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# 스플라인 생성

B-form, 텐서 곱, NURB 및 기타 유리 스플라인을 비롯한 스플라인 만들기

곡선 피팅 앱 또는 `fit` 함수를 사용하여 3차 스플라인 보간, 평활화 스플라인 및 박판 스플라인을 피팅할 수 있습니다. 다른 Curve Fitting Toolbox™ 함수를 사용하여 스플라인 생성을 보다 세부적으로 제어할 수도 있습니다. 예를 들어, 함수 `csapi`를 사용하여 3차 스플라인 보간을 수행할 수 있습니다. 자세한 내용은 How to Construct Splines 항목을 참조하십시오.

## 함수

 `bspline` B-스플라인과 그 다항식 조각 플로팅 `csape` 끝점 조건을 사용하는 3차 스플라인 보간 `csapi` 3차 스플라인 보간 `csaps` 3차 평활화 스플라인 `cscvn` “자연” 또는 주기적 보간 3차 스플라인 곡선 `franke` Franke의 이변량 테스트 함수 `getcurve` 대화형 방식으로 3차 스플라인 곡선 생성 `ppmak` Put together spline in ppform `rpmak` Put together rational spline `rscvn` Piecewise biarc Hermite interpolation `rsmak` Put together rational spline for standard geometric shapes `spap2` Least-squares spline approximation `spapi` Spline interpolation `spaps` Smoothing spline `spcrv` 균일 분할에 의한 스플라인 곡선 `splinetool` Experiment with some spline approximation methods `spmak` Put together spline in B-form `spterms` Explain spline terms `stmak` Put together function in stform `tpaps` Thin-plate smoothing spline `titanium` 티타늄 테스트 데이터

## 도움말 항목

### 스플라인 소개

스플라인 피팅 소개

Curve Fitting Toolbox의 대화형 방식 및 프로그래밍 방식 스플라인 피팅을 위한 툴.

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-스플라인 및 평활화 스플라인

B-form 및 평활화 스플라인의 정의에 대해 알아봅니다.

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.

### 기본 스플라인 방법

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:

Construction of the Chebyshev Spline

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™.

### 데이터에 스플라인 피팅하기

3차 스플라인 보간

이 예제에서는 Curve Fitting Toolbox™의 `csapi``csape` 명령을 사용하여 3차 스플라인 보간을 생성하는 방법을 보여줍니다.

3차 평활화 스플라인

이 예제에서는 Curve Fitting Toolbox™의 `csaps``spaps` 명령을 사용하여 3차 평활화 스플라인을 생성하는 방법을 보여줍니다.

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.

### 스플라인 응용 사례

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.

2차원 및 3차원에서 스플라인 곡선 생성하기

이 예제에서는 Curve Fitting Toolbox™의 `cscvn` 명령을 사용하여 2차원 및 3차원에서 3차 스플라인 곡선을 생성하는 방법을 보여줍니다.

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).

Construction of a Chebyshev Spline

This example shows how to use commands from Curve Fitting Toolbox™ to construct a Chebyshev spline.