interp3

Interpolation for 3-D gridded data in meshgrid format

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Syntax

Vq = interp3(X,Y,Z,V,Xq,Yq,Zq)

Vq = interp3(V,Xq,Yq,Zq)

Vq = interp3(V)

Vq = interp3(V,k)

Vq = interp3(___,method)

Vq = interp3(___,method,extrapval)

Description

example

Vq= interp3(X,Y,Z,V,Xq,Yq,Zq)returns interpolated values of a function of three variables at specific query points using linear interpolation. The results always pass through the original sampling of the function.X,Y, andZcontain the coordinates of the sample points.Vcontains the corresponding function values at each sample point.Xq,Yq, andZqcontain the coordinates of the query points.

Vq= interp3(V,Xq,Yq,Zq)assumes a default grid of sample points. The default grid points cover the region,X=1:n,Y=1:m,Z=1:p, where[m,n,p] = size(V)．Use this syntax when you want to conserve memory and are not concerned about the absolute distances between points.

Vq= interp3(V)returns the interpolated values on a refined grid formed by dividing the interval between sample values once in each dimension.

Vq= interp3(V,k)returns the interpolated values on a refined grid formed by repeatedly halving the intervalsktimes in each dimension. This results in2^k-1interpolated points between sample values.

example

Vq= interp3(___,method)指定一个替代插值方法:'linear','nearest','cubic','makima', or'spline'．The default method is'linear'．

example

Vq= interp3(___,method,extrapval)also specifiesextrapval, a scalar value that is assigned to all queries that lie outside the domain of the sample points.

If you omit theextrapvalargument for queries outside the domain of the sample points, then based on themethodargumentinterp3returns one of the following:

The extrapolated values for the'spline'and'makima'methods
NaNvalues for other interpolation methods

Examples

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Interpolate Using Default Method

Open Live Script

Load the points and values of the flow function, sampled at 10 points in each dimension.

[X,Y,Z,V] = flow(10);

Theflowfunction returns the grid in the arrays,X,Y,Z．The grid covers the region, $0 ． 1 \leq X \leq 10$ , $- 3 \leq Y \leq 3$ , $- 3 \leq Z \leq 3$ , and the spacing is $Δ X = 0 ． 5$ , $Δ Y = 0 ． 7$ , and $Δ Z = 0 ． 7$ ．

Now, plot slices through the volume of the sample at:X=6,X=9,Y=2, andZ=0．

figure slice(X,Y,Z,V,[6 9],2,0); shadingflat

Figure contains an axes object. The axes object contains 4 objects of type surface.

Create a query grid with spacing of 0.25.

[Xq,Yq,Zq] = meshgrid(.1:.25:10,-3:.25:3,-3:.25:3);

Interpolate at the points in the query grid and plot the results using the same slice planes.

Vq = interp3(X,Y,Z,V,Xq,Yq,Zq); figure slice(Xq,Yq,Zq,Vq,[6 9],2,0); shadingflat

Figure contains an axes object. The axes object contains 4 objects of type surface.

Interpolate Using Cubic Method

Open Live Script

Load the points and values of the flow function, sampled at 10 points in each dimension.

[X,Y,Z,V] = flow(10);

Plot slices through the volume of the sample at:X=6,X=9,Y=2, andZ =0．

figure slice(X,Y,Z,V,[6 9],2,0); shadingflat

Figure contains an axes object. The axes object contains 4 objects of type surface.

Create a query grid with spacing of 0.25.

[Xq,Yq,Zq] = meshgrid(.1:.25:10,-3:.25:3,-3:.25:3);

Interpolate at the points in the query grid using the'cubic'interpolation method. Then plot the results.

Vq = interp3(X,Y,Z,V,Xq,Yq,Zq,'cubic'); figure slice(Xq,Yq,Zq,Vq,[6 9],2,0); shadingflat

Figure contains an axes object. The axes object contains 4 objects of type surface.

Evaluate Outside the Domain of X, Y, and Z

Open Live Script

Create the grid vectors,x,y, andz．These vectors define the points associated with values inV．

x = 1:100; y = (1:50)'; z = 1:30;

Define the sample values to be a 50-by-100-by-30 random number array,V．Use therandfunction to create the array.

rng('default') V = rand(50,100,30);

EvaluateVat three points outside the domain ofx,y, andz．Specifyextrapval = -1．

xq = [0 0 0]; yq = [0 0 51]; zq = [0 101 102]; vq = interp3(x,y,z,V,xq,yq,zq,'linear',-1)

vq =1×3-1 -1 -1

All three points evaluate to-1because they are outside the domain ofx,y, andz．

输入参数

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`X,Y,Z`—Sample grid points
arrays|vectors

Sample grid points, specified as real arrays or vectors. The sample grid points must be unique.

IfX,Y, andZare arrays, then they contain the coordinates of afull grid (in meshgrid format)．Use themeshgridfunction to create theX,Y, andZarrays together. These arrays must be the same size.
IfX,Y, andZare vectors, then they are treated as agrid vectors．的值in these vectors must bestrictly monotonic, either increasing or decreasing.

Example:[X,Y,Z] = meshgrid(1:30,-10:10,1:5)

Data Types:single|double

`V`—Sample values
array

Sample values, specified as a real or complex array. The size requirements forVdepend on the size ofX,Y, andZ:

IfX,Y, andZare arrays representing a full grid (inmeshgridformat), then the size ofVmatches the size ofX,Y, orZ．
IfX,Y, andZare grid vectors, thensize(V) = [length(Y) length(X) length(Z)]．

IfVcontains complex numbers, theninterp3interpolates the real and imaginary parts separately.

Example:rand(10,10,10)

Data Types:single|double
Complex Number Support:Yes

`Xq,Yq,Zq`—Query points
scalars|vectors|arrays

Query points, specified as a real scalars, vectors, or arrays.

IfXq,Yq, andZqare scalars, then they are the coordinates of a single query point inR³．
IfXq,Yq, andZqare vectors of different orientations, thenXq,Yq, andZqare treated as grid vectors inR³．
IfXq,Yq, andZqare vectors of the same size and orientation, thenXq,Yq, andZqare treated asscattered pointsinR³．
IfXq,Yq, andZqare arrays of the same size, then they represent either a full grid of query points (inmeshgridformat) or scattered points inR³．

Example:[Xq,Yq,Zq] = meshgrid((1:0.1:10),(-5:0.1:0),3:5)

Data Types:single|double

`k`—Refinement factor
`1`(default) |real, nonnegative, integer scalar

Refinement factor, specified as a real, nonnegative, integer scalar. This value specifies the number of times to repeatedly divide the intervals of the refined grid in each dimension. This results in2^k-1interpolated points between sample values.

Ifkis0, thenVqis the same asV．

interp3(V,1)is the same asinterp3(V)．

The following illustration depictsk=2in one plane ofR³．There are 72 interpolated values in red and 9 sample values in black.

Example:interp3(V,2)

Data Types:single|double

`method`—插值法
`'linear'`(default) |`'nearest'`|`'cubic'`|`'spline'`|`'makima'`

插值法, specified as one of the options in this table.

Method	Description	Continuity	Comments
`'linear'`	The interpolated value at a query point is based on linear interpolation of the values at neighboring grid points in each respective dimension. This is the default interpolation method.	C⁰	Requires at least two grid points in each dimension Requires more memory than`'nearest'`
`'nearest'`	The interpolated value at a query point is the value at the nearest sample grid point.	Discontinuous	Requires two grid points in each dimension Fastest computation with modest memory requirements
`'cubic'`	The interpolated value at a query point is based on a cubic interpolation of the values at neighboring grid points in each respective dimension. The interpolation is based on a cubic convolution.	C¹	Grid must have uniform spacing in each dimension, but the spacing does not have to be the same for all dimensions Requires at least four points in each dimension Requires more memory and computation time than`'linear'`
`'makima'`	Modified Akima cubic Hermite interpolation. The interpolated value at a query point is based on a piecewise function of polynomials with degree at most three evaluated using the values of neighboring grid points in each respective dimension. The Akima formula is modified to avoid overshoots.	C¹	Requires at least 2 points in each dimension Produces fewer undulations than`'spline'` Computation time is typically less than`'spline'`, but the memory requirements are similar
`'spline'`	The interpolated value at a query point is based on a cubic interpolation of the values at neighboring grid points in each respective dimension. The interpolation is based on a cubic spline using not-a-knot end conditions.	C²	Requires four points in each dimension Requires more memory and computation time than`'cubic'`

`extrapval`—Function value outside domain of`X`,`Y`, and`Z`
scalar

Function value outside domain ofX,Y, andZ, specified as a real or complex scalar.interp3returns this constant value for all points outside the domain ofX,Y, andZ．

Example:5

Example:5+1i

Data Types:single|double
Complex Number Support:Yes

Output Arguments

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`Vq`— Interpolated values
scalar | vector | array

Interpolated values, returned as a real or complex scalar, vector, or array. The size and shape ofVqdepends on the syntax you use and, in some cases, the size and value of the input arguments.

Syntaxes	Special Conditions	Size of Vq	Example
`interp3(X,Y,Z,V,Xq,Yq,Zq)` `interp3(V,Xq,Yq,Zq)` and variations of these syntaxes that include`method`or`extrapval`	`Xq`,`Yq`, and`Zq`are scalars.	Scalar	`size(Vq) = [1 1]`when you pass`Xq`,`Yq`, and`Zq`as scalars.
Same as above	`Xq`,`Yq`, and`Zq`are vectors of the same size and orientation.	Vector of same size and orientation as`Xq`,`Yq`, and`Zq`	If`size(Xq) = [100 1]`, and`size(Yq) = [100 1]`, and`size(Zq) = [100 1]`, then`size(Vq) = [100 1]`．
Same as above	`Xq`,`Yq`, and`Zq`are vectors of mixed orientation.	`size(Vq) = [length(Y) length(X) length(Z)]`	If`size(Xq) = [1 100]`, and`size(Yq) = [50 1]`, and`size(Zq) = [1 5]`, then`size(Vq) = [50 100 5]`．
Same as above	`Xq`,`Yq`, and`Zq`are arrays of the same size.	Array of the same size as`Xq`,`Yq`, and`Zq`	If`size(Xq) = [50 25]`, and`size(Yq) = [50 25]`, and`size(Zq) = [50 25]`, then`size(Vq) = [50 25]`．
`interp3(V,k)` and variations of this syntax that include`method`or`extrapval`	None	Array in which the length of the`i`th dimension is `2^k * (size(V,i)-1)+1`	If`size(V) = [10 12 5]`, and`k = 3`, then`size(Vq) = [73 89 33]`．

More About

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Strictly Monotonic

A set of values that are always increasing or decreasing, without reversals. For example, the sequence,a = [2 4 6 8]is strictly monotonic and increasing. The sequence,b = [2 4 4 6 8]is not strictly monotonic because there is no change in value betweenb(2)andb(3)．The sequence,c = [2 4 6 8 6]contains a reversal betweenc(4)andc(5), so it is not monotonic at all.

Full Grid (in meshgrid Format)

Forinterp3, a full grid consists of three arrays whose elements represent a grid of points that define a region inR³．The first array contains thex-coordinates, the second array contains they-coordinates, and the third array contains thez-coordinates. The values in each array vary along a single dimension and are constant along the other dimensions.

的值in thex-array arestrictly monotonic, increasing, and vary along the second dimension. The values in they-array are strictly monotonic, increasing, and vary along the first dimension. The values in thez-array are strictly monotonic, increasing, and vary along the third dimension. Use themeshgridfunction to create a full grid that you can pass tointerp3．

Grid Vectors

Forinterp3, grid vectors consist of three vectors of mixed-orientation that define the points on a grid inR³．

For example, the following code creates the grid vectors for the region, 1 ≤x≤ 3, 4 ≤y≤ 5, and 6 ≤z≤ 8:

x = 1:3; y = (4:5)'; z = 6:8;

Scattered Points

Forinterp3, scattered points consist of three arrays or vectors,Xq,Yq, andZq, that define a collection of points scattered inR³．第i个数组包含的坐标h dimension.

For example, the following code specifies the points, (1, 19, 10), (6, 40, 1), (15, 33, 22), and (0, 61, 13).

Xq = [1 6; 15 0]; Yq = [19 40; 33 61]; Zq = [10 1; 22 13];

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Xq,Yq, andZqmust be the same size. Usemeshgridto evaluate on a grid.
For best results, provideX,Y, andZas vectors. The values in these vectors must be strictly monotonic and increasing.
Code generation does not support the'makima'interpolation method.
For the'cubic'interpolation method, if the grid does not have uniform spacing, an error results. In this case, use the'spline'interpolation method.
For best results when you use the'spline'interpolation method:
- Usemeshgridto create the inputsXq,Yq, andZq．
- Use a small number of interpolation points relative to the dimensions ofV．Interpolating over a large set of scattered points can be inefficient.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`．

This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment．

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

Vmust be a double or single 3-D array.Vcan be real or complex.
X,Y, andZmust:
- Have the same type (double or single).
- Be finite vectors or 3-D arrays with increasing and nonrepeating elements in corresponding dimensions.
- Align with Cartesian axes whenX,Y, andZare 3-D arrays (as if they were produced bymeshgrid).
- Have dimensions consistent withV．
Xq,Yq, andZqmust be vectors or arrays of the same type (double or single). IfXq,Yq, andZqare arrays, then they must have the same size. If they are vectors with different lengths, then one of them must have a different orientation.
methodmust be'linear'or'nearest'．
The extrapolation for the out-of-boundary input is not supported.

For more information, seeRun MATLAB Functions on a GPU(Parallel Computing Toolbox)．

interp3

Syntax

Description

Examples

Interpolate Using Default Method

Interpolate Using Cubic Method

Evaluate Outside the Domain of X, Y, and Z

输入参数

`X,Y,Z`—Sample grid points
arrays|vectors

`V`—Sample values
array

`Xq,Yq,Zq`—Query points
scalars|vectors|arrays

`k`—Refinement factor
`1`(default) |real, nonnegative, integer scalar

`method`—插值法
`'linear'`(default) |`'nearest'`|`'cubic'`|`'spline'`|`'makima'`

`extrapval`—Function value outside domain of`X`,`Y`, and`Z`
scalar

Output Arguments

`Vq`— Interpolated values
scalar | vector | array

More About

Strictly Monotonic

Full Grid (in meshgrid Format)

Grid Vectors

Scattered Points

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`．

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

See Also

MATLAB Documentation

金宝app

Introducing Deep Learning with MATLAB

interp3

Syntax

Description

Examples

Interpolate Using Default Method

Interpolate Using Cubic Method

Evaluate Outside the Domain of X, Y, and Z

输入参数

X,Y,Z—Sample grid pointsarrays|vectors

V—Sample valuesarray

Xq,Yq,Zq—Query pointsscalars|vectors|arrays

k—Refinement factor1(default) |real, nonnegative, integer scalar

method—插值法'linear'(default) |'nearest'|'cubic'|'spline'|'makima'

extrapval—Function value outside domain ofX,Y, andZscalar

Output Arguments

Vq— Interpolated valuesscalar | vector | array

More About

Strictly Monotonic

Full Grid (in meshgrid Format)

Grid Vectors

Scattered Points

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

Thread-Based EnvironmentRun code in the background using MATLAB®backgroundPoolor accelerate code with Parallel Computing Toolbox™ThreadPool．

GPU ArraysAccelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

See Also

MATLAB Documentation

金宝app

Introducing Deep Learning with MATLAB

`X,Y,Z`—Sample grid points
arrays|vectors

`V`—Sample values
array

`Xq,Yq,Zq`—Query points
scalars|vectors|arrays

`k`—Refinement factor
`1`(default) |real, nonnegative, integer scalar

`method`—插值法
`'linear'`(default) |`'nearest'`|`'cubic'`|`'spline'`|`'makima'`

`extrapval`—Function value outside domain of`X`,`Y`, and`Z`
scalar

`Vq`— Interpolated values
scalar | vector | array

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`．

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.