scholarly journals Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with B-Spline Curves

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Hatice Kuşak Samancı ◽  
Filiz Yağcı ◽  
Ali Çalişkan
Keyword(s):  
Experimental Period ◽  
Drop Test ◽  
Control Points ◽  
Application Process ◽  
B Spline ◽  
Geometrical Modelling ◽  
Energy Diffusion ◽  
Spline Curves ◽  
Aramid Fabric ◽  
Pointed End

The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped.

scholarly journals Control point insertion for B-spline curves

1988 ◽  
Vol 38 (2) ◽  
pp. 307-313 ◽  
Author(s):  
Heinz H. Gonska ◽  
Andreas Röth
Keyword(s):  
User Interface ◽  
Control Point ◽  
Point Of View ◽  
Control Points ◽  
Natural User Interface ◽  
B Spline ◽  
Spline Curves

Inserting new knots into B-spline curves is a well-known technique in CAGD to gain extra flexibility for design purposes. However, from a user's point of view, the insertion of knots is somewhat unsatisfactory since the newly generated control points sometimes show up in unexpected locations. The aim of this note is to show that these problems can be circumvented by inserting the control vertices directly, thus also providing a more natural user interface.

B-SPLINE BASED STEREO FOR 3D RECONSTRUCTION OF LINE-LIKE OBJECTS USING AFFINE CAMERA MODEL

2001 ◽  
Vol 15 (02) ◽  
pp. 347-358 ◽  
Author(s):  
YIJUN XIAO ◽  
MINGYUE DING ◽  
JIAXIONG PENG
Keyword(s):  
Stereo Vision ◽  
Free Form ◽  
Control Points ◽  
Invariant Property ◽  
Affine Invariant ◽  
Camera Model ◽  
B Spline ◽  
Space Curves ◽  
Spline Curves ◽  
Affine Camera

This paper presents a novel curve based algorithm of stereo vision to reconstruct 3D line-like objects. B-spline approximations of 2D edge curves are selected as primitives for the reconstruction of their corresponding space curves so that, under the assumption of affine camera model, a 3D curve can be derived from reconstructing its control points according to the affine invariant property of B-Spline curves. The superiority of B-spline model in representing free-form curves gives good geometric properties of reconstruction results. Both theoretical analysis and experimental results demonstrate the validity of our approach.

scholarly journals Shape Designing Using Quadratic Trigonometric B-Spline Curves

2019 ◽  
Vol 3 (2) ◽  
pp. 36-49
Author(s):  
Amna Abdul Sittar ◽  
Abdul Majeed ◽  
Abd Rahni Mt Piah
Keyword(s):  
Shape Parameter ◽  
Control Points ◽  
B Spline ◽  
Spline Curves ◽  
Computer Aided ◽  
And Control

The B-spline curves, particularly trigonometric B-spline curves, have attained remarkable significance in the field of Computer Aided Geometric Designing (CAGD). Different researchers have developed different interpolants for shape designing using Ball, Bezier and ordinary B-spline. In this paper, quadratic trigonometric B-spline (piecewise) curve has been developed using a new basis for shape designing. The proposed method has one shape parameter which can be used to control and change the shape of objects. Different objects like flower, alphabet and vase have been designed using the proposed method. The effects of shape parameter and control points have been discussed also.

T-B Spline Curves with a Shape Parameter

2012 ◽  
Vol 241-244 ◽  
pp. 2144-2148
Author(s):  
Li Juan Chen ◽  
Ming Zhu Li
Keyword(s):  
Shape Parameter ◽  
Simple Structure ◽  
Control Points ◽  
Curve Segment ◽  
Closed Curves ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves

A T-B spline curves with a shape parameter λ is presented in this paper, which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the curves are C^2 continuous, but when the shape parameter λ equals to 0 , the curves are C^3 continuous. Moreover, this spline curve can be used to construct open and closed curves and can express ellipses conveniently.

Collision-Free Path Planning by Using Nonperiodic B-Spline Curves

1993 ◽  
Vol 115 (3) ◽  
pp. 679-684 ◽  
Author(s):  
D. C. H. Yang
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Free Path ◽  
Computer Code ◽  
Control Points ◽  
B Spline ◽  
Spline Curves ◽  
End Effectors ◽  
Main Ideas ◽  
Fifth Order

This paper presents a method and an algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order nonperiodic B-spline curves are chosen for this purpose. The main ideas are twofold: first, to avoid collision by moving around obstacles from the less blocking sides; and second, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Case studies are given for illustration.

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

Collision-Free Path Planning by Using Non-Periodic B-Spline Curves

1990 ◽  
Author(s):  
D. C. H. Yang
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Computer Code ◽  
Control Points ◽  
A Algorithm ◽  
B Spline ◽  
Spline Curves ◽  
End Effectors ◽  
Main Ideas ◽  
Fifth Order

Abstract This paper presents a method and a algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order non-periodic curves are chosen for this purpose. The main ideas are twofold: firstly, to avoid collision by moving around obstacles from the less blocking sides; and secondly, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Cases study is given for illustration.

Aerodynamic Shape Deformation of Underwing Nacelle-Pylon Configuration Based on B-Spline Surface

2013 ◽  
Vol 444-445 ◽  
pp. 191-195
Author(s):  
Xiao Yong Ma ◽  
Jun Qiang Ai ◽  
Ji Xiang Shan ◽  
Yong Hong Li
Keyword(s):  
Shape Deformation ◽  
Control Points ◽  
Control Parameters ◽  
Local Surface ◽  
Deformation Method ◽  
B Spline ◽  
Aerodynamic Shape ◽  
Spline Surface ◽  
Spline Curves ◽  
Superposition Technique

A free deformation method based on the B-Spline (NURBS) and surface superposition technique was presented for complex aerodynamic shape deformation. The influences of control parameters including control points, order, knots and weights are analyzed with B-spline curves case. Using the developed method, the application of surface grids deformation on the wing and pylon of DLR-F6 plane shows that the control parameters only influence its local surface, and this method could describe complex surfaces effectively, which means that this method is feasible and applicable to model representation, surface grids deformation and aerodynamic shape optimization.

scholarly journals Cubic B-Spline Curves with Shape Parameter and Their Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Houjun Hang ◽  
Xing Yao ◽  
Qingqing Li ◽  
Michel Artiles
Keyword(s):  
Basis Function ◽  
Shape Parameter ◽  
Engineering Application ◽  
Shape Design ◽  
Control Points ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Smooth Connection

The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application.

Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)

2016 ◽  
Vol 10 (3) ◽  
Author(s):  
Corinna Harmening ◽  
Hans Neuner
Keyword(s):  
Target Function ◽  
Information Criterion ◽  
Point Clouds ◽  
Optimal Number ◽  
Information Criteria ◽  
Control Points ◽  
Risk Minimization ◽  
B Spline ◽  
Spline Curves ◽  
Analysis Strategies

AbstractDue to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds.Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline’s appearance; the B-spline’s complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn’t use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality.The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.

Sign in / Sign up

Export Citation Format

Share Document