Curves and Surfaces in Computer Aided Geometric Design [electronic resource] /

0. Mathematical Description of Shape Information -- 0.1 Description and Transmission of Shape Information -- 0.2 Processing and Analysis of Shapes -- 0.3 Mathematical Description of Free Form Shapes -- 0.4 The Development of Mathematical Descriptions of Free Form Curves and Surfaces -- References -- 1. Basic Theory of Curves and Surfaces -- 1.1 General -- 1.2 Curve Theory -- 1.3 Theory of Surfaces -- References -- 2. Lagrange Interpolation -- 2.1 Lagrange Interpolation Curves -- 2.2 Expression in Terms of Divided Differences -- References -- 3. Hermite Interpolation -- 3.1 Hermite Interpolation -- 3.2 Curves -- 3.3 Surfaces -- References -- 4. Spline Interpolation -- 4.1 Splines -- 4.2 Spline Functions -- 4.3 Mathematical Representation of Spline Functions -- 4.4 Natural Splines -- 4.5 Natural Splines and the Minimum Interpolation Property -- 4.6 Smoothing Splines -- 4.7 Parametric Spline Curves -- 4.8 End Conditions on a Spline Curve -- 4.9 Cubic Spline Curves Using Circular Arc Length -- 4.10 B-Splines -- 4.11 Generation of Spline Surfaces -- References -- 5. The Bernstein Approximation -- 5.1 Curves -- 5.2 Surfaces -- References -- 6. The B-Spline Approximation -- 6.1 Uniform Cubic B-Spline Curves -- 6.2 Uniform Bi-cubic B-Spline Surfaces -- 6.3 B-Spline Functions and Their Properties (1) -- 6.4 B-Spline Functions and Their Properties (2) -- 6.5 Derivation of B-Spline Functions -- 6.6 B-Spline Curve Type (1) -- 6.7 B-Spline Curve Type (2) -- 6.8 Recursive Calculation of B-Spline Functions -- 6.9 B-Spline Functions and Their Properties (3) -- 6.10 B-Spline Curve Type (3) -- 6.11 Differentiation of B-Spline Curves -- 6.12 Geometrical Properties of B-Spline Curves -- 6.13 Determination of a Point on a Curve by Linear Operations -- 6.14 Insertion of Knots -- 6.15 Curve Generation by Geometrical Processing -- 6.16 Interpolation of a Sequence of Points with a B-Spline Curve -- 6.17 Matrix Expression of B-Spline Curves -- 6.18 Expression of the Functions C0,0(t), C0,1(t), C1,0(t) and C1,1(t) by B-Spline Functions -- 6.19 General B-Spline Surfaces -- References -- 7. The Rational Polynomial Curves -- 7.1 Derivation of Parametric Conic Section Curves -- 7.2 Classification of Conic Section Curves -- 7.3 Parabolas -- 7.4 Circular Arc Formulas -- 7.5 Cubic/Cubic Rational Polynomial Curves -- 7.6 T-Conic Curves -- References -- Appendix A: Vector Expression of Simple Geometrical Relations.

Bibliographic Details

Main Authors:	Yamaguchi, Fujio. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg, 1988
Subjects:	Computer science., Arithmetic and logic units, Computer., Software engineering., Computer graphics., Computer-aided engineering., Applied mathematics., Engineering mathematics., Engineering design., Computer Science., Software Engineering/Programming and Operating Systems., Arithmetic and Logic Structures., Computer Graphics., Computer-Aided Engineering (CAD, CAE) and Design., Appl.Mathematics/Computational Methods of Engineering., Engineering Design.,
Online Access:	http://dx.doi.org/10.1007/978-3-642-48952-5
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