[MATLAB]中meshgrid函数的用法与实践（学习笔记）

今天在看点目标成像仿真程序的时候，看到了meshgrid函数，看了matlab的帮助文档后理解了一点，特此记录学习过程。

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一、meshgrid函数

meshgrid函数是MATLAB中用于生成网格采样点数的函数，通常进行2D、3D图形的绘制。

1、【X,Y】 = meshgrid(x,y) :基于向量x和y中包含的坐标返回二维网格坐标。X是一个矩阵，每一行是x的一个副本，Y也是一个矩阵，每一列是y的一个副本。坐标X和Y表示的网格有length(y)个行和length(x)个列。

2 、[X,Y] = meshgrid(x) 与 [X,Y] = meshgrid(x,x)相同，返回网格大小为length(x)*length(x)的方形网格矩阵。

3、 [X,Y，Z] = meshgrid(x,y,z),返回由向量x,y,z定义的三维网格坐标，X,Y和Z表示的网格大小为length(x)*length(y)*length(z)。

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二、举例验证

1.【X,Y】 = meshgrid(x,y) , 代码如下：

a 、b矩阵个数相同：

a = [1 2 3 4];
b = [5 6 7 8];
[A,B] = meshgrid(a,b)

结果：

A =

     1     2     3     4
     1     2     3     4
     1     2     3     4
     1     2     3     4


B =

     5     5     5     5
     6     6     6     6
     7     7     7     7
     8     8     8     8

>> 

a 、b矩阵数量不同：

a = [1 2 3];
b = [4 5 6 7];
[A,B] = meshgrid(a,b)

A =

     1     2     3
     1     2     3
     1     2     3
     1     2     3


B =

     4     4     4
     5     5     5
     6     6     6
     7     7     7

>> 

2、【X,Y】 = meshgrid(x), 代码如下：

x  = [1 2 3];
[X,Y] = meshgrid(x)
X =

     1     2     3
     1     2     3
     1     2     3

Y =

     1     1     1
     2     2     2
     3     3     3
>>
x = [1 2 3];
>> [X,Y] = meshgrid(x,x)

X =

     1     2     3
     1     2     3
     1     2     3

Y =

     1     1     1
     2     2     2
     3     3     3

>> 

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三、创建二维网格绘制曲面图

使用均匀分布的x和y坐标在-4到4之间创建二维网格：

代码如下：

x = -4:0.2:4;
y = x;
[X,Y] = meshgrid(x);
F = X.*exp(-X.^2 - Y.^2);
surf(X,Y,F);

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四、总结

为什么要使用meshgrid?
matlab使用矩阵的方式进行运算，对于2D而言，如果采样10个点(指x,y轴)，那么对于x=第一个采样点，反映到矩阵就是10个，即不管y是哪个值，x的第一采样点保持不变；对y是同理。因此，2D产生的x和y都是两维矩阵。

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五、meshgrid函数源代码（仅供参考）：

源代码：
function [xx,yy,zz] = meshgrid(x,y,z)
%MESHGRID Cartesian grid in 2-D/3-D space
% [X,Y] = MESHGRID(xgv,ygv) replicates the grid vectors xgv and ygv to
% produce the coordinates of a rectangular grid (X, Y). The grid vector
% xgv is replicated numel(ygv) times to form the columns of X. The grid
% vector ygv is replicated numel(xgv) times to form the rows of Y.
%
% [X,Y,Z] = MESHGRID(xgv,ygv,zgv) replicates the grid vectors xgv, ygv, zgv
% to produce the coordinates of a 3D rectangular grid (X, Y, Z). The grid
% vectors xgv,ygv,zgv form the columns of X, rows of Y, and pages of Z
% respectively. (X,Y,Z) are of size numel(ygv)-by-numel(xgv)-by(numel(zgv).
%
% [X,Y] = MESHGRID(gv) is equivalent to [X,Y] = MESHGRID(gv,gv).
% [X,Y,Z] = MESHGRID(gv) is equivalent to [X,Y,Z] = MESHGRID(gv,gv,gv).
%
% The coordinate arrays are typically used for the evaluation of functions
% of two or three variables and for surface and volumetric plots.
%
% MESHGRID and NDGRID are similar, though MESHGRID is restricted to 2-D
% and 3-D while NDGRID supports 1-D to N-D. In 2-D and 3-D the coordinates
% output by each function are the same, the difference is the shape of the
% output arrays. For grid vectors xgv, ygv and zgv of length M, N and P
% respectively, NDGRID(xgv, ygv) will output arrays of size M-by-N while
% MESHGRID(xgv, ygv) outputs arrays of size N-by-M. Similarly,
% NDGRID(xgv, ygv, zgv) will output arrays of size M-by-N-by-P while
% MESHGRID(xgv, ygv, zgv) outputs arrays of size N-by-M-by-P.
%
% Example: Evaluate the function x*exp(-x^2-y^2)
% over the range -2 < x < 2, -4 < y < 4,
%
% [X,Y] = meshgrid(-2:.2:2, -4:.4:4);
% Z = X .* exp(-X.^2 - Y.^2);
% surf(X,Y,Z)
%
%
% Class support for inputs xgv,ygv,zgv:
% float: double, single
% integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64
%
% See also SURF, SLICE, NDGRID.
% Copyright 1984-2013 The MathWorks, Inc.
if nargin==0 || (nargin > 1 && nargout > nargin)
error(message('MATLAB:meshgrid:NotEnoughInputs'));
end
if nargin == 2 || (nargin == 1 && nargout < 3) % 2-D array case
if nargin == 1
y = x;
end
if isempty(x) || isempty(y)
xx = zeros(0,class(x));
yy = zeros(0,class(y));
else
xrow = full(x(:)).'; % Make sure x is a full row vector.
ycol = full(y(:)); % Make sure y is a full column vector.
xx = repmat(xrow,size(ycol));
yy = repmat(ycol,size(xrow));
end
else % 3-D array case
if nargin == 1
y = x;
z = x;
end
if isempty(x) || isempty(y) || isempty(z)
xx = zeros(0,class(x));
yy = zeros(0,class(y));
zz = zeros(0,class(z));
else
nx = numel(x);
ny = numel(y);
nz = numel(z);
xx = reshape(full(x),[1 nx 1]); % Make sure x is a full row vector.
yy = reshape(full(y),[ny 1 1]); % Make sure y is a full column vector.
zz = reshape(full(z),[1 1 nz]); % Make sure z is a full page vector.
xx = repmat(xx, ny, 1, nz);
yy = repmat(yy, 1, nx, nz);
zz = repmat(zz, ny, nx, 1);
end
end