interp2
Interpolation for 2D gridded data in meshgrid format
Syntax
Description
returns
interpolated values of a function of two variables at specific query
points using linear interpolation. The results always pass through
the original sampling of the function. Vq
= interp2(X,Y
,V
,Xq,Yq
)X
and Y
contain
the coordinates of the sample points. V
contains
the corresponding function values at each sample point. Xq
and Yq
contain
the coordinates of the query points.
also
specifies Vq
= interp2(___,method
,extrapval
)extrapval
, a scalar value that is assigned
to all queries that lie outside the domain of the sample points.
If you omit the extrapval
argument for queries
outside the domain of the sample points, then based on the method
argument interp2
returns
one of the following:
Extrapolated values for the
'spline'
and'makima'
methodsNaN
values for other interpolation methods
Examples
Interpolate Over a Grid Using Default Method
Coarsely sample the peaks
function.
[X,Y] = meshgrid(3:3); V = peaks(X,Y);
Plot the coarse sampling.
figure
surf(X,Y,V)
title('Original Sampling');
Create the query grid with spacing of 0.25.
[Xq,Yq] = meshgrid(3:0.25:3);
Interpolate at the query points.
Vq = interp2(X,Y,V,Xq,Yq);
Plot the result.
figure
surf(Xq,Yq,Vq);
title('Linear Interpolation Using Finer Grid');
Interpolate Over a Grid Using Cubic Method
Coarsely sample the peaks function.
[X,Y] = meshgrid(3:3); V = peaks(7);
Plot the coarse sampling.
figure
surf(X,Y,V)
title('Original Sampling');
Create the query grid with spacing of 0.25.
[Xq,Yq] = meshgrid(3:0.25:3);
Interpolate at the query points, and specify cubic interpolation.
Vq = interp2(X,Y,V,Xq,Yq,'cubic');
Plot the result.
figure
surf(Xq,Yq,Vq);
title('Cubic Interpolation Over Finer Grid');
Refine Grayscale Image
Load some image data into the workspace.
load flujet.mat colormap gray
Isolate a small region of the image and cast it to singleprecision.
V = single(X(200:300,1:25));
Display the image region.
imagesc(V); axis off title('Original Image')
Insert interpolated values by repeatedly dividing the intervals between points of the refined grid five times in each dimension.
Vq = interp2(V,5);
Display the result.
imagesc(Vq); axis off title('Linear Interpolation')
Evaluate Outside the Domain of X and Y
Coarsely sample a function over the range, [2, 2]
in both dimensions.
[X,Y] = meshgrid(2:0.75:2); R = sqrt(X.^2 + Y.^2)+ eps; V = sin(R)./(R);
Plot the coarse sampling.
figure
surf(X,Y,V)
xlim([4 4])
ylim([4 4])
title('Original Sampling')
Create the query grid that extends beyond the domain of X
and Y
.
[Xq,Yq] = meshgrid(3:0.2:3);
Perform cubic interpolation within the domain of X
and Y
, and assign all queries that fall outside to zero.
Vq = interp2(X,Y,V,Xq,Yq,'cubic',0);
Plot the result.
figure
surf(Xq,Yq,Vq)
title('Cubic Interpolation with Vq=0 Outside Domain of X and Y');
Input Arguments
X,Y
— Sample grid points
matrices  vectors
Sample grid points, specified as real matrices or vectors. The sample grid points must be unique.
If
X
andY
are matrices, then they contain the coordinates of a full grid (in meshgrid format). Use themeshgrid
function to create theX
andY
matrices together. Both matrices must be the same size.If
X
andY
are vectors, then they are treated as grid vectors. The values in both vectors must be strictly monotonic, either increasing or decreasing.
Example: [X,Y] = meshgrid(1:30,10:10)
Data Types: single
 double
V
— Sample values
matrix
Sample values, specified as a real or complex matrix. The size
requirements for V
depend on the size of X
and Y
:
If
X
andY
are matrices representing a full grid (inmeshgrid
format), thenV
must be the same size asX
andY
.If
X
andY
are grid vectors, thenV
must be a matrix containinglength(Y)
rows andlength(X)
columns.
If V
contains complex numbers, then interp2
interpolates
the real and imaginary parts separately.
Example: rand(10,10)
Data Types: single
 double
Complex Number Support: Yes
Xq,Yq
— Query points
scalars  vectors  matrices  arrays
Query points, specified as a real scalars, vectors, matrices, or arrays.
If
Xq
andYq
are scalars, then they are the coordinates of a single query point.If
Xq
andYq
are vectors of different orientations, thenXq
andYq
are treated as grid vectors.If
Xq
andYq
are vectors of the same size and orientation, thenXq
andYq
are treated as scattered points in 2D space.If
Xq
andYq
are matrices, then they represent either a full grid of query points (inmeshgrid
format) or scattered points.If
Xq
andYq
are ND arrays, then they represent scattered points in 2D space.
Example: [Xq,Yq] = meshgrid((1:0.1:10),(5:0.1:0))
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
in 2^k1
interpolated points between sample values.
If k
is 0
, then Vq
is
the same as V
.
interp2(V,1)
is the same as interp2(V)
.
The following illustration shows the placement of interpolated
values (in red) among nine sample values (in black) for k=2
.
Example: interp2(V,2)
Data Types: single
 double
method
— Interpolation method
'linear'
(default)  'nearest'
 'cubic'
 'spline'
 'makima'
Interpolation method, 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.  C^{0} 

'nearest'  The interpolated value at a query point is the value at the nearest sample grid point.  Discontinuous 

'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.  C^{1} 

'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.  C^{1} 

'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 notaknot end conditions.  C^{2} 

extrapval
— Function value outside domain of X
and Y
scalar
Function value outside domain of X
and Y
,
specified as a real or complex scalar. interp2
returns
this constant value for all points outside the domain of X
and Y
.
Example: 5
Example: 5+1i
Data Types: single
 double
Complex Number Support: Yes
Output Arguments
Vq
— Interpolated values
scalar  vector  matrix
Interpolated values, returned as a real or complex scalar, vector,
or matrix. The size and shape of Vq
depends on
the syntax you use and, in some cases, the size and value of the input
arguments.
Syntaxes  Special Conditions  Size of Vq  Example 

interp2(X,Y,V,Xq,Yq) interp2(V,Xq,Yq) and variations of these syntaxes that include method or extrapval  Xq , Yq are scalars  Scalar  size(Vq) = [1 1] when you pass Xq and Yq as
scalars. 
Same as above  Xq , Yq are vectors of
the same size and orientation  Vector of same size and orientation as Xq and Yq  If size(Xq) = [100 1] and size(Yq)
= [100 1] , then size(Vq) = [100
1] . 
Same as above  Xq , Yq are vectors of
mixed orientation  Matrix in which the number of rows is length(Yq) ,
and the number of columns is length(Xq)  If size(Xq) = [1 100] and size(Yq)
= [50 1] , then size(Vq) = [50 100] . 
Same as above  Xq , Yq are matrices or
arrays of the same size  Matrix or array of the same size as Xq and Yq  If size(Xq) = [50 25] and size(Yq)
= [50 25] , then size(Vq) = [50
25] . 
interp2(V,k) and variations of this syntax that include method or extrapval  None  Matrix in which the number of rows is:  If size(V) = [10 20] and k
= 2 , then size(Vq) = [37 77] . 
More About
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 between b(2)
and b(3)
.
The sequence, c = [2 4 6 8 6]
contains a reversal
between c(4)
and c(5)
, so it
is not monotonic at all.
Full Grid (in meshgrid Format)
For interp2
, the full
grid is a pair of matrices whose elements represent a grid of points
over a rectangular region. One matrix contains the xcoordinates,
and the other matrix contains the ycoordinates.
The values in the xmatrix are strictly monotonic and increasing
along the rows. The values along its columns are constant. The values
in the ymatrix are strictly monotonic and increasing
along the columns. The values along its rows are constant. Use the meshgrid
function to create a full grid
that you can pass to interp2
.
For example, the following code creates a full grid for the region, –1 ≤ x ≤ 3 and 1 ≤ y ≤ 4:
[X,Y] = meshgrid(1:3,(1:4))
X = 1 0 1 2 3 1 0 1 2 3 1 0 1 2 3 1 0 1 2 3 Y = 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4
Grid vectors are a more compact format to represent a grid than the full grid. The
relation between the two formats and the matrix of sample values
V
is
Grid Vectors
For interp2
, grid vectors consist of a pair of vectors
that define the x and ycoordinates in a
grid. The row vector defines xcoordinates, and the column vector
defines ycoordinates.
For example, the following code creates the grid vectors that specify the region, –1 ≤ x ≤ 3 and 1 ≤ y ≤ 4:
x = 1:3; y = (1:4)';
Scattered Points
For interp2
, scattered
points consist of a pair of arrays that define a collection of points
scattered in 2D space. One array contains the xcoordinates,
and the other contains the ycoordinates.
For example, the following code specifies the points, (2,7), (5,3), (4,1), and (10,9):
x = [2 5; 4 10]; y = [7 3; 1 9];
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Xq
andYq
must be the same size. Usemeshgrid
to evaluate on a grid.For best results, provide
X
andY
as 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:Use
meshgrid
to create the inputsXq
andYq
.Use a small number of interpolation points relative to the dimensions of
V
. Interpolating over a large set of scattered points can be inefficient.
GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
Usage notes and limitations:
Xq
andYq
must be the same size. Usemeshgrid
to evaluate on a grid.For best results, provide
X
andY
as 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:Use
meshgrid
to create the inputsXq
andYq
.Use a small number of interpolation points relative to the dimensions of
V
. Interpolating over a large set of scattered points can be inefficient.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
V
must be a double or single 2D array.V
can be real or complex.V
cannot be a vector.X
andY
must:Have the same type (double or single).
Be finite vectors or 2D arrays with increasing and nonrepeating elements in corresponding dimensions.
Align with Cartesian axes when
X
andY
are nonvector 2D arrays (as if they were produced bymeshgrid
).Have dimensions consistent with
V
.
Xq
andYq
must be vectors or arrays of the same type (double or single). IfXq
andYq
are arrays, then they must have the same size. If they are vectors with different lengths, then they must have different orientations.method
must be'linear'
,'nearest'
, or'cubic'
.The extrapolation for the outofboundary input is not supported.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
See Also
griddata
 interp1
 interp3
 interpn
 meshgrid
 griddedInterpolant
 scatteredInterpolant
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