scholarly journals Fuzzy B-Spline Surface Modeling

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
R. U. Gobithaasan
Keyword(s):  
Final Section ◽  
Uncertain Data ◽  
Surface Modeling ◽  
Surface Model ◽  
Data Sets ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Data Points

This paper discusses the construction of a fuzzy B-spline surface model. The construction of this model is based on fuzzy set theory which is based on fuzzy number and fuzzy relation concepts. The proposed theories and concepts define the uncertainty data sets which represent fuzzy data/control points allowing the uncertainties data points modeling which can be visualized and analyzed. The fuzzification and defuzzification processes were also defined in detail in order to obtain the fuzzy B-spline surface crisp model. Final section shows an application of fuzzy B-spline surface modeling for terrain modeling which shows its usability in handling uncertain data.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

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.

On the Modeling and Analysis of an Improved CNC Interpolation Algorithm

2009 ◽  
Vol 626-627 ◽  
pp. 459-464 ◽  
Author(s):  
Lei Luo ◽  
L. Wang ◽  
Jun Hu
Keyword(s):  
Interpolation Method ◽  
Control Points ◽  
Interpolation Algorithm ◽  
Modeling And Analysis ◽  
B Spline ◽  
Spline Curve ◽  
Spline Surface ◽  
Cnc Interpolation ◽  
Data Points ◽  
Back Calculation

An improved interpolation method is presented based on B-spline curve back calculation which regards data points as control points. First, a B-spline surface reconstruction is done, and a favorable condition for real-time interpolation can be provided for NC machining. Then, by prejudging the trajectory feedrate, the tangent vectors of spline curve junction can be calculated, which can be used to establish the spline curve equations based on time. At last, with the equations mentioned above, the trajectory and feedrate profile can be generated simultaneously by the improved interpolation algorithm. An error analysis is also discussed and the feasibility of the improved algorithm is verified by the simulation results.

Iterative Genetic-Algorithm-Based Surface Reconstruction Method for Repair of Twisted Blade

2014 ◽  
Vol 722 ◽  
pp. 125-130 ◽  
Author(s):  
Hai Dong Wu ◽  
Jie Dong Chen
Keyword(s):  
Genetic Algorithm ◽  
Surface Reconstruction ◽  
Complex Surface ◽  
Reconstruction Method ◽  
Control Points ◽  
Least Squares Approximation ◽  
B Spline ◽  
Spline Surface ◽  
Data Points ◽  
Twisted Blade

When remanufacturing complex surface parts, such as twisted blade, it is difficult to obtain an accurate model. An iterative Genetic-algorithm-based-surface reconstruction method for repair of twisted blade is presented. Genetic algorithm is applied in parametrizing data points and computing knot vectors. Then, the control points of the fitting B-spline surface are calculated by least-squares approximation through either SVD or LU methods. It shows that the accuracy of the method is improved significantly when three different twisted blades surfaces are verified by using the method.

Sequential B-Spline Surface Construction Using Multiresolution Data Clouds

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.

scholarly journals A Reconstruction Algorithm for Blade Surface Based on Less Measured Points

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jia Liu ◽  
Ji Zhao ◽  
Xu Yang ◽  
Jiming Liu ◽  
Xingtian Qu ◽  
...  
Keyword(s):  
Reconstruction Algorithm ◽  
Surface Model ◽  
Machining Accuracy ◽  
Blade Surface ◽  
B Spline ◽  
Design Concepts ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Machining Allowance ◽  
Curvature Continuity

A reconstruction algorithm for blade surface from less measured points of section curves is given based on B-spline surface interpolation. The less measured points are divided into different segments by the key geometric points and throat points which are defined according to design concepts. The segmentations are performed by different fitting algorithms with consideration of curvature continuity as their boundary condition to avoid flow disturbance. Finally, a high-quality reconstruction surface model is obtained by using the B-spline curve meshes constructed by paired points. The advantage of this algorithm is the simplicity and effectivity reconstruction of blade surface to ensure the aerodynamic performance. Moreover, the obtained paired points can be regarded as measured points to measure and reconstruct the blade surface directly. Experimental results show that the reconstruction blade surface is suitable for precisely representing blade, evaluating machining accuracy, and analyzing machining allowance.

Filling N-Sided Holes With Trimmed B-Spline Surfaces Based on Energy-Minimization Method

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiaodong Liu
Keyword(s):  
Energy Minimization ◽  
Computer Aided Design ◽  
Control Points ◽  
Minimization Method ◽  
B Spline ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Key Issues ◽  
Complex Constraints ◽  
Aided Design

Using a trimmed rectangular B-Spline surface to fill an n-sided hole is a much desired operation in computer aided design (CAD), but few papers have addressed this issue. Based on an energy-minimization or variational B-Spline technique, the paper presents the technique of using one single trimmed rectangular B-Spline surface to fill an n-sided hole. The method is efficient and robust, and takes a fraction of a second to fill n-sided holes with high-quality waterproof B-Spline surfaces under complex constraints. As the foundation of filling n-sided holes, the paper also presents the framework and addresses the key issues on variational B-Spline technique. Without any precalculation, the variational B-Spline technique discussed in this paper can solve virtually any B-Spline surface with up to 20,000 control points in real time, which is much more efficient and powerful than previous work in the variational B-Spline field. Moreover, the result is accurate and satisfies CAD systems' high-precision requirements.

Filling N-Sided Holes Using Trimmed B-Spline Surfaces

2012 ◽  
Author(s):  
Xiaodong Liu
Keyword(s):  
Energy Minimization ◽  
Control Points ◽  
Variational Technique ◽  
High Quality ◽  
B Spline ◽  
Cad Systems ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Key Issues ◽  
Complex Constraints

Using one single trimmed B-Spline surface to fill an n-sided hole is a much desired operation in CAD, but few papers have addressed this issue. The paper presents the method of using trimmed B-Spline surfaces to fill n-sided holes based on energy minimization or variational technique. The method is efficient and robust, and takes less than one second to fill n-sided holes with high quality B-Spline surfaces under complex constraints. As the foundation of filling n-sided holes, some key issues on variational B-Spline technique are also discussed. The variational technique discussed is significantly much more efficient and powerful than previous research, and the result is very accurate to satisfy CAD systems’ high-precision requirements. We demonstrate that, without any pre-calculation, the discussed technique is efficient enough to solve a B-Spline surface with up to 20,000 control points in real time while satisfying an arbitrary combination of point and curve constraints.

Curve and Surface Representation by Iterative B-Spline Fit to a Data Point Set

1987 ◽  
Vol 16 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Marilyn Lord
Keyword(s):  
Computer Aided Design ◽  
Control Point ◽  
The Body ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Data Points ◽  
Point Set ◽  
Support Surfaces ◽  
Aided Design

The method of B-splines provides a very powerful way of representing curves and curved surfaces. The definition is ideally suited to applications in Computer Aided Design (CAD) where the designer is required to remodel the surface by reference to interactive graphics. This particular facility can be advantageous in CAD of body support surfaces, such as design of sockets of limb prostheses, shoe insoles, and custom seating. The B-spline surface is defined by a polygon of control points which in general do not lie on the surface, but which form a convex hull enclosing the surface. Each control point can be adjusted to remodel the surface locally. The resultant curves are well behaved. However, in these biomedical applications the original surface prior to modification is usually defined by a limited set of point measurements from the body segment in question. Thus there is a need initially to define a B-spline surface which interpolates this set of data points. In this paper, a computer-iterative method of fitting a B-spline surface to a given set of data points is outlined, and the technique is demonstrated for a curve. Extension to a surface is conceptually straightforward.

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