Bezier Curve Research Papers - Academia.edu (original) (raw)

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- by
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- Engineering, Computational Geometry, Algorithm, Mathematical Sciences
- by 宜儒何
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- Robotics, Dynamic programming, Bezier Curve, Voronoi Diagrams

For analysis & optimization purposes, it is necessary to represent an airfoil with fewer
parameters. In this paper, the two-dimensional surface of an airfoil has been represented by 5th order
Bézier curve. So, each of the upper and lower surface of the airfoil can be represented by (5+1) = 6 control
points only. For optimization purposes, control points of the cubic B-spline are used for modeling the airfoil
as analyses are done with Qblade. Here, the design space has been defined as the 25% above and 25%
below the y coordinates of the control points. Within this design space, two optimized shapes are obtained
by using Genetic Algorithm (GA) and the Particle Swarm Optimization (PSO) tool of Matlab respectively.
Each shape has a higher coefficient of lift-to-drag ratio (Cl/Cd) than that of the original airfoil for a range
of angle of attack (AoA). So, these two shapes can definitely be used in various aerodynamic applications
like in wind turbine and in aircraft wings to get better lift and reduced amount of drag force.

- by Leopoldo Armesto
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- Approximation Theory, Path planning, Automation, Mobile Robots
- by Horst Engels
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- Multivariate Analysis, Biological Sciences, Mathematical Sciences, Bezier Curve
- by Congduc Pham
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- Computer Science, Scheduling, Wireless Sensor Networks, Risk Management

In this paper, a kind of quasi-cubic Bézier curves by the blending of algebraic polynomials and trigonometric polynomials using weight method is presented, named WAT Bézier curves. Here weight coefficients are also shape parameters, which are called weight parameters. The interval [0, 1] of weight parameter values can be extended to [-2,π2/(π2-6)]. The WAT Bézier curves include cubic Bézier curves and C-Bézier curves () as special cases. Unlike the existing techniques based on C-Bézier methods which can approximate the Bézier curves only from single side, the WAT Bézier curves can approximate the Bézier curve from the both sides, and the change range of shape of the curves is wider than that of C-Bézier curves. The geometric effect of the alteration of this weight parameter is discussed. Some transcendental curves can be represented by the introduced curves exactly.

- by Co. SEP
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- Bezier Curve
- by Yichen Han
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- Applied Mathematics, Bezier Curve, Shape Parameters
- by S. Morigi
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- Engineering, Computational Geometry, Algorithm, Mathematical Sciences
- by Andreas Nearchou
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- Engineering, Bezier Curve, Real Time, Cross Section
- by Kouichi Konno
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- Cognitive Science, Bezier Curve
- by Muhammad Sarfraz
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- Engineering, Mathematical Sciences, Bezier Curve, Information Sciences
- by Helmut Pottmann
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- Mechanical Engineering, Computer Aided Design, NURBS, Bezier Curve

In minimally invasive robotic surgery (MIRS), a surgeon teleoperates a robotic arm from a
master console. This arm operates inside the patient's body through a small orifice which constrains
the end-effector's translation along two axes. The workspace of such a robotic arm depends on its
design as well as orifice location. Conventionally, the design of such an arm is optimized for large
workspace and high dexterity. However, this large workspace might be reachable through only a few
orifices, thus making the workspace volume and operation quite sensitive to the orifice location. To
overcome this problem, we optimized the design of a 3 degrees of freedom serial robotic arm to attain
multiple adjacent (desired number of) possible orifice locations, through which a planar workspace of
pre-specified geometry can be traced. To achieve this goal, an algorithm was developed to relate the
design of such an MIRS arm to the possible orifice positions. The optimization problem was solved
using several metaheuristics such as simulated annealing, Tabu search, artificial bee colonization and
genetic algorithm, and their performance was compared.

- by Gabriel Elkaim
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- Path planning, Feedback Control, Bezier Curve, Autonomous Vehicle

The paper's aim is to study old and new problems regarding the Bézier curves, which are important tools in the geometric modelling of shapes. We use the Matlab software to study the estimation error of fitting data using Bézier curves least square fitting and to find new methods within a study that is currently under development about minimizing the distance between the curve and the approximated data.

- by Academia EduSoft
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- Bezier Curve, Data Fitting
- by P. Dierckx and +1
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- Applied Mathematics, Wavelets, Triangulation, Wavelet Transform

This paper discusses a method for controlling a hyper-redundant arm to manipulate an object on a plane. The hyper-redundant arm can perform simple whole-arm manipulation by coiling or wrapping around the object and then pulling the object toward the goal position. The process of object manipulation can be separated into two steps: encircling the object and transporting the object. In the process of encircling the object, the arm is controlled by a set of virtual constraints that guide the arm to reach around the object and encircle it, keeping the arm within a specified bound to ensure the circular shape around the object. In the process of transporting the object, a simplified desired shape is generated from a Bézier curve according to a given goal position and the arm geometry. Then, the gradient descent method is used to update the joint angles of the arm at each step to move the arm toward the desired shape until the object reaches its target position. The proposed method has been tested in both simulation and real experiments.

Biaxial tensile tests of cold-rolled steel sheet were carried out using newly designed cruciform specimens. The specimens were deformed under linear loading paths in a servo-controlled biaxial tensile testing machine. The maximum equivalent strain attained was 0.04. Plastic orthotropy remained coaxial with the principal stresses throughout every experiment. However, the successive contours of plastic work in biaxial stress space changed their shapes progressively, exemplifying a phenomenon which has been termed differential work hardening by Hill and Hutchinson (Trans. ASME J. Appl. Mech. 59 (1992) 1) and by Hill et al. (Int. J. Solids Struct. 31 (1994) 2999). The geometry of the entire family of the work contours was compared with the yield loci calculated from several existing yield criteria. Hill’s quadratic yield criterion overestimated the measured work contours; in particular, in the neighborhood of balanced biaxial tension, the discrepancy was large, while the other yield criteria described the behavior of the work contours well. The only yield criterion that could describe the general trends of the work contours as well as the in-plane r-value distribution with good accuracy was Gotoh’s biquadratic yield criterion. Moreover, it was observed that the components of an increment of logarithmic plastic strain are proportional to the components of the associated normal to the current work contour in stress space. Accordingly, it appears that the work contours act instantaneously as plastic potentials, at least under linear loading paths.

- by Sudhir Jangra
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- Materials Engineering, Mechanical Engineering, Titanium, Anisotropy
- by D. Binosi
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- GUI, Mathematical Sciences, Graphic User Interface Design, Physical sciences

FOLD PROFILER is a MATLAB code for classifying the shapes of profiles of folded surfaces. The classification is based on the comparison of the natural fold profile with curves representing mathematical functions. The user is offered a choice of four methods, each based on a different type of function: cubic Bezier curves, conic sections, power functions and superellipses. The comparison is carried out by the visual matching of the fold profile displayed on-screen from an imported digital image and computed theoretical curves which are superimposed on the image of the fold. To improve the fit with the real fold shape, the parameters of the theoretical curves are changed by simple mouse actions. The parameters of the mathematical function that best fits the real folds are used to classify the fold shape.FOLD PROFILER allows the rapid implementation of four existing methods for fold shape analysis. The attractiveness of this analytical tool lies in the way it gives an instant visual ap...

- by Jesus Aller
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- Engineering, Earth Sciences, Structural Geology, Bezier Curve
- by In-Kwon Lee
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- Mechanical Engineering, Image Processing, Computer Aided Design, Bezier Curve
- by Sarbajit Pal
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- Computer Science, Face Recognition, Image segmentation, Hidden Markov Models
- by Horst Nowacki
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- Engineering, Mathematical Sciences, Computer Aided Geometric Design, Bezier Curve
- by Ferdous Ahmed Sohel and +1
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- Information Technology, Computer Aided Design, Process Control, Vehicle Dynamics
- by Marsha Berry
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- Genetics, Non-photorealistic rendering, Bezier Curve, Population Size

Summary In this paper, we develop a new hybrid curve fitting model using fuzzy set and rough set theory. The developed method differs from classical curve fitting techniques and algorithms. For produced rule sets of model to create by using fuzzy logic technique and the membership functions of input and output functions, the range of membership functions and the relations

- by Ahmet Arslan
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- Data Mining, Fuzzy Logic, Computer Aided Geometric Design, Bezier Curve
- by lin eagle
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- Engineering, Computer Aided Design, Singularity, Mathematical Sciences
- by Shankar Krishnan
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- Engineering, Computational Geometry, Algorithm, Geometric model

This paper presents a Web based system for capturing outlines of 2D shapes using Matlab Web Server. From a simple user interface in HTML, any Web user can upload his data and view the results. Cubi c Bezier curve design is used to capture... more

- by Muhammad Sarfraz
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- User Interface, Bezier Curve, Human Interaction, Web Based System
- by ekta walia
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- Bezier Curve, Computer Graphic, Visual Quality

Fractals are famous both for their strange appearance and for their odd geometric properties. The Sierpinski gasket and the Koch snowflake in Figure 1 are two well known examples of fractal curves. The Koch snowflake is continuous... more

- by Ron Goldman
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- Computer Science, Computational Geometry, Iterative Methods, Convergence

We provide an simple algorithm for constructing an polynomial Bézier approximation of degree n1 to an nth degree Bézier curve. This algorithm makes previous work of Lachance more transparent as formulas are given which express the... more

- by J MAN
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- Engineering, Mechanical Engineering, Computer Aided Design, Mathematical Sciences

Neutrosophic set concept is defined with membership, non-membership and indeterminacy degrees. This concept is the solution and representation of the problems with various fields. In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic B` ezier curves.

- by Selçuk Topal
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- Data Analysis, Bezier Curve, Neutrosophic Sets
- by Chand John
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- Bezier Curve, Iterated Function System
- by Yichen Han
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- Applied Mathematics, Computer Aided Design, Numerical Analysis, Primary
- by Jan-Henrik Haunert
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- Computer Graphics, Ubiquitous Computing, Visual Analytics, Data Visualization

This article proposes a technique for the geometrically stable modeling of high-degree B-spline curves based on S-polygon in a float format, which will allow the accurate positioning of the end points of curves and the direction of the tangent vectors. The method of shape approximation is described with the purpose of providing geometrical proximity between the original and approximating curve. The content of the notion of a "harmonious, regular form" of B-spline curve's S-polygon in a float format is revealed as a factor in achieving a high-quality of fit for the generated curve. The expediency of the shape modeling method based on S-polygon in a float format at the end portions of the curve for quality control of curve modeling and editing is substantiated. The results of a comparative test are presented, demonstrating the superlative efficacy of using the Mineur-Farin configuration for constructing constant and monotone curvature curves based on an S-polygon in a float format. The findings presented in this article confirm that it is preferable to employ the principle of "constructing a control polygon of a harmonious form (or the Mineur-Farin configuration) of a parametric polynomial" to a B-spline curve's S-polygon in a float format, and not to a B-polygon of the Bézier curve. Recommendations are given for prospective studies in the field of applying the technique of constructing a high-quality B-spline curves to the approximation of log-aesthetic curves, Ziatdinov's superspirals, etc. The authors of the article developed a technique for constructing smooth connections of B-spline curves with ensuring a high order of smoothness of the composite curve. The proposed techniques are implemented in the FairCurveModeler program as a plug-in to engineering CAD systems.

- by Michael Kurtov
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- Film and Media Studies, Bezier Curve