[MATLAB]中meshgrid函数的用法与实践（学习笔记）

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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。

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)。

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 >> 

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); 

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。

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