Thesis (Ph.D) - University of Birmingham, Department of Mechanical Engineering, 1996.
|Statement||by Andrzej Mark Czerkawski.|
The fitting of a curve or surface through a set of observational data is a recurring problem across numerous disciplines such as applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with tensor product splines. It gives a survey of possibilities, benefits, and problems Cited by: In this chapter we enter the realm of free-form (or sculptured) curves and surfaces. We study fitting,i.e., the construction of NURBS curves and surfaces which fit a rather arbitrary set of geometric data, such as points and derivative vectors. We distinguish two types of fitting, interpolation and approximation. In interpolation we construct a Cited by: 3. PART II: CURVE FITTING 3 CURVE FITTING: AN INTRODUCTION 43 Curve fitting: a constructive approach 43 Curve fitting with splines 44 A survey of methods 44 Some extensions 51 4 LEAST-SQUARES SPLINE CURVE FITTING 53 Least-squares splines with fixed knots 53 The normal equations 54 An orthogonalization method In this chapter we enter the realm of free-form (or sculptured) curves and surfaces. We study fitting, i.e., the construction of NURBS curves and surfaces which fit a rather arbitrary set of geometric data, such as points and derivative vectors. We distinguish two types of fitting, interpolation and approximation. In interpolation we construct.
Fitting a straight line to a set of paired observations (x1;y1);(x2;y2);;(xn;yn). Mathematical expression for the straight line (model) y = a0 +a1x where a0 is the intercept, and a1 is the slope. Deﬁne ei = yi;measured ¡yi;model = yi ¡(a0 +a1xi) Criterion for a best ﬁt: minSr = min a0;a1 Xn i=1 e2 i = min a0;a1 Xn i=1 (yi ¡a0 ¡a1xi. Numerical Methods Lecture 5 - Curve Fitting Techniques page 94 of We started the linear curve fit by choosing a generic form of the straight line f(x) = ax + b This is just one kind of function. There are an infinite number of generic forms we could choose from for almost any shape we want. An introduction to curve fitting and nonlinear regression can be found in the chapter entitled Curve Fitting, so these details will not be repeated here. Here are some examples of the curve fitting that can be accomplished with this procedure. This program is general purpose curve fitting procedure providing many new technologies that have not. When a book of any kind warrants a fifth edition, there must be more than just a few things right about it. In the case of Curves and Surfaces for CAGD (Computer Aided Graphics and Design), Gerald Farin has written and maintained a definitive work on computer graphics and graphics programming.. The fourth edition of this work was published in Reviews: 4.
This paper presents a new approach for object reconstruction by means of smooth NURBS curves and surfaces. Compared to the common object reconstruction algorithms that first, fit a curve or surface to a dataset and then, try to make it smooth in a post-processing fairing stage, this article proposes to apply the fitting and fairing procedures simultaneously to achieve desirable results. You can use the Curve Fitting Toolbox™ library of models for data fitting with the fit function. You use library model names as input arguments in the fit, fitoptions, and fittype functions. Library Model Types. The following tables describe the library model types for curves and surfaces. In other words, size_u and size_v arguments are used to fit curves of the surface on the corresponding parametric dimension. Degree of the output spline geometry is important to determine the knot vector(s), compute the basis functions and build the coefficient matrix,. Most of the time, fitting to a quadratic (degree = 2) or a cubic (degree. ISBN: X OCLC Number: Description: xvii, pages: Contents: PART I: SPLINE FUNCTIONS; PART II: CURVE FITTING; PART III: SURFACE.