样条构造

创建样条，包括 B-型、张量积、NURB 以及其他有理样条

使用曲线拟合器或 fit 函数，您可以拟合三次样条插值、平滑样条和薄板样条。其他 Curve Fitting Toolbox™ 函数允许对样条构造进行更专门的控制。例如，您可以使用 csapi 函数进行三次样条插值。有关详细信息，请参阅How to Construct Splines。

函数

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B 样条拟合

bspline Plot B-spline and its polynomial pieces

样条插值

`csape`	Cubic spline interpolation with end conditions
`csapi`	Cubic spline interpolation
`cscvn`	“Natural” or periodic interpolating cubic spline curve
`rscvn`	Piecewise biarc Hermite interpolation
`spapi`	Spline interpolation
`tpaps`	Thin-plate smoothing spline

平滑样条拟合

`csaps`	Cubic smoothing spline
`spaps`	Smoothing spline
`spcrv`	通过均匀细分生成样条曲线
`tpaps`	Thin-plate smoothing spline

最小二乘拟合

spap2 Least-squares spline approximation

样条创建

`ppmak`	Put together spline in ppform
`rpmak`	Put together rational spline
`rsmak`	Put together rational spline for standard geometric shapes
`spmak`	Put together spline in B-form
`stmak`	Put together function in stform

数据集

titanium Titanium test data

测试函数

franke Franke's bivariate test function

交互式工具

`bspligui`	Experiment with B-spline as function of its knots
`getcurve`	Interactive creation of cubic spline curve
`splinetool`	Experiment with some spline approximation methods
`spterms`	Explain spline terms

主题

样条简介

Introducing Spline Fitting
Tools for interactive and programmatic spline fitting in Curve Fitting Toolbox.
Curve Fitting Toolbox Splines and MATLAB Splines
How Curve Fitting Toolbox extends the splines (or piecewise-polynomial functions) of MATLAB^®.
Types of Splines: ppform and B-form
Learn about the definitions of the ppform and B-form splines.
B-Splines and Smoothing Splines
Learn about the definitions of the B-form and smoothing splines.
Multivariate and Rational Splines
Learn how to construct multivariate and rational splines.
The ppform
Learn about the definition of the ppform spline.
The B-form
Learn about the definition of B-form splines.
NURBS and Other Rational Splines
Learn about the definitions of rational splines.

基本样条方法

Cubic Spline Interpolation
Use cubic splines to interpolate smooth data, choosing knots and smoothness.
Vector-Valued Functions
Use vector-valued splines to plot curves through given points.
Fitting Values at N-D Grid with Tensor-Product Splines
Use vector-valued splines to approximate gridded data in any number of variables using tensor-product splines.
Fitting Values at Scattered 2-D Sites with Thin-Plate Smoothing Splines
Use the thin-plate smoothing spline for work with scattered bivariate data. Tensor-product splines are good for gridded (bivariate and even multivariate) data.
Constructing and Working with ppform Splines
Learn how to construct ppform splines.
Constructing and Working with B-form Splines
Learn how to construct B-form splines.
Multivariate Tensor Product Splines
Learn how to construct multivariate splines.
Constructing and Working with Rational Splines
Learn how to construct rational splines.
Constructing and Working with stform Splines
Learn how to construct stform splines.
Least-Squares Approximation by Natural Cubic Splines
The construction of a least-squares approximant usually requires that one have in hand a basis for the space from which the data are to be approximated.
Solving A Nonlinear ODE
This section discusses these aspects of a nonlinear ODE problem:
Chebyshev Spline Construction
This section discusses these aspects of the Chebyshev spline construction:
Approximation by Tensor Product Splines
Because the toolbox can handle splines with vector coefficients, it is easy to implement interpolation or approximation to gridded data by tensor product splines, as the following illustration is meant to show.
How to Construct Splines
This example shows how to construct splines in various ways using the spline functions in Curve Fitting Toolbox™.
Construct and Work with the B-form
This example shows how to construct and work with the B-form of a spline in Curve Fitting Toolbox™.
Construct and Work with the PPFORM
This example shows how to construct and work with the ppform of a spline in Curve Fitting Toolbox™.
How to Choose Knots
This example shows how to select and optimize knots using the optknt and newknt commands from Curve Fitting Toolbox™.

对数据进行样条拟合

Cubic Spline Interpolation
This example shows how to use the csapi and csape commands from Curve Fitting Toolbox™ to construct cubic spline interpolants.
三次平滑样条
此示例说明如何使用 Curve Fitting Toolbox™ 中的 csaps 和 spaps 命令来构造三次平滑样条。
Fitting a Spline to Titanium Test Data
This example shows how to use commands from Curve Fitting Toolbox™ to fit a spline to titanium test data with manual and automatic selection of knots.

样条应用

Splines in the Plane
This example shows how to use the spmak, spcrv, cscvn and rscvn commands from Curve Fitting Toolbox™ to construct spline curves in the plane.
构造二维和三维样条曲线
此示例说明如何使用 Curve Fitting Toolbox™ 中的 cscvn 命令来构造二维和三维三次样条曲线。
Smoothing a Histogram
This example shows how to use spline commands from Curve Fitting Toolbox™ to smooth a histogram.
Bivariate Tensor Product Splines
This example shows how to use the spline commands in Curve Fitting Toolbox™ to fit tensor product splines to bivariate gridded data.
Solving a Nonlinear ODE with a Boundary Layer by Collocation
This example shows how to use spline commands from Curve Fitting Toolbox™ solve a nonlinear ordinary differential equation (ODE).
Construct Chebyshev Spline
This example shows how to use commands from Curve Fitting Toolbox™ to construct a Chebyshev spline.

精选示例

Construct and Work with the B-form

Construct and work with the B-form of a spline in Curve Fitting Toolbox™.

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Construct and Work with the PPFORM

Construct and work with the ppform of a spline in Curve Fitting Toolbox™.

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构造二维和三维样条曲线

此示例说明如何使用 Curve Fitting Toolbox™ 中的 cscvn 命令来构造二维和三维三次样条曲线。

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Splines in the Plane

Use the spmak, spcrv, cscvn and rscvn commands from Curve Fitting Toolbox™ to construct spline curves in the plane. This includes plotting tangents and computing the area enclosed by a curve.

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