Design of refractive spline surface for generating required irradiance distribution with large angular dimension

2010 ◽  
Vol 57 (7) ◽  
pp. 536-544 ◽  
Author(s):  
M.A. Moiseev ◽  
L.L. Doskolovich
Keyword(s):  
Angular Dimension ◽  
Spline Surface

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.

Continuity Transition with a Single Regular Curved-Knot Spline Surface

2014 ◽  
Vol 33 (5) ◽  
pp. 1-5
Author(s):  
Kan-Le Shi ◽  
Jun-Hai Yong ◽  
Jia-Guang Sun ◽  
Jean-Claude Paul
Keyword(s):  
Spline Surface

A Smooth Contact Algorithm Using Cubic Spline Surface Interpolation for Rigid and Flexible Bodies

2013 ◽  
Author(s):  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Contact Force ◽  
Cubic Spline ◽  
Surface Representation ◽  
Flexible Bodies ◽  
Contact Algorithm ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Smooth Contact ◽  
Representation Method ◽  
Detailed Search

The contact analysis of multi-flexible-body dynamics (MFBD) has been an important issue in the area of computational dynamics because the realistic dynamic analysis of many mechanical systems includes the contacts among rigid and flexible bodies. But, until now, the contact analysis in the multi-flexible-body dynamics has still remained as a big, challenging area. Especially, the most of contact algorithms have been developed based on the facetted triangles. As a result, the contact force based on the facetted surface was not accurate and smooth because the geometrical error is already included in the contact surface representation stage. This kind of error can be very important in the precise mechanism such as gear contact or cam-valve contact problems. In order to resolve this problem, this study suggests a cubic spline surface representation method and related contact algorithms. The proposed contact algorithms are using the compliant contact force model based on the Hertzian contact theory. In order to evaluate the smooth contact force, the penetration depth and contact normal directions are evaluated by using the cubic spline surface interpolation. Also, for the robust and efficient contact algorithm development, the contact algorithms are divided into four main parts which are a surface representation, a pre-search, a detailed search and a contact force generation. In the surface representation part, we propose a smooth surface representation method which can be used for smooth rigid and flexible bodies. In the pre-search, the algorithm performs collision detection and composes the expected contact pairs for the detailed search. In the detailed search, the penetration depth and contact reference frame are calculated with the cubic spline surface interpolation in order to generate the accurate and smooth contact force. Finally in the contact force generation part, we evaluate the contact force and Jacobian matrix for the implicit time integrator.

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document