3D sketching for aesthetic design using fully free-form deformation features

To limit low-level manipulations of free-form surfaces, the concept of Fully Free Form Deformation Features (δ-F4) have been introduced. They correspond to shapes obtained by deformation of a surface area according to specified geometric constraints. In our work, we mainly focused on those features aimed at enforcing the visual effect of the so-called character lines, extensively used by designers to specify the shape of an object. Therefore, in the proposed approach, 3D lines are used to drive surface deformation over specified areas. Depending on the wished shape and reflection light effects, the insertion of character lines may generate surface tangency discontinuities. In CAD systems, such kind of discontinuities is generally created by a decomposition of the initial surface into several patches. This process can be tedious and very complex, depending on the shape of the deformation area and the desired surface continuity. Here, a method is proposed to create discontinuities on a surface, using the trimming properties of surfaces. The corresponding deformation features produce the resulting surface in a single modification step and handle simultaneously more constraints than current CAD systems. The principle of the proposed approach is based on arbitrary shaped discontinuities in the parameter domain of the surface to allow the surface exhibiting geometric discontinuities at user-prescribed points or along lines. The proposed approach is illustrated with examples obtained using our prototype software.

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Fully free-form deformation features for aesthetic shape design

Journal of Engineering Design ◽

10.1080/09544820500031617 ◽

2005 ◽

Vol 16 (2) ◽

pp. 115-133 ◽

Cited By ~ 18

Author(s):

Jean-philippe Pernot ◽

Bianca Falcidieno ◽

Franca Giannini ◽

Jean-claude Léon

Keyword(s):

Free Form ◽

Shape Design ◽

Free Form Deformation ◽

Deformation Features

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Shape Tuning in Fully Free-Form Deformation Features

Journal of Computing and Information Science in Engineering ◽

10.1115/1.1884146 ◽

2005 ◽

Vol 5 (2) ◽

pp. 95-103 ◽

Cited By ~ 13

Author(s):

J-P. Pernot ◽

S. Guillet ◽

J-C. Léon ◽

B. Falcidieno ◽

F. Giannini

Keyword(s):

Objective Function ◽

Optimization Problem ◽

Surface Deformation ◽

Deformation Energy ◽

Free Form ◽

System Perspective ◽

Free Form Deformation ◽

Deformation Features ◽

Shape Tuning ◽

Free Form Surfaces

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 (δ‐F4) which have been proposed to avoid low-level manipulations of free form surfaces. In our approach, δ‐F4 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 δ‐F4 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 δ‐F4 can be controlled globally, with a unique minimization, or locally with different minimizations applied to subdomains of the surface.

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Multi-minimisations for shape control of fully free-form deformation features (γ-F/sup 4/)

Proceedings Shape Modeling Applications, 2004. ◽

10.1109/smi.2004.1314493 ◽

2004 ◽

Author(s):

J.-P. Pernot ◽

S. Guillet ◽

J.-C. Leon ◽

B. Falcidieno ◽

F. Giannini

Keyword(s):

Shape Control ◽

Free Form ◽

Free Form Deformation ◽

Deformation Features

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Airfoil Optimization Using Area-Preserving Free-Form Deformation

Volume 1: Advances in Aerospace Technology ◽

10.1115/imece2015-50904 ◽

2015 ◽

Author(s):

Stavros N. Leloudas ◽

Giorgos A. Strofylas ◽

Ioannis K. Nikolos

Keyword(s):

Cross Sectional Area ◽

Equality Constraint ◽

Optimization Process ◽

Free Form ◽

Sectional Area ◽

Cross Sectional ◽

Airfoil Optimization ◽

Free Form Deformation ◽

Correction Problem ◽

Area Preserving

Given the importance of structural integrity of aerodynamic shapes, the necessity of including a cross-sectional area equality constraint among other geometrical and aerodynamic ones arises during the optimization process of an airfoil. In this work an airfoil optimization scheme is presented, based on Area-Preserving Free-Form Deformation (AP FFD), which serves as an alternative technique for the fulfillment of a cross-sectional area equality constraint. The AP FFD is based on the idea of solving an area correction problem, where a minimum possible offset is applied on all free-to-move control points of the FFD lattice, subject to the area preservation constraint. Due to the linearity of the area constraint in each axis, the extraction of an inexpensive closed-form solution to the area preservation problem is possible by using Lagrange Multipliers. A parallel Differential Evolution (DE) algorithm serves as the optimizer, assisted by two Artificial Neural Networks as surrogates. The use of multiple surrogate models, in conjunction with the inexpensive solution to the area correction problem, render the optimization process time efficient. The application of the proposed methodology for wind turbine airfoil optimization demonstrates its applicability and effectiveness.

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