Ebook: Interpolating cubic splines
Author: Gary D. Knott
- Genre: Mathematics // Computational Mathematics
- Tags: Математика, Вычислительная математика
- Series: Progress in Computer Science and Applied Logic
- Year: 1999
- Publisher: Birkhäuser Boston
- City: Berlin Heidelberg New York
- Edition: 1
- Language: English
- djvu
Much work has focused on approximating splines such as B-splines and Bezier splines. In contrast, this book emphasizes interpolating splines. Almost always, the cubic polynomial form is treated in depth.
{it Interpolating Cubic Splines} covers a wide variety of explicit approaches to designing splines for the interpolation of points in the plane by curves, and the interpolation of points in 3-space by surfaces. These splines include various estimated-tangent Hermite splines and double-tangent splines, as well as classical natural splines and geometrically-continuous splines such as beta-splines and nu-splines.
A variety of special topics are covered, including monotonic splines, optimal smoothing splines, basis representations, and exact energy-minimizing physical splines. An in-depth review of the differential geometry of curves and a broad range of exercises, with selected solutions, and complete computer programs for several forms of splines and smoothing splines, make this book useful for a broad audience: students, applied mathematicians, statisticians, engineers, and practicing programmers involved in software development in computer graphics, CAD, and various engineering applications.