Author | Knott, Gary D. author |
---|---|
Title | Interpolating Cubic Splines [electronic resource] / by Gary D. Knott |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1320-8 |
Descript | XII, 244 p. online resource |
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 Whittakerโs 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 Bรฉzier 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