scholarly journals A Geometric Modeling Method Based on TH-Type Uniform B-Splines

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jin Xie
Keyword(s):  
Geometric Modeling ◽  
Modeling Method ◽  
Control Points ◽  
Hyperbolic Functions ◽  
Hyperbolic Polynomial ◽  
B Splines ◽  
Control Polygon ◽  
The Given

A geometric modeling method based on TH-type uniform B-splines which are composed of trigonometric and hyperbolic polynomial with parameters is introduced in this paper. The new splines possess many important properties of quadratic and cubic B-splines. Taking different values of the parameters, one can not only locally adjust the shape of the curves, but also change the type of some segments of a curve between trigonometric and hyperbolic functions as well. The given curves can also interpolate directly control polygon locally by selecting special parameters. Moreover, the introduced splines can represent some quadratic curves and transcendental curves with selecting proper control points and parameters.

Cubic TP B-Spline Curves with a Shape Parameter

2013 ◽  
Vol 11 ◽  
pp. 59-72 ◽  
Author(s):  
Mridula Dube ◽  
Reenu Sharma
Keyword(s):  
Tensor Product ◽  
Shape Parameter ◽  
Control Points ◽  
Shape Parameters ◽  
Special Shape ◽  
B Spline ◽  
Control Polygon ◽  
Spline Curves ◽  
Trigonometric Spline ◽  
The Given

In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.

A Dynamics-Based Optimal Trajectory Generation for Controlling an Automated Excavator

2010 ◽  
Vol 224 (10) ◽  
pp. 2109-2119 ◽  
Author(s):  
S Yoo ◽  
C-G Park ◽  
S-H You ◽  
B Lim
Keyword(s):  
Optimal Trajectory ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Control Points ◽  
Weighting Functions ◽  
B Splines ◽  
Finite Dimensional ◽  
Motion Optimization ◽  
Save Energy

This article presents a new methodology to generate optimal trajectories in controlling an automated excavator. By parameterizing all the actuator displacements with B-splines of the same order and with the same number of control points, the coupled actuator limits, associated with the maximum pump flowrate, are described as the finite-dimensional set of linear constraints to the motion optimization problem. Several weighting functions are introduced on the generalized actuator torque so that the solution to each optimization problems contains the physical meaning. Numerical results showing that the generated motions of the excavator are fairly smooth and effectively save energy, which can prevent mechanical wearing and possibly save fuel consumption, are presented. A typical operator's manoeuvre from experiments is referred to bring out the standing features of the optimized motion.

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.

Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Corinna Harmening ◽  
Hans Neuner
Keyword(s):  
Data Analysis ◽  
Laser Scanner ◽  
Point Clouds ◽  
Optimal Number ◽  
Deformation Analysis ◽  
Control Points ◽  
Trial And Error ◽  
B Spline ◽  
B Splines ◽  
Spline Surfaces

AbstractFreeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis.A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures.In [The present paper continues these investigations. If necessary, the methods proposed in [The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.

Data Modeling Using NURBs Curves and Modified Genetic Algorithms

2010 ◽  
Author(s):  
Christopher Hammond ◽  
Cameron J. Turner
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Trial Data ◽  
Data Sets ◽  
Control Points ◽  
Nurbs Curve ◽  
B Splines ◽  
Modified Genetic Algorithm ◽  
Nurbs Curves ◽  
2D Data

Non-Uniform Rational B-Splines (NURBS) curves have long been used to model 1D and 2D data because they are efficient to calculate, easy to manipulate, and capable of handling discontinuities and drastic changes in the general topology of the data. However, the user must assist in defining the control points, weights, knots and an order for the curve in order to fit the curve to the data. This paper uses a modified Genetic Algorithm (GA) to choose and manipulate these various parameters to produce a NURBS curve that minimizes the error between the data and the curve and also minimizes the time it takes the algorithm to compute the solution. The algorithm is tested on several 1D trial data sets and the results are explained. Then, several general difficulties for this application of the GA are explained and possible methods for overcoming them are discussed.

Optimum 3D Rapping of CAD Models Using Single NURBS

2014 ◽  
Author(s):  
Mohamed A. El-Komy ◽  
Sayed M. Metwalli
Keyword(s):  
Corner Point ◽  
Basis Functions ◽  
Control Points ◽  
Nurbs Curve ◽  
B Splines ◽  
Full Control ◽  
Solid Models ◽  
Cad Models ◽  
3D Solid ◽  
Number Of Segments

Non-Uniform Rational B-Splines (NURBS) can represent curves and surfaces of any degree. Usually in the same curve, however, the degree is unique. The goal of this work is to identify single and exact corner point of lines represented by cubic or other NURBS. The combination of arcs and lines can then be represented by one NURBS with error not to exceed (10−12). The developed procedure can represent any NURBS curve and surface of any degree with full control on all parameters, control points, weights, knot vectors, and number of segments representing the curve or surface, in addition to, the basis functions examination. The optimization identifies the parameters and geometry to insure any required level of accuracy to represent singular corner solid models to allow a single cubic or other NURBS representing the whole solid. It is concluded that the singular corner point can be identified with cubic NURBS. Applications to several 3D solid CAD models are used to verify such a technique.

scholarly journals Optimal Number of Control Points for Fitting B-Splines in Wind Turbine Blade Measurement

2019 ◽  
Vol 20 (9) ◽  
pp. 1507-1517 ◽  
Author(s):  
Ching Hin Lydia Chan ◽  
Qing Wang ◽  
Roger Holden ◽  
Songling Huang ◽  
Wei Zhao
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Optimal Number ◽  
Wind Turbine Blade ◽  
Control Points ◽  
B Splines

Optimization of the number of control points for curve fitting using b-splines

2015 ◽  
Author(s):  
Carlos Eduardo Fanti ◽  
João Carlos Mendes Carvalho
Keyword(s):  
Curve Fitting ◽  
Control Points ◽  
B Splines

Ensuring the Requirements of Ergonomics in the Automated the Layout of Equipment

2019 ◽  
Vol 7 (3) ◽  
pp. 70-85
Author(s):  
Вин Тун Е ◽  
Vin Tun E ◽  
Л. Маркин ◽  
Leonid Markin
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Modeling Method ◽  
Point Of View ◽  
Design Solution ◽  
C Programs ◽  
Additional Information ◽  
Receptor Models ◽  
Service Areas ◽  
Assembly Operations

The article discusses the solution to the problem of automating the design of layouts of various equipment, taking into account ergonomics, by which is meant the provision of service areas. The article describes the development of methods and algorithms that provide access to installation tools and workspace during installation and maintenance of already placed equipment. The solution method is geometric modeling of both the placed objects and the installation equipment necessary for its maintenance, as well as the trajectory of its movement to the service area. Thus, both the installation equipment and the movement paths are treated as composable objects, the intersection of which with other objects is unacceptable. As a modeling method, receptor-based geometric models that discretize the allocation space were used. The choice of receptor models is due to the fact that the solid-state model of all the instantaneous positions of the installation tool in the process of its delivery and operation is extremely complex from a geometrical point of view. The possibility of relatively easy to determine the fact of the intersection of all objects of the scene, described by receptor models, and is the rationale for the choice in our study of the receptor method of geometric modeling. Based on the receptor design model, a procedure has been developed for determining the trajectory of a mounting tool at a given operating point, as well as the formation of the space required for operation, or establishing the fact that it is impossible to service a particular object, which indicates an unsatisfactory (non-ergonomic) given design solution. In this study a feature of using receptor models is the use of 6-digit codes in the receptor matrices, which, with some complication of the modeling method, allows to obtain additional information about problem areas in the layout under study (impossibility of carrying a tool, impossibility of performing assembly operations, etc.). Algorithms for solving this problem, as well as a graphical shell that visualizes the results of computer-aided design, are implemented as C# programs.

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