Fiber Path Optimization of a Composite Lamina Based on Non-uniform Rational B-Spline Surface

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

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Three-dimensional range data interpolation using B-spline surface fitting

10.1117/12.386620 ◽

2000 ◽

Author(s):

Songtao Li ◽

Dongming Zhao

Keyword(s):

Three Dimensional ◽

Surface Fitting ◽

Range Data ◽

Data Interpolation ◽

B Spline ◽

Spline Surface ◽

Dimensional Range

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Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

16th Design Automation Conference: Volume 1 — Computer Aided and Computational Design ◽

10.1115/detc1990-0032 ◽

1990 ◽

Author(s):

Joanna M. Brown ◽

Malcolm I. G. Bloor ◽

M. Susan Bloor ◽

Michael J. Wilson

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Spline Approximation ◽

The Finite Element Method ◽

B Spline ◽

B Splines ◽

Spline Surface ◽

Spline Surfaces ◽

Spline Basis ◽

Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

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Sequential B-Spline Surface Construction Using Multiresolution Data Clouds

Journal of Computing and Information Science in Engineering ◽

10.1115/1.4006000 ◽

2012 ◽

Vol 12 (2) ◽

Author(s):

Yuan Yuan ◽

Shiyu Zhou

Keyword(s):

Control Points ◽

Finite Sample ◽

B Spline ◽

Spline Surface ◽

Spline Surfaces ◽

Filtering Technique ◽

Engineering Practices ◽

Asymptotical Convergence ◽

Surface Construction ◽

Fitting Error

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.

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Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

Mathematical Problems in Engineering ◽

10.1155/2014/706247 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

C. H. Garcia-Capulin ◽

F. J. Cuevas ◽

G. Trejo-Caballero ◽

H. Rostro-Gonzalez

Keyword(s):

Genetic Algorithm ◽

Geometric Modeling ◽

Data Set ◽

Surface Approximation ◽

B Spline ◽

B Splines ◽

Spline Surface ◽

Spline Surfaces ◽

Surface Dimension ◽

Hierarchical Genetic Algorithm

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.

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