Spline Toolbox Getting Started Introduction What Is the Spline Toolbox? New Features in Version 3.2 ND-Valued Data and Spline Functions Repeated Sites Updated Demos Other Enhancements Using this Guide Splines in MATLAB Expected Background Technical Conventions Examples Tutorial Some Simple Examples Cubic Spline Interpolation Periodic Data Other End Conditions General Spline Interpolation Knot Choices Smoothing Least Squares Using the Spline Fits Vector-Valued Functions Fitting Values at N-D Grid Fitting Values at Scattered 2-D Sites Splines: An Overview Polynomials vs. Splines ppform B-form Knot Multiplicity B-Spline Properties Constructive vs. Variational Multivariate Splines The ppform Breaks ppform Construction Use The B-form B-form B-Splines Knot Multiplicity Choice of Knots Splines Construction Example: A Spline Curve Use Tensor Product Splines B-form ppform NURBS and Other Rational Splines Rational Splines Example: Circle Example: Sphere rsform Use The stform stform Use Example: A Nonlinear ODE Problem Approximation Space Discretization Numerical Problem Linearization Linear System to Be Solved Iteration Example: Construction of the Chebyshev Spline What Is a Chebyshev Spline? Choice of Spline Space Initial Guess Remez Iteration Example: Approximation by Tensor Product Splines Choice of Sites and Knots Least Squares Approximation as Function of y Approximation to Coefficients as Functions of x The Bivariate Approximation Switch in Order Approximation to Coefficients as Functions of y The Bivariate Approximation Comparison and Extension Functions -- Categorical List GUIs Construction of Splines Operators Work with Breaks, Knots, and Sites Customized Linear Equation Solver Information About Splines and the Toolbox Demonstrations Utilities Functions -- Alphabetical List Glossary Introduction List of Terms Release Notes Spline Toolbox 3.2 Release Notes New Features ND-Valued Data and Spline Functions Repeated Sites Updated Demos Toolbox Function Summary Upgrading from an Earlier Release NaNs and Infs Simplified csape Input Updated spap2, spapi Input Requirements Spline Toolbox 3.1.1 Release Notes New Features Smoothing Splines for Scattered Bivariate Data splinetool Command History M-File Spline-Specific Zero Finder Spline-Specific Minimum Finder Function Summary Major Bug Fixes Upgrading from an Earlier Release Use playshow Command to Run Slideshow Style Demos Spline Toolbox 3.0 Release Notes New Features Spline Tool Provides a Visual Interface to the Spline Toolbox Automatic Knot Choice Simplifies Use of spapi and spap2 Automatic Smoothing Parameter Choice Simplifies Use of csaps Use of Rational Splines B-Spline Visual Interface Other New Functions Other Enhancements Major Bug Fixes spmak and ppmak Use Size Argument to Correctly Construct Multivariate Splines Upgrading from an Earlier Release optknt and newknt Output No Longer Needs To Be Run Through augknt Printable Documentation (PDF) Product Page (Web)