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 |
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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 |
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 |
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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 |
ISBN | 9781461213208 |
URL | http://dx.doi.org/10.1007/978-1-4612-1320-8 |
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