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.

Electronic Cam Trajectory Generation Algorithm Based on Global Optimal Control Points of Non-Uniform B-Spline

2013 ◽  
Vol 418 ◽  
pp. 219-224 ◽  
Author(s):  
Shen Hang Wang ◽  
Jian Hua Hu ◽  
Yun Kuan Wang ◽  
Zheng Jun ◽  
Xiao Fei Qin ◽  
...  
Keyword(s):  
Optimal Control ◽  
Global Optimization ◽  
Control Point ◽  
Trajectory Generation ◽  
Control Points ◽  
Kinematic Constraints ◽  
Generation Algorithm ◽  
B Spline ◽  
Global Optimal ◽  
Trajectory Generation Algorithm

In order to improve the smoothness of electronic cam motion,an electronic cam trajectory generation algorithm based on global optimal control points of quintic non-uniform B-spline is prop-osed. This algorithm solves the problem of non-global optimization in existing approaches caused by transferring kinematic constraints into control point constraints to avoid the semi-infinite constraints problem. The interval ranges of the reserved free control point variables are calculated first, followed by partitioning and checking the subinterval with the property of the objective function and kinemat-ical constraints repeatedly until finding the global optimal control point. Compared with the existing control point constraints algorithm, the object function is optimized further and the electronic cam trajectory is smoother. Finally an practical example of electronic cam proves the effectiveness of the proposed algorithm.

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.

scholarly journals Can local NURBS refinement be achieved by modifying only the user interface?

2020 ◽  
Author(s):  
Neil Dodgson ◽  
J Kosinka
Keyword(s):  
User Interface ◽  
Data Structures ◽  
Control Point ◽  
Control Points ◽  
Control Mesh

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

scholarly journals Can local NURBS refinement be achieved by modifying only the user interface?

2020 ◽  
Author(s):  
Neil Dodgson ◽  
J Kosinka
Keyword(s):  
User Interface ◽  
Data Structures ◽  
Control Point ◽  
Control Points ◽  
Control Mesh

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

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.

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