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3 results on '"zier curve"'

1. Rational quadratic trigonometric Bézier curve based on new basis with exponential functions

Author

Wu Beibei, Yin Junfeng, Li Chunjing, and Jin Meng

Subjects
shape parameters, exponential functions, zier curve, rational quadratic trigonometric B&#233, lcsh:Science (General), ComputingMethodologies_COMPUTERGRAPHICS, quadratic trigonometric basis functions, lcsh:Q1-390
Abstract

We construct a rational quadratic trigonometric Bézier curve with four shape parameters by introducing two exponential functions into the trigonometric basis functions in this paper. It has the similar properties as the rational quadratic Bézier curve. For given control points, the shape of the curve can be flexibly adjusted by changing the shape parameters and the weight. Some conics can be exactly represented when the control points, the shape parameters and the weight are chosen appropriately. The C0, C1 and C2 continuous conditions for joining two constructed curves are discussed. Some examples are given.

Published
2017

2. Bezier curves and de Casteljau algorithm

Author

Dudaš, Dorotea and Marković, Darija

Subjects
Computer Science::Graphics, Bernstein polynomials, B\'{, e}, zier curve, de Casteljau algorithm, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

We will present some of the basic ideas of Computer Aided Geometric Design (CAGD). It is essential that we can manipulate geometric objects very effectively and rapidly on the computer, i. e. that the entered parameters have a geometric meaning, in other words, that we have an idea of the given curve. For that purpose we will define Bernstein polynomials, present their basic properties and introduce Bezier curves as a representation of a polynomial through the Bernstein basis. We will also demonstrate the de Casteljau algorithm. All programs will be made using software \textit{;Mathematica};. We will use graphic options and animation of the iterative process.

Published
2003

3. A Novel Method for Accurate Evaluation of Size for Cylindrical Components

Author

Ramaswami, Hemant

Subjects
Mechanical Engineering, Size of a Cylinder, Actual Value, Open Uniform B-Spline Curve, B&233, zier Curve, Particle Swarm Optimization
Abstract

The objective of this thesis is to develop a methodology to calculate the size of a cylindrical profile accurately per ANSI standards. The ANSI Y 14.5.1M-1994 standard defines the size of a cylinder as the size of the largest ball rolling on a spine such that all points on the surface of the cylinder are external to it, or the size of the smallest ball rolling on a spine such that all points on the surface of the cylinder are internal to it.Current methods of size evaluation reduce the complexity of the spine and model it as a straight line. A novel methodology to evaluate the control points of the spine modeled as a Bezier curve or an Open Uniform B-Spline curve of a pre-specified degree based on points collected on the surface of the cylinder has been developed in this thesis. This provides a quantitative measure of the size of the cylinder in accordance with ANSI standards. The formulations to evaluate the maximum inscribing spine and the minimum circumscribing spine are presented as multi-level optimization problems. The outer level optimization is used to identify the optimal set of control points for the spline representing the path of the rolling ball. The inner level optimization is used to find the nearest point on the curve corresponding to every point in the dataset.The optimization formulation has been used to calculate the true size of cylinders for several published, simulated and real datasets. These results have been compared to traditional estimates for size of a cylinder, such as the maximum inscribed, minimum circumscribed and least squares cylinders. The results indicate that the method presented in this research conforms better to the ANSI standards as compared to the traditional methods. Further analysis is presented to observe the effect of sample size on the results of the algorithm. It is observed that with an increase in the sample size, the difference between the results of the presented algorithm and the traditional methods increases with the presented method providing more accurate estimates of the size of the cylinder.

Published
2010

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