Interpolating Cubic Splines
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Interpolating Cubic Splines
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Author : Gary D. Knott
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Interpolating Cubic Splines written by Gary D. Knott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Computers categories.
The study of spline functions is an outgrowth of basic mathematical concepts arising from calculus, analysis and numerical analysis. Spline modelling affects a number of fields: statistics; computer graphics; CAD programming, and other areas of applied mathematics.
Interpolating Cubic Splines
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Author : Gary D. Knott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Interpolating Cubic Splines written by Gary D. Knott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.
Introduction To Cubic Spline Interpolation With Examples In Python
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Author : Thomas Maindl
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-04-09
Introduction To Cubic Spline Interpolation With Examples In Python written by Thomas Maindl and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with categories.
This textbook will enable you to - discuss polynomial and spline interpolation - explain why using splines is a good method for interpolating data - construct cubic interpolating splines for your own projects It is a self-contained course for students who wish to learn about interpolating cubic splines and for lecturers who seek inspiration for designing a spline interpolation module. The book's innovative concept combines - a slide-based lecture with textual notes - a thorough introduction to the mathematical formalism - exercises - a "rocket science" project that implements constructing interpolating splines in Python for answering questions about the velocity, g-force, and covered distance after the first launch of SpaceX(R)' Falcon(R) Heavy Target group: STEM (science, technology, engineering, and math) students and lecturers at colleges and universities Contents: Preface 1 Cubic spline interpolation 2 Mini-script for constructing cubic splines 3 Spline exercises 4 The rocket launch project 5 Closing remarks Appendix A notebook for periodic cubic splines Index
Interpolating Cubic Splines
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Author : Gary D. Knott
language : en
Publisher: Birkhäuser
Release Date : 2012-10-15
Interpolating Cubic Splines written by Gary D. Knott and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-15 with Computers categories.
A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.
The Theory Of Splines And Their Applications
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Author : J. H. Ahlberg
language : en
Publisher: Elsevier
Release Date : 2016-06-03
The Theory Of Splines And Their Applications written by J. H. Ahlberg and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Interpolating Cubic Splines
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Author : Gary D. Knott
language : en
Publisher: Birkhauser
Release Date : 2000
Interpolating Cubic Splines written by Gary D. Knott and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Interpolation categories.
An Introduction To Splines For Use In Computer Graphics And Geometric Modeling
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Author : Richard H. Bartels
language : en
Publisher: Morgan Kaufmann
Release Date : 1995-09
An Introduction To Splines For Use In Computer Graphics And Geometric Modeling written by Richard H. Bartels and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09 with Computers categories.
As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.
Cardinal Spline Interpolation By I J Schoenberg
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Author : Isaac J. Schoenberg
language : en
Publisher:
Release Date : 1973
Cardinal Spline Interpolation By I J Schoenberg written by Isaac J. Schoenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Interpolation categories.
Handbook On Splines For The User
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Author : Eugene V. Shikin
language : en
Publisher: CRC Press
Release Date : 1995-07-14
Handbook On Splines For The User written by Eugene V. Shikin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-14 with Mathematics categories.
Splines find ever increasing application in the numerical methods, computer-aided design, and computer graphics areas. The Handbook on Splines for the User not only provides an excellent introduction to basic concepts and methods but also includes the SplineGuide-a computer diskette that allows the reader to practice using important programs.These programs help the user to build interpolating and smoothing cubic and bicubic splines of all classes. Programs are described in Fortran for spline functions and C for geometric splines. The Handbook describes spline functions and geometric splines and provides simple, but effective algorithms. It covers virtually all of the important types of cubic and bicubic splines, functions, variables, curves, and surfaces. The book is written in a straightforward manner and requires little mathematical background. When necessary, the authors give theoretical treatments in an easy-to-use form. Through the Handbook on Splines for the User, introduce yourself to the exciting world of splines and learn to use them in practical applications and computer graphics.
Multivariate Approximation And Splines
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Author : Günther Nürnberger
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Multivariate Approximation And Splines written by Günther Nürnberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This volume presents refereed papers covering a variety of topics in the growing field of multivariate approximation and slines.