User Manual 4.0 Interpolation Methods - Historique des versions

Admin : /* Features Description */

2018-02-27T10:24:47Z

Features Description

← Version précédente		Version du 27 février 2018 à 10:24
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	== Features Description ==		== Features Description ==
	=== Spline interpolation ===		=== Spline interpolation ===
	The'''''spline interpolator''''' generates an interpolating function <math>f(x): \mathbb{R} \rightarrow \mathbb{R}</math>. The user gives as entries 2 sets of values, the values of x, y. The interpolator gives the function f such as <math>y=f(x)</math>.		The '''''spline interpolator''''' generates an interpolating function <math>f(x): \mathbb{R} \rightarrow \mathbb{R}</math>. The user gives as entries 2 sets of values, the values of x, y. The interpolator gives the function f such as <math>y=f(x)</math>.

	For the linear equation <math>y=2x+1</math>		For the linear equation <math>y=2x+1</math>
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	=== Bicubic interpolation ===		=== Bicubic interpolation ===
	The'''''bicubic interpolator''''' generates an interpolating function <math>f(x,y): \mathbb{R}^2 \rightarrow \mathbb{R}</math>. The interpolator computes internally the coefficients of the bicubic function that is the interpolating function. The user gives as entries 3 sets of values, the values of x, y and z. The interpolator gives the function f such as <math>z=f(x,y)</math>.		The '''''bicubic interpolator''''' generates an interpolating function <math>f(x,y): \mathbb{R}^2 \rightarrow \mathbb{R}</math>. The interpolator computes internally the coefficients of the bicubic function that is the interpolating function. The user gives as entries 3 sets of values, the values of x, y and z. The interpolator gives the function f such as <math>z=f(x,y)</math>.

	For the equation of the plane <math>z=2x-3y + 5</math>		For the equation of the plane <math>z=2x-3y + 5</math>
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	=== Tricubic interpolation ===		=== Tricubic interpolation ===
	The'''''tricubic interpolator''''' generates an interpolating function <math>f(x,y,z): \mathbb{R}^3 \rightarrow \mathbb{R}</math>. The interpolator computes internally the coefficients of the tricubic function that is the interpolating function. The user gives as entries 4 sets of values, the values of x, y, z and w. The interpolator gives the function f such as <math>w=f(x,y,z)</math>.		The '''''tricubic interpolator''''' generates an interpolating function <math>f(x,y,z): \mathbb{R}^3 \rightarrow \mathbb{R}</math>. The interpolator computes internally the coefficients of the tricubic function that is the interpolating function. The user gives as entries 4 sets of values, the values of x, y, z and w. The interpolator gives the function f such as <math>w=f(x,y,z)</math>.

	For the equation of the plane <math>w=2x- 3y - z + 5</math>		For the equation of the plane <math>w=2x- 3y - z + 5</math>
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	=== Lagrange interpolation ===		=== Lagrange interpolation ===
	The'''''Lagrange interpolator''''' generates an interpolating function <math>f(x): \mathbb{R} \rightarrow \mathbb{R}</math>. The user gives as entries 2 sets of values, the values of x, y. The interpolator gives the function f such as <math>y=f(x)</math>.		The '''''Lagrange interpolator''''' generates an interpolating function <math>f(x): \mathbb{R} \rightarrow \mathbb{R}</math>. The user gives as entries 2 sets of values, the values of x, y. The interpolator gives the function f such as <math>y=f(x)</math>.

	For the linear equation <math>y=2x+1</math>		For the linear equation <math>y=2x+1</math>
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	=== Newton interpolation ===		=== Newton interpolation ===
	The'''''Newton interpolator''''' generates an interpolating function <math>f(x): \mathbb{R} \rightarrow \mathbb{R}</math>. The user gives as entries 2 sets of values, the coefficients <math>c_i</math>and the centers <math>x_i</math>such as the polynomial function <math>P(x)=c_0 + c_1 (x - x_0) + ... + c_n (x - x_n)</math>. The interpolator gives the function f such as <math>y=P(x)</math>.		The '''''Newton interpolator''''' generates an interpolating function <math>f(x): \mathbb{R} \rightarrow \mathbb{R}</math>. The user gives as entries 2 sets of values, the coefficients <math>c_i</math>and the centers <math>x_i</math>such as the polynomial function <math>P(x)=c_0 + c_1 (x - x_0) + ... + c_n (x - x_n)</math>. The interpolator gives the function f such as <math>y=P(x)</math>.

	For the linear equation <math>y=2x+1</math>		For the linear equation <math>y=2x+1</math>

Admin : /* Contents */

2018-02-21T08:29:44Z

Contents

Voir les modifications

Admin : /* Package Overview */

2018-02-21T08:24:28Z

Package Overview

← Version précédente		Version du 21 février 2018 à 08:24
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	=== Package Overview ===		=== Package Overview ===
	The package <~~syntaxhighlight lang="java"~~>fr.cnes.sirius.patrius.math		The package <code>fr.cnes.sirius.patrius.math.analysis.interpolation</code> contains all the interpolation classes described in this section.
	.analysis.interpolation</~~syntaxhighlight~~> contains all the interpolation classes described in this section.

	[[File:PATRIMOINESIRIUSSUMDiagInterpolation.png]]		[[File:PATRIMOINESIRIUSSUMDiagInterpolation.png]]

Admin : /* Javadoc */

2018-02-21T08:24:10Z

Javadoc

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 === Javadoc ===
 The interpolation objects are available in the package <code>fr.cnes.sirius.patrius.math.analysis.interpolation</code> and in the  package <code>fr.cnes.sirius.patrius.propagation.analytical.covariance</code>.
 === Links ===

Admin le 20 février 2018 à 16:45

2018-02-20T16:45:22Z

← Version précédente		Version du 20 février 2018 à 16:45
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			__NOTOC__

	== Introduction ==		== Introduction ==
	=== Scope ===		=== Scope ===

Admin le 19 février 2018 à 09:33

2018-02-19T09:33:13Z

← Version précédente		Version du 19 février 2018 à 09:33
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	\|'''BiLinearIntervalsInterpolator'''\|Interpolator of linear two-dimensional functions.\|[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/interpolation/BiLinearIntervalsInterpolator.html ...]		\|'''BiLinearIntervalsInterpolator'''\|Interpolator of linear two-dimensional functions.\|[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/interpolation/BiLinearIntervalsInterpolator.html ...]
	\|'''TriLinearIntervalsInterpolator'''\|Interpolator of linear three-dimensional functions.\|[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/interpolation/TriLinearIntervalsInterpolator.html ...]		\|'''TriLinearIntervalsInterpolator'''\|Interpolator of linear three-dimensional functions.\|[{{PathCurrentJavaDoc}}/fr/cnes/sirius/patrius/math/analysis/interpolation/TriLinearIntervalsInterpolator.html ...]

			[[Category:User_Manual_4.0_Mathematics]]

Admin : /* 2D interpolation */

2018-02-19T09:31:32Z

2D interpolation

← Version précédente		Version du 19 février 2018 à 09:31
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	Let <math>f</math> be a real function <math>\mathbb{R}^2 \rightarrow \mathbb{R}</math> and <math>[x_1,x_2] \times [y_1,y_2]</math> the interpolation interval.		Let <math>f</math> be a real function <math>\mathbb{R}^2 \rightarrow \mathbb{R}</math> and <math>[x_1,x_2] \times [y_1,y_2]</math> the interpolation interval.
	First, a 1D interpolation in the <math>y</math> direction is made, leading to		First, a 1D interpolation in the <math>y</math> direction is made, leading to
	<math>f(x,y_1) = f(x_1,y_1) + (y-y_1) \frac{f(x_2,y_1)- f(x_1,y_1)}{y_2-y_1},</math>		<math>f(x,y_1) = f(x_1,y_1) + (y-y_1) \frac{f(x_2,y_1)- f(x_1,y_1)}{y_2-y_1},</math>

	<math>f(x,y_2) = f(x_1,y_2) + (y-y_1) \frac{f(x_2,y_2)- f(x_1,y_2)}{y_2-y_1}.</math>		<math>f(x,y_2) = f(x_1,y_2) + (y-y_1) \frac{f(x_2,y_2)- f(x_1,y_2)}{y_2-y_1}.</math>

	Then a second 1D interpolation is made in the <math>x</math> direction with the previous two interpolated values :		Then a second 1D interpolation is made in the <math>x</math> direction with the previous two interpolated values :
	<math>f(x,y) = f(x,y_1) + (x-x_1) \frac{f(x,y_2)- f(x, y_1)}{x_2-x_1}.</math>		<math>f(x,y) = f(x,y_1) + (x-x_1) \frac{f(x,y_2)- f(x, y_1)}{x_2-x_1}.</math>

	==== 3D interpolation ====		==== 3D interpolation ====

Admin : /* 3D interpolation */

2018-02-19T09:30:50Z

3D interpolation

← Version précédente		Version du 19 février 2018 à 09:30
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	<math>f(x,y,z_1)</math> is interpolated from <math>f(x,y_1,z_1)</math> and <math>f(x,y_2,z_1)</math>.		<math>f(x,y,z_1)</math> is interpolated from <math>f(x,y_1,z_1)</math> and <math>f(x,y_2,z_1)</math>.

	<math>f(x,y,z_2)</math> is interpolated from <math>f(x,y_1,z_2)</math> and <math>f(x,y_2,z_2)</math>.		<math>f(x,y,z_2)</math> is interpolated from <math>f(x,y_1,z_2)</math> and <math>f(x,y_2,z_2)</math>.


	<math>f(x,y_1,z_1)</math> is interpolated from <math>f(x_1,y_1,z_1)</math> and <math>f(x_2,y_1,z_1)</math>.		<math>f(x,y_1,z_1)</math> is interpolated from <math>f(x_1,y_1,z_1)</math> and <math>f(x_2,y_1,z_1)</math>.

	<math>f(x,y_2,z_1)</math> is interpolated from <math>f(x_1,y_2,z_1)</math> and <math>f(x_2,y_2,z_1)</math>.		<math>f(x,y_2,z_1)</math> is interpolated from <math>f(x_1,y_2,z_1)</math> and <math>f(x_2,y_2,z_1)</math>.

	<math>f(x,y_1,z_2)</math> is interpolated from <math>f(x_1,y_1,z_2)</math> and <math>f(x_2,y_1,z_1)</math>.		<math>f(x,y_1,z_2)</math> is interpolated from <math>f(x_1,y_1,z_2)</math> and <math>f(x_2,y_1,z_1)</math>.

	<math>f(x,y_2,z_2)</math> is interpolated from <math>f(x_1,y_2,z_2)</math> and <math>f(x_2,y_2,z_2)</math>.		<math>f(x,y_2,z_2)</math> is interpolated from <math>f(x_1,y_2,z_2)</math> and <math>f(x_2,y_2,z_2)</math>.


	== Getting Started ==		== Getting Started ==

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User Manual 4.0 Interpolation Methods - Historique des versions

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