I'm trying to use Matlab for some data plotting. In particular I need to plot a series of lines, some times given two points belonging to it, some times given the orthogonal vector.
I've used the following to obtain the plot of the line:
Line given two points A = [A(1), A(2)] B = [B(1), B(2)]:
plot([A(1),B(1)],[A(2),B(2)])
Line given the vector W = [W(1), W(2)]':
if( W(1) == 0 )
plot( [W(1), rand(1)] ,[W(2), W(2)])
else
plot([W(1), W(1) + (W(2)^2 / W(1))],[W(2),0])
end
where I'm calculating the intersection between the x-axis and the line using the second theorem of Euclid on the triangle rectangle formed by the vector W and the line.
My problem as you can see from the picture above is that the line will only be plotted between the two points and not on all the range of my axis.
I have 2 questions:
How can I have a line going across the whole axis range?
Is there a more easy and direct way (maybe a function?) to plot the line perpendicular to a vector? (An easier and more clean way to solve point 2 above.)
Thanks in advance.
Do you know the bounds of your axis for displaying the plot? If so, you can specify the range of the plot with the axis([xmin, xmax, ymin, ymax]) function.
So, from your question, if you know the slope m and intercept b, you can make sure your function plots the line across the whole window by specifying:
plot([xmin, xmax], [m*xmin + b, m*xmax + b]);
axis([xmin, xmax, min(m*xmin+b, m*xmax+b), max(m*xmin+b, m*xmax+b)]);
where xmin and xmax are values you specify as the range of your x-axis. This will make your line go from the corner of your plot to the other corner. If you want a buffer in the y-direction, then add one like so:
buffer = 5; % for example, you set this to something that looks good.
axis([xmin, xmax, min(m*xmin+b, m*xmax+b)-buffer, max(m*xmin+b, m*xmax+b)+buffer]);
Related
I wanted to generate a plot (X vs Y), and Z values depend on the Y. The example is shown in the figure below. The matrix size of X is same with Z but not Y. I can plot Z against X, but I wanted to combine all the plot into a single plot and become Y against X. I can plot multiple plots into a single plot but the plot is overlapping each other.
My question is there any method I can merge multiple plots into a single plot without overlapping each plot as the difference between each plot is very small (e.g Z1=1,2,3,4,5 and Z2=1.0001,2.0002,3.0001,4.0002,5.0001). So, I wanted to set each Z plot at different Y axis. (e.g Z1 at Y=0, Z2 at Y=2 ...)
Does anyone have any suggestions or idea?
Thank You
I'll clarify the ideas I wrote in a comment.
First, let's get some data:
x = 470:0.1:484;
z1 = cos(x)/2;
z2 = sin(x)/3;
z3 = cos(x+0.2)/2.3;
I'll plot just three data sets, all of this is trivial to extend to any number of data sets.
Idea 1: multiple axes
The idea here is simply to use subplot to create a small-multiple type plot:
ytick = [-0.5,0.0,0.5];
ylim = [-0.9,0.9]);
figure
h1 = subplot(3,1,1);
plot(x,z1);
set(h1,'ylim',ylim,'ytick',ytick);
title('z1')
h2 = subplot(3,1,2);
plot(x,z2);
set(h2,'ylim',ylim,'ytick',ytick);
title('z2')
h3 = subplot(3,1,3);
plot(x,z3);
set(h3,'ylim',ylim,'ytick',ytick);
title('z3')
Note that it is possible to, e.g., remove the tick labels from the top two plot, leaving only labels on the bottom one. You can then also move the axes so that they are closer together (which might be necessary if there are lots of these lines in the same plot):
set(h1,'xticklabel',[],'box','off')
set(h2,'xticklabel',[],'box','off')
set(h3,'box','off')
set(h1,'position',[0.13,0.71,0.8,0.24])
set(h2,'position',[0.13,0.41,0.8,0.24])
set(h3,'position',[0.13,0.11,0.8,0.24])
axes(h1)
title('')
ylabel('z1')
axes(h2)
title('')
ylabel('z2')
axes(h3)
title('')
ylabel('z3')
Idea 2: same axes, plot with offset
This is the simpler approach, as you're dealing only with a single axis. #Zizy Archer already showed how easy it is to shift data if they're all in a single 2D matrix Z. Here I'll just plot z1, z2+2, and z3+4. Adjust the offsets to your liking. Next, I set the 'ytick' property to create the illusion of separate graphs, and set the 'yticklabel' property so that the numbers along the y-axis match the actual data plotted. The end result is similar to the multiple axes plots above, but they're all in a single axes:
figure
plot(x,z1);
hold on
plot(x,z2+2);
plot(x,z3+4);
ytick = [-0.5,0.0,0.5];
set(gca,'ytick',[ytick,ytick+2,ytick+4]);
set(gca,'yticklabel',[ytick,ytick,ytick]);
text(484.5,0,'z1')
text(484.5,2,'z2')
text(484.5,4,'z3')
The simplest would be to shift Z data. But note that Z2 would look like to be oscillating around 1 - so this is a neat visual representation, but might mislead.
% Simple version - shift Z curves by 0, 1, ... (as recommended by #Cris Luengo)
shiftMat = repmat(0 : size(Z, 2)-1, size(Z,1), 1);
Z = Z + shiftMat;
%Min shift up to have non-overlapping - curves touching
for i = 2 : size(Z, 2)
Zdif = (Z(:, i-1) - Z(:, i));
Z(:, i) = Z(:, i) + max(Zdif); % + 0.01 to separate them a little bit.
end
%Bigger shift up, to have all points of Z(2) equal or above all points of z1.
for i = 2 : numZ
Zdif = max(Z(:, i-1))-min(Z(:, i));
Z(:, i) = Z(:, i) + Zdif;
end
Another possibility is to have multiple Y axis and each Z curve plotted against its own Y axis. This is likely fancier and shouldn't mislead, but it is way more work, even after you grab the function, as you still need to position all those axes. MATLAB by default lets you use only 2 axes, so grab a function from fileexchange to add more: https://www.mathworks.com/matlabcentral/fileexchange/9016-addaxis
I suppose this is not something difficult but i wonder if there is any function or any optimal way.
Consider that after an image process i have a matrix-image with 0 everywhere and 1 at the contour.
Now i want to find the x y along that contour line
The important is that eg [ x(2) y(2) ] should be the next pixel to [x(1) y(1)]
I have used this:
[c h]=contour(image,1)
x=c(1,:)
y=c(2,:)
But the result is not very good and it gives some noise points which is very bad (and for some reason it appears mirrored)
If you have the image processing toolbox, I highly suggest using bwperim which returns a logical image where true is a perimeter or contour point and false otherwise.... not to mention that it's faster.
Try doing:
bw = bwperim(image == 1); % image == 1 to ensure binary
[y, x] = find(bw);
The first line of code finds an image that only contains contour points, and we can use find after that on the result to find the row and column locations. Here y represents the row and x represents the column locations.
If you desire that the contour is ordered, then use the bwtraceboundary function instead. However, this will require that you specify an initial contour point prior to running the function.
An easy way to do this would be to find any non-zero point along the contour of your object. You could use bwperim first and sample any point from here. Choosing just any point may not give you an actual contour point.
Therefore:
bw = bwperim(image == 1); % image == 1 to ensure binary
[y, x] = find(bw, 1); % Find the first contour point
ctr = bwtraceboundary(image == 1, [y, x], 'SE');
'SE' is the direction of where to look first given the initial contour point. Here I've chosen south east. This will produce a N x 2 matrix where the first column contains the rows and second column contains the columns of the ordered contour points starting at the initial position provided by y and x.
I have posted my complete solution to help other people:
Problem:
I have a grayscale image and i want to find the coordinates X Y in order along the contour .
Solution:
Set a threshold for black and white and make the image binary (optional)
`image=image>0.5 %This is optional but some may found it usefull`
Find the Start Point:
[yStart xStart]=find(image,1);
This will scan the image column by column from left to right and up to down and will return the first non zero pixel. So this will return the 'left-est up' pixel of the image. Remember, X is the column and Y is the row. Zero is at the top-left corner!
Find the contour:
contour=bwtraceboundary(image, [yStart, xStart],'NE');
or
contour = bwtraceboundary(image,[yStart xStart],'NE',8,Inf,'clockwise');
NE is the initial direction (NorthEast)
x=contour(:,2)
y=contour(:,1)
If the point [yStart xStart] is not on the contour of an image this will not work !
If you plot (x,y) that will be mirrored. This is because the zero at the coordinate system is at the top left corner of the image and not at the bottom left. To do it properly you can do this:
y=-y
y=y+abs(min(y))+1 % +1 is to avoid y=0
Im just trying to draw a line through the following points in matlab. Currently the line extends only to the points. I need to to extend and intercept the x axis. The code is below
A = [209.45 198.066 162.759];
B = [1.805 1.637 1.115];
plot(A,B,'*');
axis([0 210 0 2]);
hold on
line(A,B)
hold off
If you want to augment your points with a corresponding y==0 point, I suggest using interp1 to obtain the x-intercept:
A = [209.45 198.066 162.759];
B = [1.805 1.637 1.115];
x0 = interp1(B,A,0,'linear','extrap'); %extrapolate (y,x) at y==0 to get x0
[newA, inds] = sort([x0 A]); %insert x0 where it belongs
newB = [0 B];
newB = newB(inds); %keep the same order with B
plot(A,B,'b*',newA,newB,'b-');
This will use interp1 to perform a linear interpolant, with extrapolation switched on. By interpolating (B,A) pairs, we in effect invert your linear function.
Next we add the (x0,0) point to the data, but since matlab draws lines in the order of the points, we have to sort the vector according to x component. The sorting order is then used to keep the same order in the extended B vector.
Finally the line is plotted. I made use of plot with a linespec of '-' to draw the line in the same command as the points themselves. If it doesn't bother you that the (x0,0) point is also indicated, you can plot both markers and lines together using plot(newA,newB,'*-'); which ensures that the colors match up (in the above code I manually set the same blue colour on both plots).
Can someone share a technique using MATLAB to plot the surface f(x,y)=(21/4)x^2y over the region x^2 <= y <= 1?
Also, if anyone is aware of some tutorials or links that would help with this type of problem, could you please share them?
Thanks.
Here is another approach:
%%
close all
x=linspace(-1,1,40);
g1=x.^2;
g2=ones(1,40);
y=[];
n=20;
for k=0:n
y=[y;g1+(g2-g1)*k/n];
end
x=x(ones(1,n+1),:);
z=21/4*x.^2.*y;
meshz(x,y,z)
axis tight
xlabel('x-axis')
ylabel('y-axis')
view(136,42)
And the result:
And finally, you can map the region (-1,1)x(0,1) in the uv-plane into the region bounded by $y=x^2 and y=1 in the xy-plane with the parametrization:
f(u,v) = (u\sqrt{v},v)
Capture from: https://math.stackexchange.com/questions/823168/transform-rectangular-region-to-region-bounded-by-y-1-and-y-x2
This code produces the same image shown above:
close all
[u,v]=meshgrid(linspace(-1,1,40),linspace(0,1,20));
x=u.*sqrt(v);
y=v;
z=21/4*x.^2.*y;
meshz(x,y,z)
axis tight
xlabel('x-axis')
ylabel('y-axis')
view(136,42)
First off, let's look at your valid region of values. This is telling us that y >= x^2 and also y <= 1. This means that your y values need to be on the positive plane bounded by the parabola x^2 and they also must be less than or equal to 1. In other words, your y values must be bound within the area dictated from y = x^2 to y = 1. Pictorially, your y values are bounded within this shape:
As such, your x values must also be bound between -1 and 1. Therefore, your actual boundaries are: -1 <= x <= 1 and 0 <= y <= 1. However, this only locates our boundaries for x and y but it doesn't handle where the plot has valid values. We'll tackle that later.
Now that we have that established, you can use ezsurf to plot surface plots in MATLAB that are dictated by a 2D equation.
You call ezsurf like so:
ezsurf(FUN, [XMIN,XMAX,YMIN,YMAX]);
FUN is a function or a string that contains the equation you want, and XMIN,XMAX,YMIN,YMAX contain the lowest and highest x and y values you want to plot. Plotting without these values assumes a span from -2*pi to 2*pi in both dimensions. As such, let's create a new function that will handle when we have valid values, and when we don't. Use this code, and save it to a new file called myfun.m. Make sure you save this to your current Working Directory.
function z = myfun(x,y)
z = (21/4)*x.^2.*y;
z(~(x.^2 <= y & y <= 1)) = nan;
end
This will allow you to take a series of x and y values and output values that are dictated by the 2D equation that you have given us. Any values that don't satisfy the condition of x^2 <= y <= 1, you set them to NaN. ezsurf will not plot NaN values.
Now, call ezsurf like so:
ezsurf(#myfun, [-1,1,0,1]);
You thus get:
This will spawn a new figure for you, and there are some tools at the top that will allow you interact with your 3D plot. For instance, you can use the rotation tool that's at the top bar beside the hand to rotate your figure around and see what this looks like. Click on this tool, then left click your mouse and hold the left mouse button anywhere within the surface plot. You can drag around, changing the azimuth and the latitude to get the perspective that you want.
Edit: June 4th, 2014
Noting your comments, we can decrease the jagged edges by increasing the number of points in the plot. As such, you can append a final parameter to ezsurf which is N, the number of points to add in each dimension. Increasing the number of points will decrease the width in between each point and so the plot will look smoother. The default value of N is 60 in both dimensions. Let's try increasing the amount of points in each dimension to 100.
ezsurf(#myfun, [-1,1,0,1], 100);
Your plot will look like:
Hope this helps!
Try the following to make the required function, compute the values, and plot only the region that is desired:
% Make the function. You could put this in a file by itself, if you wanted.
f = #(x,y) (21/4)*x.^2.*y;
[X Y] = meshgrid(linspace(0,1));
Z = f(X,Y);
% compute the values we want to plot:
valsToPlot = (X.^2 <= Y) & (Y <= 1);
% remove the values that we don't want to plot:
X(~valsToPlot) = nan;
Y(~valsToPlot) = nan;
Z(~valsToPlot) = nan;
% And... plot.
figure(59382);
clf;
surf(X,Y,Z);
Im trying to create a triangle wave in matlab with equal rise and fall slope.
I searched around abit and found a code example:
n=input ('Enter the length of the sequence N= ');
t=0:n;
y=(-1).^t;
stem(t,y);
ylabel ('Amplitude');
xlabel ('Time Index');
TITLE ('Triangular waveform');
This code creates the the triangle form, but there are only data plots at the tip of each triangle. I want more data plots that follow the lines of the triangles.
Is there any function in matlab that can fill in data points with a specific width between the plots in the plotted lines from the graph?
If no, how am I supposed to solve this?
You need to linearly interpolate:
t2 = 0:0.5:n;
y2 = interp1(t, y, t2);
where t and y are the arrays from your example. You can use any size of interval for t2:
t2 = 0:0.1:n;
for example.
Change t=0:n; to t=0:0.1:n; and y=(-1).^t; to y=2*abs(mod(t,2)-1)-1;
This is what I got: