scholarly journals The Calculation of Roughness Uncertainty by Fitting B-Spline Filter Assessment Middle Lines

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Gaiyun He ◽  
Chenhui Liu ◽  
Yicun Sang ◽  
Xiaochen Sun
Keyword(s):  
Surface Morphology ◽  
Least Square ◽  
Spline Smoothing ◽  
Middle Line ◽  
B Spline ◽  
Test Part ◽  
Smoothing Filter ◽  
Line Method ◽  
Spline Filter

The roughness and uncertainty are important parameters of surface morphology. The least square middle line method is often used to estimate the roughness and its uncertainty. However, the roughness and its uncertainty obtained by the least square middle line method are inaccurate. This paper proposes a method to calculate exactly the roughness and its uncertainty by piecewise fitting the smooth B-spline filter assessment middle lines. A B-spline smoothing filter is selected to determine the assessment middle line of roughness. The B-spline filter can not only give the accurate roughness, but also obtain the smooth assessment middle line. The model of roughness uncertainty is proposed by piecewise fitting B-spline filter middle lines as the quadratic curves. The S-shaped test part is used to verify the model of roughness uncertainty.

Optimization of regularized B-spline smoothing for turbulent Lagrangian trajectories

2021 ◽  
pp. 110376
Author(s):  
Adam Cheminet ◽  
Yasar Ostovan ◽  
Valentina Valori ◽  
Christophe Cuvier ◽  
Fançois Daviaud ◽  
...  
Keyword(s):  
Spline Smoothing ◽  
B Spline

scholarly journals Influence of curve fitting techniques on hydrostatic characteristics of ship

1970 ◽  
Vol 39 (2) ◽  
pp. 100-112
Author(s):  
Md Mashud Karim ◽  
Md Ashim Ali ◽  
Kho. Sahriar Iqbal
Keyword(s):  
Curve Fitting ◽  
Mechanical Engineering ◽  
Cubic Spline ◽  
Ship Hull ◽  
Least Square ◽  
Ship Stability ◽  
Hull Form ◽  
B Spline ◽  
Using Data ◽  
Table Data

This paper presents influence of curve fitting techniques on hydrostatic characteristics of marine vessels.  Three vessels having lengths of 32.16m, 70.0m and 25.6m are selected for this study. The hull geometries of these vessels are represented by three curve fitting techniques such as least square, cubic spline and B-spline methods. At first, hydrostatic characteristics of the vessels are calculated using data only available in offset table and then using more data generated by curve fitting techniques. Finally, results obtained by offset table data are compared to those by fitted data. It is seen that there are some influences of curve fitting technique on the hydrostatic characteristics of ship especially at lightly loaded condition. Keywords: Curve fitting technique, ship hull form, offset table, hydrostatic characteristics, ship stability, cross curve. doi:10.3329/jme.v39i2.1853 Journal of Mechanical Engineering, Vol. ME39, No. 2, Dec. 2008 100-112

scholarly journals Modeling technology of curved surface development for puffer fish

2020 ◽  
Vol 12 (4) ◽  
pp. 168781402091602
Author(s):  
Honggen Zhou ◽  
Jie Cui ◽  
Guizhong Tian ◽  
Yesheng Zhu ◽  
Changfeng Jia
Keyword(s):  
Three Dimensional ◽  
Least Square ◽  
Curved Surface ◽  
B Spline ◽  
Implicit Equation ◽  
Moving Least Square ◽  
Average Value ◽  
Modeling Technology ◽  
Surface Development ◽  
Puffer Fish

The drag reduction mechanism of puffer epidermis was closely related to its real geometry. In order to solve the modeling problem of epidermal spines on the puffer surface, a modeling method for the expansion of puffer shape was proposed. The three-dimensional scanning and non-uniform rational B-spline surface modeling technology was used to reconstruct the puffer model. According to the curvature characteristics, the surface mathematical equations including exponential, logarithmic, and sinusoidal functions were established based on the multinomial function. The surface was generated by a mathematical equation, and the surface was divided into several non-uniform rational B-spline patches according to curvature. After discretization, the point cloud Gaussian curvature and average value were calculated based on the implicit equation of moving least square surface, and whether the surface is approximately extensible or not was judged. Finally, the puffer surface was divided into 46 curved patches. In this article, the surface expansion algorithm gave priority to ensure the area unchanged, and four feature surfaces were selected according to the epidermal spines arrangement of the puffer surface. The results showed that the technique can simply and efficiently unfold the curved surface of the puffer fish, thus the mapping relationship between the epidermal spines on the surface and the plane was determined, which established a foundation for the accurate arrangement and modeling of the epidermal spines on the surface.

USE OF B-SPLINE FUNCTION IN ELEMENT FREE GALERKIN METHOD FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATION

2009 ◽  
Vol 06 (03) ◽  
pp. 349-360
Author(s):  
K. SANDEEP ◽  
K. KAMAL KUMAR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Spline Function ◽  
Least Square ◽  
Partial Differential ◽  
Order Continuity ◽  
B Spline ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

The paper presents application of a B-spline function in place of a shape function obtained by using moving least square approximant with B-spline weight and linear basis. The piecewise polynomial function of B-spline with C2 and lower order continuity is efficiently used in element free Galerkin (EFG) method to generate a new fast algorithm for the solution of one-dimensional partial differential equation. The support of B-spline function is assumed as the domain of influence of EFG method. The results of bar deflection are compared with those obtained by other researchers.

Lagrangian Analysis Method with Least Square Cubic B-Spline

2011 ◽  
Vol 94-96 ◽  
pp. 1681-1684
Author(s):  
Wei Jun Tao ◽  
Shi Huan ◽  
Xiang Qian Tan ◽  
Guo Ping Jiang
Keyword(s):  
Least Square ◽  
Analysis Method ◽  
Lagrangian Analysis ◽  
B Spline ◽  
One Dimensional ◽  
Field Information ◽  
Strain Stress ◽  
Stress Profiles ◽  
Physical Quantities ◽  
Stress Relation

The Lagrangian analysis method is re-analyzed. It is shown that when a series of stress profiles (or strain profiles, or particle velocity profiles) are measured to determine the strain-stress relation. In this paper, the stress histories at different Lagrange positions are measured by one dimensional SHPB experiments. The variation histories of various physical quantities are fitted to least square cubic B-spline function with a sufficient accuracy definite condition. The path lines of these quantities are constructed in terms of a least square quadratic polynomial. A program for inert flow of Lagrangian analysis (IFLA) is worked out. Taking the data of experiments as the input for the IFLA, the flow field information is solved. The error analysis shows that such a method has a definite reliability and stability.

The Application of Surface Fairing Technique in Progressive Lens Processing

2007 ◽  
Vol 364-366 ◽  
pp. 1246-1250
Author(s):  
Jian Jun Du ◽  
Suet To ◽  
Chi Fai Cheung ◽  
Wing Bun Lee ◽  
Xiang Wen Miao
Keyword(s):  
Single Point ◽  
Least Square ◽  
Spline Method ◽  
Diamond Cutting ◽  
B Spline ◽  
Ultra Precision ◽  
Progressive Lenses

Based on the analysis of characteristics of progressive lens, it can be found that lens uneven change of curvature is an important reason of defect on progressive lens processed by single-point diamond cutting technique. By applying least square fairing method to fair the surface which is fitted and interpolated by Double Cubic B-Spline method, the curvature change of progressive surface becomes even. The processing experiment shows that the method in this paper can eliminate the defect effectively in the ultra-precision processing of progressive lenses.

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