Comparison of B-Spline Surface and Free-Form Deformation Geometry Control for Aerodynamic Optimization

AIAA Journal ◽  
2017 ◽  
Vol 55 (1) ◽  
pp. 228-240 ◽  
Author(s):  
Christopher Lee ◽  
David Koo ◽  
David W. Zingg
Keyword(s):  
Free Form ◽  
Aerodynamic Optimization ◽  
B Spline ◽  
Spline Surface ◽  
Free Form Deformation

Computation of Voxel Maps Containing Tool Access Directions for Machining Free-Form Shapes

1996 ◽  
Author(s):  
Johan W. H. Tangelder ◽  
Joris S. M. Vergeest ◽  
Mark H. Overmars
Keyword(s):  
Free Form ◽  
Geometric Accuracy ◽  
Surface Sampling ◽  
B Spline ◽  
Spline Surface ◽  
Surface Data

Abstract An algorithm that derives tool access directions for machining free-form shapes is presented. A free-form shape to be machined is given by a preliminary B-spline model. We allow that the B-spline surface data are as inaccurate as the user-selected geometric accuracy of the prototype to be machined. Using surface sampling a visibility voxel map is obtained. From this map a voxel map is derived that contains per voxel a set of tool access directions. From the obtained voxel map regions can be selected that can be machined with a fixed tool access direction per region.

An Efficient Sensing Localization Algorithm for Free-Form Surface Digitization

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Yunbao Huang ◽  
Xiaoping Qian
Keyword(s):  
Search Time ◽  
Divide And Conquer ◽  
Free Form ◽  
Point Problem ◽  
Localization Algorithm ◽  
B Spline ◽  
Divide And Conquer Algorithm ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Free Form Surface

We present a divide-and-conquer method that efficiently finds a near-optimal distribution of sensing locations for free-form surface digitization. We formulate a next-best-point problem and transform the uncertainty of a B-spline surface into a higher-dimensional B-spline surface. This technique allows the use of the convex hull and subdivision properties of B-spline surfaces in the divide-and-conquer algorithm. It thus greatly reduces the search time for determining the next best sensing location.

PB-Spline Hybrid Surface Fitting Technique

2009 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Large Scale ◽  
Free Form ◽  
Rectangular Array ◽  
B Spline ◽  
Large Scale Data ◽  
Spline Surface ◽  
Spline Basis ◽  
Data Points ◽  
Free Form Surfaces ◽  
Scale Data

This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization of tensor product splines, are adopted. The basic idea of this paper is to fit large scale data with a tensorial B-spline surface and to refine the surface until a specified tolerance is met. Since some isolated domains exceeding tolerance may result, detail features on these domains are modeled by a tensorial B-spline basis with a finer resolution, superimposed by employing the PB-spline approach. The present method leads to an efficient model of free form surfaces, since both large scale data and local geometrical details can be efficiently fitted. Two application examples are presented. The first one concerns the fitting of a set of data points sampled from an interior car trim with a central geometrical detail. The second one refers to the modification of the tensorial B-spline surface representation of a mould in order to create a local adjustment. Considerations regarding strengths and limits of the approach then follow.

Accurate B-spline Free-Form Deformation of Polygonal Objects

1998 ◽  
Vol 3 (3) ◽  
pp. 11-27 ◽  
Author(s):  
Jieqing Feng ◽  
Pheng-Ann Heng ◽  
Tien-Tsin Wong
Keyword(s):  
Free Form ◽  
B Spline ◽  
Free Form Deformation

Reproducing Existing Nacelle Geometries With the Free-Form Deformation Parametrization

2018 ◽  
Author(s):  
Konstantin Rusch ◽  
Martin Siggel ◽  
Richard-Gregor Becker
Keyword(s):  
Inverse Problem ◽  
Spline Approximation ◽  
Aircraft Design ◽  
Free Form ◽  
Design Phase ◽  
B Spline ◽  
Preliminary Aircraft Design ◽  
Least Squares Fit ◽  
Free Form Deformation ◽  
Grid Points

In the conceptual and preliminary aircraft design phase the Free-Form Deformation (FFD) is one of various parametrization schemes to define the geometry of an engine’s nacelle. This paper presents a method that is able to create a C2 continuous periodic approximation of existing reference nacelles with the B-spline based FFD, which is a generalization of the classical FFD. The basic principle of this method is to start with a rotational symmetric B-spline approximation of the reference nacelle, which is subsequently deformed with a FFD grid that is placed around the initial geometry. A method is derived that computes the displacement of the FFD grid points, such that the deformed nacelle approximates the reference nacelle with minimal deviations. As this turns out to be a linear inverse problem, it can be solved with a linear least squares fit. To avoid overfitting effects — like degenerative FFD grids which imply excessive local deformations — the inverse problem is regularized with the Tikhonov approach. The NASA CRM model and the IAE V2500 engine have been selected as reference geometries. Both resemble nacelles that are typically found on common aircraft models and both deviate sufficiently from the rotational symmetry. It is demonstrated that the mean error of the approximation decreases with an increase of the number of FFD grid points and how the regularization affects these results. Finally, the B-spline based FFD with the classical Bernstein based FFD are compared for both models. The results conceptually prove the usability of the FFD approach for the construction of nacelle geometries in the preliminary aircraft design phase.

Real-time B-spline Free-Form Deformation via GPU acceleration

2013 ◽  
Vol 37 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
Yuanmin Cui ◽  
Jieqing Feng
Keyword(s):  
Real Time ◽  
Gpu Acceleration ◽  
Free Form ◽  
B Spline ◽  
Free Form Deformation
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