このページのリンク

Interpolating Cubic Splines / by Gary D. Knott
(Progress in Computer Science and Applied Logic ; 18)

データ種別 電子ブック
出版者 Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser
出版年 2000
本文言語 英語
大きさ XII, 244 p : online resource

所蔵情報を非表示

URL 電子ブック


EB0064974

書誌詳細を非表示

内容注記 1 Mathematical Preliminaries
1.1 The Pythagorean Theorem
1.2 Vectors
1.3 Subspaces and Linear Independence
1.4 Vector Space Bases
1.5 Euclidean Length
1.6 The Euclidean Inner Product
1.7 Projection onto a Line
1.8 Planes in-Space
1.9 Coordinate System Orientation
1.10 The Cross Product
2 Curves
2.1 The Tangent Curve
2.2 Curve Parameterization
2.3 The Normal Curve
2.4 Envelope Curves
2.5 Arc Length Parameterization
2.6 Curvature
2.7 The Frenet Equations
2.8 Involutes and Evolutes
2.9 Helices
2.10 Signed Curvature
2.11 Inflection Points
3 Surfaces
3.1 The Gradient of a Function
3.2 The Tangent Space and Normal Vector
3.3 Derivatives
4 Function and Space Curve Interpolation
5 2D-Function Interpolation
5.1 Lagrange Interpolating Polynomials
5.2 Whittaker’s Interpolation Formula
5.3 Cubic Splines for 2D-Function Interpolation
5.4 Estimating Slopes
5.5 Monotone 2D Cubic Spline Functions
5.6 Error in 2D Cubic Spline Interpolation Functions
6 ?-Spline Curves With Range Dimension d
7 Cubic Polynomial Space Curve Splines
7.1 Choosing the Segment Parameter Limits
7.2 Estimating Tangent Vectors
7.3 Bézier Polynomials
8 Double Tangent Cubic Splines
8.1 Kochanek-Bartels Tangents
8.2 Fletcher-McAllister Tangent Magnitudes
9 Global Cubic Space Curve Splines
9.1 Second Derivatives of Global Cubic Splines
9.2 Third Derivatives of Global Cubic Splines
9.3 A Variational Characterization of Natural Splines
9.4 Weighted v-Splines
10 Smoothing Splines
10.1 Computing an Optimal Smoothing Spline
10.2 Computing the Smoothing Parameter
10.3 Best Fit Smoothing Cubic Splines
10.4 Monotone Smoothing Splines
11 Geometrically Continuous Cubic Splines
11.1 Beta Splines
12 Quadratic Space Curve Based Cubic Splines
13 Cubic Spline Vector Space Basis Functions
13.1 Bases for C1 and C2 Space Curve Cubic Splines
13.2 Cardinal Bases for Cubic Spline Vector Spaces
13.3 The B-Spline Basis for Global Cubic Splines
14 Rational Cubic Splines
15 Two Spline Programs
15.1 Interpolating Cubic Splines Program
15.2 Optimal Smoothing Spline Program
16 Tensor Product Surface Splines
16.1 Bicubic Tensor Product Surface Patch Splines
16.2 A Generalized Tensor Product Patch Spline
16.3 Regular Grid Multi-Patch Surface Interpolation
16.4 Estimating Tangent and Twist Vectors
16.5 Tensor Product Cardinal Basis Representation
16.6 Bicubic Splines with Variable Parameter Limits
16.7 Triangular Patches
16.8 Parametric Grids
16.9 3D-Function Interpolation
17 Boundary Curve Based Surface Splines
17.1 Boundary Curve Based Bilinear Interpolation
17.2 Boundary Curve Based Bicubic Interpolation
17.3 General Boundary Curve Based Spline Interpolation
18 Physical Splines
18.1 Computing a Space Curve Physical Spline Segment
18.2 Computing a 2D Physical Spline Segment
References
一般注記 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
著者標目 *Knott, Gary D. author
SpringerLink (Online service)
件 名 LCSH:Computer science
LCSH:Computer science -- Mathematics  全ての件名で検索
LCSH:Application software
LCSH:Computer-aided engineering
LCSH:Applied mathematics
LCSH:Engineering mathematics
LCSH:Computer mathematics
FREE:Computer Science
FREE:Math Applications in Computer Science
FREE:Computational Mathematics and Numerical Analysis
FREE:Applications of Mathematics
FREE:Computer-Aided Engineering (CAD, CAE) and Design
FREE:Computer Applications
分 類 DC23:004.0151
巻冊次 ISBN:9781461213208 REFWLINK
ISBN 9781461213208
URL http://dx.doi.org/10.1007/978-1-4612-1320-8
目次/あらすじ

 類似資料