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.

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.

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.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

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.

Multiresolution Curve Editing With Linear Constraints*

2001 ◽  
Vol 1 (4) ◽  
pp. 347-355 ◽  
Author(s):  
Gershon Elber
Keyword(s):  
Linear Constraints ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Freeform Surfaces ◽  
Modeling Tool ◽  
B Spline ◽  
Curves And Surfaces ◽  
Orthogonality Constraints ◽  
Spline Curves ◽  
Computer Aided

The use of multiresolution control toward the editing of freeform curves and surfaces has already been recognized as a valuable modeling tool [1–3]. Similarly, in contemporary computer aided geometric design, the use of constraints to precisely prescribe freeform shape is considered an essential capability [4,5]. This paper presents a scheme that combines multiresolution control with linear constraints into one framework, allowing one to perform multiresolution manipulation of nonuniform B-spline curves, while specifying and satisfying various linear constraints on the curves. Positional, tangential, and orthogonality constraints are all linear and can be easily incorporated into a multiresolution freeform curve editing environment, as will be shown. Moreover, we also show that the symmetry as well as the area constraints can be reformulated as linear constraints and similarly incorporated. The presented framework is extendible and we also portray this same framework in the context of freeform surfaces.

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.

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