Abstract
This chapter provides an overview at fitting parametric polynomials with control points coefficients. These polynomials have several properties, including flexibility and stability. Bézier, B-spline, Nurb, and Bézier trigonometric polynomials are the most significant of these kinds. These fitting polynomials are offered in two dimensions (2D) and three dimensions (3D). This type of polynomial is useful for enhancing mathematical methods and models in a variety of domains, the most significant of which being interpolation and approximation. The utilization of parametric polynomials minimizes the number of steps in the solution, particularly in programming, as well as the fact that polynomials are dependent on control points. This implies having more choices when dealing with the generated curves and surfaces in order to produce the most accurate results in terms of errors. Furthermore, in practical applications such as the manufacture of automobile exterior constructions and the design of surfaces in various types of buildings, this kind of polynomial has absolute preference.
Reference30 articles.
1. Adcock RJ. Note on the method of least squares. The Analyst, Des Moines, Iowa. 1877;:183-184
2. ISO 10360-6. Geometrical Product Specifications (GPS)—Acceptance and Reverification Test for Coordinate Measuring Machines (CMM)—Part 6: Estimation of Errors in Computing Gaussian Associated Features. Geneva, Switzerland: ISO; 2001
3. Pearson K. On lines and planes of closest fit to systems of points in space. The Philisophy Magazine. 1991;(11):559-572
4. Ahn SJ, Rauh W, Cho HS, Warnecke H-J. Orthogonal distance fitting of implicit curves and surfaces. IEEE Transactions on Pattern Analytical Machine Intellectual. 2002;(5):620-638
5. Ahn SJ, Westkämper E, Rauh W. Orthogonal distance fitting of parametric curves and surfaces. In: Levesley J et al., editors. Proc. 4th Int'l Symp. Algorithms for Approximation. UK: Univ. of Huddersfield; 2002. pp. 122-129