【Matlab】 3D drawing summary

Reference material ：
《Matlab Programming and its application Lecture 3 》—— Lu Wei
《Matlab Help document 》

1. Three dimensional curve

Draw three-dimensional curves ： First there must be three $1\times n$ Matrix , And then use plot3 function , Examples are as follows ：

clear; clc;
t = 0 : pi/20 : 8*pi;
x = sin(t);
y = cos(t);
z = 1.5*t;
hp = plot3(x, y, z);
set(hp, 'linewidth', 2, 'color', 'r');
grid on;
axis square;
shg;

The result of the drawing ：

2. Space surfaces

Draw a space surface , First, there must be two rows corresponding to the same two-dimensional matrix $X$ and $Y$（ The number of rows and columns can be different ）, And then there's a function $Z=f(X,Y)$, With these three arrays, you can use the following drawing function .

But before that , Given first meshgrid Function usage ：

% Format ：[X, Y] = meshgrid(a, b); a  and  b  It's all line vectors 
% notes ：[X, Y] = meshgrid(a)  Equivalent to [X, Y] = meshgrid(a, a);
%X It's a matrix , Each line is a Copy of ,Y It's a matrix , Each of these columns is y'(y Transposition ) Copy of .
% By coordinates X and Y The grid represented has length(y) Row sum length(x) Column .  
clear; clc;
x = [1 2 3];
y = [1 2 3 4 5];
[X, Y] = meshgrid(x, y);
disp(X);
disp(Y);

% The output is as follows ：
1     2     3
1     2     3
1     2     3
1     2     3
1     2     3

1     1     1
2     2     2
3     3     3
4     4     4
5     5     5

Here are some drawing functions .

2.1 mesh function

2.1.1 Use format

Use format ：

mesh(X, Y, Z)
%{ Create a grid line with color 、 A three-dimensional surface grid with no color on the surface . The color of the gridlines depends on  Z  Specified height 
 The gradient .%}

mesh(Z)
% Similar to the above , Just use Z The indexes of the columns and rows of the elements in are used as X and Y coordinate .

mesh(__, C) % here  C  be called  color array, Hereunder  2.1.3  Will be used in 
%{ Input by including the fourth matrix  C  To specify the color of the grid . Grid diagram uses  Z  Said height ,C Color .
 Use 【 Color mapping 】 Assign colors ,【 Color mapping 】 Use a single number to represent the color on the spectrum . When you use 【 Yan 
 Color mapping 】 when ,C And Z The dimensions of are the same . Add a... To the drawing < Color bar >( Use  colorbar  command ), To display 
C How the data values in are related to 【 Color mapping 】 The colors in correspond to .%}

2.1.2 A few simple examples

Let's start using mesh Example ：

% example 1
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3, -5 : 0.1 : 5);
Z = peaks(X, Y);
% notes ：peaks yes matlab A more complex built-in function , Expression for ：
%{
z =  3*(1-x).^2.*exp(-(x.^2) - (y+1).^2) ... 
   - 10*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ... 
   - 1/3*exp(-(x+1).^2 - y.^2) 
%}
mesh(X, Y, Z); % All three matrices are 101 ride 61 Matrix 

example 1 Drawing results of ：

% example 2
clear; clc;

[X, Y] = meshgrid(-8 : 0.1 : 8);
% What's generated here X and Y It's all one 61 ride 61 Matrix of 

r = sqrt(X.^2+Y.^2);
% Sometimes at the end of the above formula  + eps,eps Is a very small double precision number , To make the denominator not 0, But it's OK not to add it 

Z = sin(r)./r;
% Notice the './' Is to operate on each element in the array , Use '/' Will report a mistake 

mesh(X, Y, Z); % All three matrices are one 161 ride 161 Matrix of 

example 2 Drawing results of （ This picture is commonly known as Mexican hat ）：

% example 3, In case 2 Add a color map based on , And use colorbar Display color and C The corresponding relationship between the values in 
clear; clc;

[X, Y] = meshgrid(-8 : 0.1 : 8);
r = sqrt(X.^2+Y.^2);

C = X.*Y; 
% '.*' representative X and Y The elements in are multiplied by each other , and '*' It means matrix multiplication 

Z = sin(r)./r;
% Notice the './' Is to operate on each element in the array , Use '/' Will report a mistake 

mesh(X, Y, Z, C);% All four matrices are one 161 ride 161 Matrix of 
colorbar;
% notes ： If not C, It can also be used  colorbar  Ordered 

example 3 Drawing results of ：

2.1.3 Add additional properties

1）EdgeColor attribute

Examples of use ：

% All edges use only one color 
mesh(X, Y, Z, 'EdgeColor', 'r');

% According to the matrix  C  Value , Use different colors for each edge .
mesh(X, Y, Z, 'EdgeColor', 'flat');

% According to the matrix  C  Values of use interpolated shading for each edge .
mesh(X, Y, Z, 'EdgeColor', 'interp');

2）FaceColor attribute

Examples of use ：

% All mesh faces use only one color 
mesh(X, Y, Z, 'FaceColor', 'b');

% According to the matrix  C  Value , Use different colors for each mesh face .
mesh(X, Y, Z, 'FaceColor', 'flat');

% According to the matrix  C  Value , Use interpolated shading for each mesh face .
mesh(X, Y, Z, 'FaceColor', 'interp');

3）LineStyle attribute

Examples of use ：

% Remove the gridlines from the graph 
mesh(X, Y, Z, 'LineStyle', 'none');% In this case, it is suggested to add 'FaceColor' attribute , Otherwise, the picture will be pure white ( Because mesh faces are not shaded by default )

% Use other linetypes . This is the same as the previous two-dimensional drawing , Let's take an example of point line type 
mesh(X, Y, Z, 'LineStyle', '-.');% Note here '.-' Will report a mistake 

4）FaceAlpha attribute

This can be used to adjust the transparency of the image , The smaller the value given , The more transparent the picture is . The default value is 1, For opacity . Only the most common uses are listed here ：

% Property is followed by a 0 To 1 Between the value of the , The default is 1
mesh(X, Y, Z, 'FaceAlpha', '0.2');

2.2 meshc function

Create a grid diagram , Here's an outline （ Can be seen as x-y There is a contour map on the plane ）.

The format and attributes used are the same as mesh The function is almost , I won't repeat , Just give me an example .

% Example 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
meshc(X, Y, Z);

The result of the drawing ：

2.3 meshz function

Draw with curtain （ It is equivalent to adding a curtain to the boundary ） Grid graph of .

The format and attributes used are the same as mesh The function is almost , I won't repeat , Just give me an example .

% Example 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
meshz(X, Y, Z);

The result of the drawing ：

2.4 waterfall function

Draw a waterfall , This is one along Y Grid diagram with partial curtain in dimension . This produces “ The waterfall ” effect ！

The format and attributes used are the same as mesh The function is almost , I won't repeat , Just give me an example .

% Example 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
waterfall(X, Y, Z);

The result of the drawing ：

2.5 surf function

Created a 3D surface , Different from the previous ones , The edges and faces of the graph it creates have colors . namely
mesh Draw a grid ,surf Draw a shaded 3D surface .

The format and attributes used are the same as mesh The function is almost , I won't repeat , Just give me an example .

% Example 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
surf(X, Y, Z);

The result of the drawing ：

2.6 colormap function

2.6.1 Use format

Here are two common uses ：

The first one is ：

colormap mapname;
%{ The above statement is equivalent to 
colormap('mapname');
%}

here ,mapname yes matlab Preset color map , As shown in the following table ：

mapname	explain
hsv	HSV The color comparison table of
hot	representative ” heat “ The color comparison table of
cool	representative ” cold “ The color comparison table of
spring	representative ” spring “ The color comparison table of
summer	representative ” summer “ The color comparison table of
autumn	representative ” autumn “ The color comparison table of
winter	representative ” winter “ The color comparison table of
gray	representative ” gray “ The color comparison table of
copper	representative ” coppery “ The color comparison table of
bone	representative ” X Photo chip “ The color comparison table of
pink	representative ” pink “ The color comparison table of
flag	representative ” The flag “ The color comparison table of

The second kind ：

colormap(map);

here ,map It's a $n\times 3$ Matrix , Each line represents a RGB The ingredients of , A color .matlab When drawing , Match the color of the first row to the highest point of the surface , The last line of colors corresponds to the lowest point of the surface , Other height colors are given by linear interpolation .

2.6.2 A few simple examples

% example 1, Use the first method 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
mesh(X, Y, Z);
colormap hot;

The result of the drawing ：

% example 2, Still use the first method , In another form 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
mesh(X, Y, Z);
colormap('copper');

The result of the drawing ：

% example 3, Use the second method 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);

mesh(X, Y, Z);

colormap(rand(100, 3));
% notes ：rand(m, n) Function to generate a  m  ride  n  Matrix 

The result of the drawing ：

3. Contour map

Draw contour map , First, there must be two rows corresponding to the same two-dimensional matrix $X$ and $Y$（ The number of rows and columns can be different ）, And then there's a function $Z=f(X,Y)$, With these three arrays, you can use the following drawing function .

3.1 contour function

Draw contour lines on a plane .

3.1.1 Use format

contour(X, Y, Z);
% Draw contour lines on a plane 

contour(Z);
% This is the same thing as contour(X, Y, Z), among [X, Y] = meshgrid(x, y)
%x The default is Z A matrix of row indexes ,y The default is Z A matrix composed of column indexes of 

contour(__, levels);
% Specify the level ,levels The bigger it is , The finer the height , The more contour lines there are 

3.1.2 A few simple examples

% example 1
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
contour(X, Y, Z, 20);

The result of the drawing ：

% example 2
clear; clc;
[X, Y] = meshgrid(-5 : 0.1 : 5);
Z = peaks(X, Y);
contour(Z, 50);

The result of the drawing ：

3.1.3 Add additional properties

1）LineSpec attribute

This does not need to add keywords , Directly specify the type . Examples of use ：

% And two-dimensional drawing plot The function is the same 

% The color is specified as blue , The linetype is specified as a dashed line 
contour(X, Y, Z, '--b');

2）ShowText attribute

Examples of use ：

% The default value is 'off', Set to 'on' after , Contour labels will be displayed in the figure 
contour(X, Y, Z, 'ShowText', 'on');

There is another way to display contour labels , Use clabel function . Examples of use ：

M = contour(X, Y, Z);
clabel(M);
% notes ：M  Is the contour matrix , It contains the vertices of each layer (x, y) coordinate .

3）LineWidth attribute

Examples of use ：

% The default value is 0.5
contour(X, Y, Z, 'LineWidth', 1.2);

3.2 contour3 function

Create a 3D contour map .

The format and attributes used are the same as contour The function is almost , I won't repeat , Just give me an example .

% Example 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
contour3(X, Y, Z, 20);

The result of the drawing ：

3.3 contourf function

Draw a plane contour map of fill color .

The format and attributes used are the same as contour The function is almost , I won't repeat , Just give me an example .

% Example 
clear; clc;
[X, Y] = meshgrid(-3 : 0.1 : 3);
Z = peaks(X, Y);
contourf(X, Y, Z, 20);

The result of the drawing ：

4. v = f(x, y, z) Visualization

The commonly used method is to slice the three-dimensional volume , At the cross section, different colors are used to represent the size of the function value at this point . It uses slice function .

4.1 Use format

Use format ：

slice(X, Y, Z, V, sx, sy, sz)

X, Y, Z It is three three-dimensional matrices with the same length in each dimension ,V It's about X, Y, Z A function of .sx For a row vector , Each element represents a x section （ Parallel to the yoz Plane ）,sy And sz It has the same meaning sx Be the same in essentials while differing in minor points .

4.2 Example

Examples of use ：

% Example 
clear; clc;
[X, Y, Z] = meshgrid(-2 : 0.1 : 2);
V = X.*exp(-X.^2 - Y.^2 - Z.^2);
xslice = [-1, 1];
yslice = 2;
zslice = [-2, 0];
slice(X, Y, Z, V, xslice, yslice, zslice);

The result of the drawing ：

5. At the end

If there is any mistake, please point it out , Learning together , Common progress ！

If there are any questions , Welcome to ask questions ！

thank you ！

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