Question

matlab中interp2函数的数学公式是什么？

Answer 1

ZI=interp2（X，Y，Z，XI，YI，method），
其中X和Y为由自变量组成的数组，X与Y尺寸相同，Z为2维函数数组。
XI和YI为插值点的自变量数组，method为插值方法选项，提供了4种方法；‘nearest’、‘linear’、‘spline’、‘cubic’等。
二维插值主要应用于图形图像处理和三维曲线拟合等领域。

简单来说就是 二维数据插值
下面是matlab给出的解释
INTERP2 2-D interpolation (table lookup).
ZI = INTERP2(X,Y,Z,XI,YI) interpolates to find ZI, the values of the
underlying 2-D function Z at the points in matrices XI and YI.
Matrices X and Y specify the points at which the data Z is given.

XI can be a row vector, in which case it specifies a matrix with
constant columns. Similarly, YI can be a column vector and it
specifies a matrix with constant rows.

ZI = INTERP2(Z,XI,YI) assumes X=1:N and Y=1:M where [M,N]=SIZE(Z).
ZI = INTERP2(Z,NTIMES) expands Z by interleaving interpolates between
every element, working recursively for NTIMES. INTERP2(Z) is the
same as INTERP2(Z,1).

ZI = INTERP2(...,METHOD) specifies alternate methods. The default
is linear interpolation. Available methods are:

'nearest' - nearest neighbor interpolation
'linear' - bilinear interpolation
'spline' - spline interpolation
'cubic' - bicubic interpolation as long as the data is
uniformly spaced, otherwise the same as 'spline'

For faster interpolation when X and Y are equally spaced and monotonic,
use the syntax ZI = INTERP2(...,*METHOD).

ZI = INTERP2(...,METHOD,EXTRAPVAL) specificies a method and a scalar
value for ZI outside of the domain created by X and Y. Thus, ZI will
equal EXTRAPVAL for any value of YI or XI which is not spanned by Y
or X respectively. A method must be specified for EXTRAPVAL to be used,
the default method is 'linear'.

All the interpolation methods require that X and Y be monotonic and
plaid (as if they were created using MESHGRID). If you provide two
monotonic vectors, interp2 changes them to a plaid internally.
X and Y can be non-uniformly spaced.

For example, to generate a coarse approximation of PEAKS and
interpolate over a finer mesh:
[x,y,z] = peaks(10); [xi,yi] = meshgrid(-3:.1:3,-3:.1:3);
zi = interp2(x,y,z,xi,yi); mesh(xi,yi,zi)

Class support for inputs X, Y, Z, XI, YI:
float: double, single

Answer 2

简单来说就是 二维数据插值
下面是matlab给出的解释
INTERP2 2-D interpolation (table lookup).
ZI = INTERP2(X,Y,Z,XI,YI) interpolates to find ZI, the values of the
underlying 2-D function Z at the points in matrices XI and YI.
Matrices X and Y specify the points at which the data Z is given.

XI can be a row vector, in which case it specifies a matrix with
constant columns. Similarly, YI can be a column vector and it
specifies a matrix with constant rows.

ZI = INTERP2(Z,XI,YI) assumes X=1:N and Y=1:M where [M,N]=SIZE(Z).
ZI = INTERP2(Z,NTIMES) expands Z by interleaving interpolates between
every element, working recursively for NTIMES. INTERP2(Z) is the
same as INTERP2(Z,1).

ZI = INTERP2(...,METHOD) specifies alternate methods. The default
is linear interpolation. Available methods are:

'nearest' - nearest neighbor interpolation
'linear' - bilinear interpolation
'spline' - spline interpolation
'cubic' - bicubic interpolation as long as the data is
uniformly spaced, otherwise the same as 'spline'

For faster interpolation when X and Y are equally spaced and monotonic,
use the syntax ZI = INTERP2(...,*METHOD).

ZI = INTERP2(...,METHOD,EXTRAPVAL) specificies a method and a scalar
value for ZI outside of the domain created by X and Y. Thus, ZI will
equal EXTRAPVAL for any value of YI or XI which is not spanned by Y
or X respectively. A method must be specified for EXTRAPVAL to be used,
the default method is 'linear'.

All the interpolation methods require that X and Y be monotonic and
plaid (as if they were created using MESHGRID). If you provide two
monotonic vectors, interp2 changes them to a plaid internally.
X and Y can be non-uniformly spaced.

For example, to generate a coarse approximation of PEAKS and
interpolate over a finer mesh:
[x,y,z] = peaks(10); [xi,yi] = meshgrid(-3:.1:3,-3:.1:3);
zi = interp2(x,y,z,xi,yi); mesh(xi,yi,zi)

Class support for inputs X, Y, Z, XI, YI:
float: double, single

Answer 3

ZI=interp2（X，Y，Z，XI，YI，method），
其中X和Y为由自变量组成的数组，X与Y尺寸相同，Z为2维函数数组。
XI和YI为插值点的自变量数组，method为插值方法选项，提供了4种方法；‘nearest’、‘linear’、‘spline’、‘cubic’等。
二维插值主要应用于图形图像处理和三维曲线拟合等领域。