scholarly journals Shapes Modeling of 3-D Objects Using B-spline Surface Model Based on Projection Expression

2002 ◽  
Vol 2002 (0) ◽  
pp. 7-12 ◽  
Author(s):  
Makoto Maeda ◽  
Kousuke Kumamaru ◽  
Katsuhiro Inoue
Keyword(s):  
Surface Model ◽  
B Spline ◽  
Model Based ◽  
Spline Surface

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.

A Fast Grid Deformation Algorithm for Aerodynamic Shape Optimization

2010 ◽  
Author(s):  
Kaveh Mohamed ◽  
Kurt Sermeus ◽  
Eric Laurendeau
Keyword(s):  
Optimization Problems ◽  
Flow Simulation ◽  
Surface Model ◽  
Initial Surface ◽  
Surface Mesh ◽  
B Spline ◽  
Mesh Movement ◽  
Spline Surface ◽  
The Difference ◽  
Volume Mesh

A mesh movement algorithm suitable for aerodynamic design optimization problems is presented. It involves B-spline surface construction, projection and evaluation on B-spline faces for the surface mesh movement, as well as inverse-distance and 2D/3D TFI interpolations for the volume mesh deformation. The algorithm is fast and exhibits an excellent parallel efficiency. It is used to deform the surface and volume mesh of an ONERA-M6 wing undergoing several planform changes. The quality of the deformed mesh is preserved as long as the difference between the initial surface mesh and the B-spline surface model is small. A good agreement reported between the flow simulation results on the deformed mesh and those obtained on initial fixed mesh.

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.

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

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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