivity matrices

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Figure 5

Geometric constraints assignment

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Figure 6

Deformations of a glass model obtained applying different global minimizations with the same target line constraint

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Figure 7

Combination of different minimizations applied to two “full” partitions

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Figure 8

Deformation of a cap considering two vertical partitions

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Figure 9

Cup handle modifications (b) using a bounding sphere (a) for the parameterization of the unary multiminimization

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Figure 10

Examples of shapes obtained while applying some of the basic minimizations to the whole deformation area

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Figure 11

Surface partitioning in the case of one open target line (a) and of one closed target line



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