Some Simple Examples
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Shows you some simple ways to make use of the commands in this toolbox.
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Splines: An Overview
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Explains the advantage of splines over polynomials, introduces the two forms in which splines are described in this toolbox, and highlights the role of knot multiplicity. Also compares the constructive and variational approaches to splines, and touches on multivariate splines.
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The ppform
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Describes the parts of the piecewise polynomial form (ppform) for a univariate spline: breaks and coefficients. Lists ways for constructing and using a ppform.
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The B-form
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Describes the parts of the B-spline form (B-form) for a univariate spline: knots and coefficients. Also discusses the B-splines on which this form is based, the role of knot multiplicity, and lists ways for constructing and use a B-form.
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Tensor Product Splines
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Describes the tensor-product construct for creating multivariate spline functions, both in ppform and B-form.
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NURBS and Other Rational Splines
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Describes the construction and use of rational splines, in terms of the rsform.
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The stform
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Introduces the thin-plate spline, for the interpolation and and smoothing of bivariate scatttered data, and their description by the parts of a scattered-translates form (stform): centers and coefficients.
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Example: A Nonlinear ODE
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Illustrates the use of the toolbox in the construction of a spline approximation to the solution of a second-order nonlinear ordinary differential equation two-point boundary value problem with a boundary layer.
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Example: Construction of the Chebyshev Spline
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Illustrates the use of the toolbox to construct a maximally equioscillating spline for prescribed knots and order, an iterative process that also requires the differentation of a spline.
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Example: Approximation by Tensor Product Splines
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A detailed account by example of the ideas behind the tensor product way of creating multivariate splines.
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