Matlab drawing - points and vectors: method and source code of vector addition and subtraction

Preface ：

Some blogs just turn Matlab  In Chinese , But his explanation , He himself said it was not quite right .

This paper starts from practice , Detailed introduction Matlab Yes   Drawing method of points and vectors in coordinate space .

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1 Concept and drawing method of point ：

1.1 A point on a plane

plot(2, 3, '.', 'MarkerSize', 16,"Color",'r');

【 case 】, In this case , Draw a red dot , Coordinates are in Cartesian coordinates (2,3).

1.2 A point in space ：

fig1 = figure(1)
plot3(1, 2,3, '.', 'MarkerSize', 16,"Color",'r')

1.3 In a space 2 A little bit ：

fig1 = figure(1)
plot3(1, 2,3, '.', 'MarkerSize', 16,"Color",'r')
hold on
plot3(4, 5,6, '.', 'MarkerSize', 16,"Color",'b')

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The concept of vector ：

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2 How to draw vectors ：

2.1 Drawing of a two-dimensional vector ：

The code draws three vectors with different starting points , 

fig1 = figure(1)
scale = 1;
quiver(0,0,2,3,scale,'b');
grid on;
hold on;
quiver(1,1,2,3,scale,'g');
grid on;
hold on;
quiver(4,1,2,3,scale,'r');
grid on;
%  The first two numbers represent the starting coordinates of the two-dimensional vector 
%  The last two numbers represent the endpoint coordinates of the two-dimensional vector 
% scale=1 It means that the length of the vector is not expanded 
% 'b' Representing blue 

2.2 The rendering of a three-dimensional vector ：

scale = 1;
quiver3(0,0,0,1,1,1,scale,'b');
hold on;
quiver3(1,1,0,1,1,1,scale,'r');
hold on;
quiver3(6,1,0,1,1,1,scale,'g');
%  The first three numbers represent the starting coordinates of the three-dimensional vector 
%  The last three numbers represent the end coordinates of the three-dimensional vector 

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2.3 Drawing of vector addition and subtraction ：

 2.3.1  Dimensionally

fig1 = figure(1)
scale = 1;
quiver(0,0,2,3,scale,'b');
grid on;
hold on;
quiver(2,3,1,3,scale,'g');
grid on;
hold on;
quiver(0,0,2+1,3+3,scale,'r');
grid on;

2.3.2 

 

scale = 1;
quiver3(0,0,0,1,1,1,scale,'b');
hold on;
quiver3(1,1,1,2,2,0,scale,'r');
hold on;
quiver3(0,0,0,3,3,1,scale,'g');

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3 The use of reference ：

1 function ：quiver And the drawing of vector field

quiver(X,Y,U,V) plots arrows with directional components U and V at the Cartesian coordinates specified by X and Y.【X,Y Vector At the beginning of Descartes , The horizontal movement unit multiple of the vector is U, The vertical movement unit multiple is V】【 case , An important concept in the understanding of vectors is instruction, It refers to the number of unit coordinate steps of each coordinate component of the vector 】

For example, the first arrow originates from the point X(1) and Y(1), extends horizontally according to U(1), and extends vertically according to V(1). By default, the quiver function scales the arrow lengths so that they do not overlap.

【quiver Functions seem to follow this rule , The following explanation also verifies this paragraph , from (1,1) As a starting point , Then extend vertically 【 Move 】 A unit v(1), Then extend a unit horizontally U(1), Of course. , Avoid vector arrows overlapping , He i Automatically scale overlapping vectors , This paragraph has not yet found a suitable example to verify the practice 】

【 Official website , An example of drawing vector graph is given , Draw a vector diagram of North American wind speed 】

load wind.mat;
load('wind','x','y','u','v')
X = x(11:22,11:22,1);
Y = y(11:22,11:22,1);
U = u(11:22,11:22,1);
V = v(11:22,11:22,1);
quiver(X,Y,U,V)
axis equal

It's used here wind.mat Open source data ：【 This is introduced in the next section of this article 】

【Franklin case , Here we choose No 11 To 22 That's ok ,11 To 22 Column position sensor 1 Location and wind speed data , And then call quiver Drawing , We can understand it as , Yes 12*12 A vector matrix composed of vectors 】

 【 Here the length of the arrow , Is the length of the vector , It vividly shows the speed of the wind , meanwhile quiver Functions have the function of avoiding overlap , therefore , The length of some vectors should be adjusted 】

2 wind data

3-D data on air currents over North America. The data consists of (x,y,z) position components and (u,v,w) velocity components.

File Size: 142 KB

Data Size: Six matrices of size 35-by-41-by-15

load wind.mat
【wind data It's a 3 Data set of dimensions , Is a data set of North American air flow , Include ,xyz A location element of , And a uvw Speed element of , Specifically wind Use of data , stay MT There is a very detailed explanation in a video introduction of wind energy 】

use MT load After the data , We saw it wind data The details of ：

Is, indeed, 6 Matrix , Every matrix is 35-by-41-by-15

  Let's first look at the location data x matrix ,Y matrix ,U matrix ：

You can see the ,XYZ Matrix data of , On different lines X The value of is the same ,Y Values are different , however , stay Page The corresponding words on , It's all the same , Have reason to believe Page It's the sensor ID, There are about 15 A sensor .

then ,U,V The value of is the wind speed and other parameters measured by the sensor in different reverse directions , This data is quite random .

X			Y			U
val(:,:,1) =	val(:,:,5) =		val(:,:,1) =	val(:,:,10) =		val(:,:,1) =	val(:,:,2) =
Column 1	Column 1
			Column 1	Column 1		Column 1	Column 1
70.1879	70.1879
70.1879	70.1879		17.4999	17.4999		0.5685	-2.8479
70.1879	70.1879		18.7499	18.7499		0.5685	-2.8479
70.1879	70.1879		19.9999	19.9999		0.5685	-2.8479
70.1879	70.1879		21.2499	21.2499		0.8791	-2.2267
70.1879	70.1879		22.4999	22.4999		1.1897	-1.295
70.1879	70.1879		23.7499	23.7499		1.5003	-0.3632
70.1879	70.1879		24.9999	24.9999		1.5003	0.5685
70.1879	70.1879		26.2499	26.2499		2.1214	2.1214
70.1879	70.1879		27.4999	27.4999		3.0531	3.3637
70.1879	70.1879		28.7499	28.7499		4.606	6.1589
70.1879	70.1879		29.9999	29.9999		4.606	7.4013
70.1879	70.1879		31.2499	31.2499		4.9166	9.2647
70.1879	70.1879		32.4999	32.4999		4.9166	10.507
70.1879	70.1879		33.7499	33.7499		5.2272	13.9234
70.1879	70.1879		34.9999	34.9999		5.2272	15.4763
70.1879	70.1879		36.2499	36.2499		5.2272	15.4763
70.1879	70.1879		37.4999	37.4999		5.5378	17.0292
70.1879	70.1879		38.7499	38.7499		6.1589	20.135
70.1879	70.1879		39.9999	39.9999		5.5378	19.8244
70.1879	70.1879		41.2499	41.2499		3.3637	18.2715
70.1879	70.1879		42.4999	42.4999		1.5003	13.9234
70.1879	70.1879		43.7499	43.7499		0.8791	10.507
70.1879	70.1879		44.9999	44.9999		0.2579	5.2272
70.1879	70.1879		46.2499	46.2499		-0.6738	1.5003
70.1879	70.1879		47.4999	47.4999		-2.2267	-3.1584
70.1879	70.1879		48.7499	48.7499		-3.1584	-5.6431
70.1879	70.1879		49.9999	49.9999		-3.7796	-5.6431
70.1879	70.1879		51.2499	51.2499		-4.4008	-6.8854
70.1879	70.1879		52.4999	52.4999		-4.7113	-8.4383
70.1879	70.1879		53.7499	53.7499		-3.7796	-8.1277
70.1879	70.1879		54.9999	54.9999		-2.5373	-7.196
70.1879	70.1879		56.2499	56.2499		-1.295	-6.2642
70.1879	70.1879		57.4999	57.4999		-0.9844	-4.7113
70.1879	70.1879		58.7499	58.7499		-1.295	-3.1584
			59.9999	59.9999		-2.5373	-2.8479

Column 2	Column 2
			Column 2	Column 2		Column 2	Column 2
71.7907	71.7907
71.7907	71.7907		17.4999	17.4999		0.5685	-2.5373
71.7907	71.7907		18.7499	18.7499		0.5685	-2.5373
71.7907	71.7907		19.9999	19.9999		0.8791	-2.5373
71.7907	71.7907		21.2499	21.2499		0.8791	-1.6055
71.7907	71.7907		22.4999	22.4999		1.1897	-0.9844
71.7907	71.7907		23.7499	23.7499		1.5003	0.2579
71.7907	71.7907		24.9999	24.9999		1.1897	0.5685
71.7907	71.7907		26.2499	26.2499		2.1214	3.0531
71.7907	71.7907		27.4999	27.4999		3.6743	5.5378
71.7907	71.7907		28.7499	28.7499		3.3637	6.1589
71.7907	71.7907		29.9999	29.9999		3.3637	7.0907
71.7907	71.7907		31.2499	31.2499		4.2955	8.6436
71.7907	71.7907		32.4999	32.4999		4.9166	9.5753
71.7907	71.7907		33.7499	33.7499		5.2272	12.0599
71.7907	71.7907		34.9999	34.9999		5.5378	16.408
71.7907	71.7907		36.2499	36.2499		4.9166	17.3398
71.7907	71.7907		37.4999	37.4999		4.9166	16.408
71.7907	71.7907		38.7499	38.7499		4.606	16.7186
71.7907	71.7907		39.9999	39.9999		4.606	17.0292
71.7907	71.7907		41.2499	41.2499		4.2955	17.0292
71.7907	71.7907		42.4999	42.4999		0.5685	12.0599
71.7907	71.7907		43.7499	43.7499		1.5003	9.5753
71.7907	71.7907		44.9999	44.9999		0.8791	5.5378
71.7907	71.7907		46.2499	46.2499		0.2579	2.432
71.7907	71.7907		47.4999	47.4999		-1.6055	-2.8479
71.7907	71.7907		48.7499	48.7499		-2.5373	-5.3325
71.7907	71.7907		49.9999	49.9999		-2.8479	-5.6431
71.7907	71.7907		51.2499	51.2499		-2.8479	-6.2642
71.7907	71.7907		52.4999	52.4999		-3.469	-6.8854
71.7907	71.7907		53.7499	53.7499		-2.8479	-6.8854
71.7907	71.7907		54.9999	54.9999		-1.295	-6.2642
71.7907	71.7907		56.2499	56.2499		-0.6738	-4.4008
71.7907	71.7907		57.4999	57.4999		-2.2267	-3.1584
71.7907	71.7907		58.7499	58.7499		-2.8479	-3.7796
			59.9999	59.9999		-2.8479	-2.8479

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Reference resources ：

Quiver or vector plot - MATLAB quiver (mathworks.com)

 matlab The drawing method of vector in _ Chentengfei's blog -CSDN Blog _matlab Draw vector

Matlab Draw vector graph and plane graph - You know (zhihu.com)