I've got a series of XY point pairs in MATLAB. These pairs describe points around a shape in an image; they're not a function, meaning that two or more y points may exist for each x value.
I can plot these points individually using something like
plot(B(:,1),B(:,2),'b+');
I can also use plot to connect the points:
plot(B(:,1),B(:,2),'r');
What I'm trying to retrieve are my own point values I can use to connect the points so that I can use them for further analysis. I don't want a fully connected graph and I need something data-based, not just the graphic that plot() produces. I'd love to just have plot() generate these points (as it seems to do behind the scenes), but I've tried using the linseries returned by plot() and it either doesn't work as I understand it or just doesn't give me what I want.
I'd think this was an interpolation problem, but the points don't comprise a function; they describe a shape. Essentially, all I need are the points that plot() seems to calculate; straight lines connecting a series of points. A curve would be a bonus and would save me grief downstream.
How can I do this in MATLAB?
Thanks!
Edit: Yes, a picture would help :)
The blue points are the actual point values (x,y), plotted using the first plot() call above. The red outline is the result of calling plot() using the second approach above. I'm trying to get the point data of the red outline; in other words, the points connecting the blue points.
Adrien definitely has the right idea: define a parametric coordinate then perform linear interpolation on the x and y coordinates separately.
One thing I'd like to add is another way to define your parametric coordinate so you can create evenly-spaced interpolation points around the entire shape in one pass. The first thing you want to do, if you haven't already, is make sure the last coordinate point reconnects to the first by replicating the first point and adding it to the end:
B = [B; B(1,:)];
Next, by computing the total distance between subsequent points then taking the cumulative sum, you can get a parametric coordinate that makes small steps for points close together and larger steps for points far apart:
distance = sqrt(sum(diff(B,1,1).^2,2)); %# Distance between subsequent points
s = [0; cumsum(distance)]; %# Parametric coordinate
Now, you can interpolate a new set of points that are evenly spaced around the edge along the straight lines joining your points using the function INTERP1Q:
sNew = linspace(0,s(end),100).'; %'# 100 evenly spaced points from 0 to s(end)
xNew = interp1q(s,B(:,1),sNew); %# Interpolate new x values
yNew = interp1q(s,B(:,2),sNew); %# Interpolate new y values
These new sets of points won't necessarily include the original points, so if you want to be sure the original points also appear in the new set, you can do the following:
[sAll,sortIndex] = sort([s; sNew]); %# Sort all the parametric coordinates
xAll = [B(:,1); xNew]; %# Collect the x coordinates
xAll = xAll(sortIndex); %# Sort the x coordinates
yAll = [B(:,2); yNew]; %# Collect the y coordinate
yAll = yAll(sortIndex); %# Sort the y coordinates
EXAMPLE:
Here's an example to show how the above code performs (I use 11 pairs of x and y coordinates, one of which is repeated for the sake of a complete example):
B = [0.1371 0.1301; ... %# Sample data
0.0541 0.5687; ...
0.0541 0.5687; ... %# Repeated point
0.0588 0.5863; ...
0.3652 0.8670; ...
0.3906 0.8640; ...
0.4090 0.8640; ...
0.8283 0.7939; ...
0.7661 0.3874; ...
0.4804 0.1418; ...
0.4551 0.1418];
%# Run the above code...
plot(B(:,1),B(:,2),'b-*'); %# Plot the original points
hold on; %# Add to the plot
plot(xNew,yNew,'ro'); %# Plot xNew and yNew
I'd first define some parametric coordinate along the different segments (i.e. between the data points)
s = 1:size(B,1);
Then, just use interp1 to interpolate in s space. e.g. If you want to generate 10 values on the line between data point 5 and 6 :
s_interp = linspace(5,6,10); % parametric coordinate interpolation values
x_coord = interp1(s,B(:,1),s_interp,'linear');
y_coord = interp1(s,B(:,2),s_interp,'linear');
This should do the trick.
A.
Actually there is a MATLAB function "improfile", which might help you in your problem. Lets say these are the 4 coordinates which you want to find the locations between these coordinates.
xi=[15 30 20 10];
yi=[5 25 30 50];
figure;
plot(xi,yi,'r^-','MarkerSize',12)
grid on
Just generate a random image and run the function
n=50; % total number of points between initial coordinates
I=ones(max([xi(:);yi(:)]));
[cx,cy,c] = improfile(I,xi,yi,n);
hold on, plot(cx,cy,'bs-','MarkerSize',4)
Hope it helps
Related
I make point plots like this one:
But now I need to plot all the lines between the points as well to create rectangular mesh under a deformation (i.e. do the connection to the closest neighbors in x and y direction - not connect all the points with all the points).
How can I convince matlab/octave to do that?
The code I have used is here:
%T,H,W and k are defined above, it doesn't matter for the plot.
for ii=1:2:H
for jj=1:2:W
k=0.1;
x=jj;
y=ii;
U(ii,jj)=7*exp(0.05*(y-H))*cos(k*x-T);
V(ii,jj)=4*exp(0.1*(y-H))*sin(k*x-T);
X(ii,jj)=jj;
Y(ii,jj)=ii;
end
end
plot(X+U,Y+V,'k.');
A plot as you want it is easily done with mesh(X,Y,Z).
The problem with your code is that you have a lot of zeros in your matrices. These might be intentional. In that case I could provide another solution. But mesh() connects neighboring points in a matrix. Therefore having the 0 in every second line and row would connect every point to (0,0). The easiest way is to just let your ii,jj grow in steps of 1.
%T,H,W and k are defined above, it doesn't matter for the plot.
H = 20;
W = 40;
T = 2*pi;
for ii=1:1:H
for jj=1:1:W
k=0.1;
x=jj;
y=ii;
U(ii,jj)=7*exp(0.05*(y-H))*cos(k*x-T);
V(ii,jj)=4*exp(0.1*(y-H))*sin(k*x-T);
X(ii,jj)=jj;
Y(ii,jj)=ii;
end
end
plot(X+U,Y+V,'k.');
hold on
mesh(X+U, Y+V, zeros(size(X)));
I want to build a contourf plot of a certain aspect in my Plate. The plate is divided in triangle elements, which I have the coordinates (x,y) of each knot of the triangle.
So, How can I make a meshgrid for my knots so I can make my contourf plot?? I have the coordinates of everything and have the value of my function Z in each knot. (I'm a beginner in Matlab, sorry for this "basic" question)
If your goal is just to visualise the triangles then there is another way that's probably simpler and more robust (see the end of this post).
If you definitely need to generate contours then you will need to interpolate your triangular mesh over a grid. You can use the scatteredInterpolant class for this (documentation here). It takes the X and Y arguments or your triangular vertices (knots), as well as the Z values for each one and creates a 'function' that you can use to evaluate other points. Then you create a grid, interpolate your triangular mesh over the grid and you can use the results for the countour plot.
The inputs to the scatteredInterpolanthave to be linear column vectors, so you will probably need to reshape them using the(:)`notation.
So let's assume you have triangular data like this
X = [1 4; 8 9];
Y = [2 3; 4 5];
Z = [0.3 42; 16 8];
you would work out the upper and lower limits of your range first
xlimits = minmax(X(:));
ylimits = minmax(Y(:));
where the (:) notation serves to line up all the elements of X in a single column.
Then you can create a meshgrid that spans that range. You need to decide how fine that grid should be.
spacing = 1;
xqlinear = xlimits(1):spacing:xlimits(2);
yqlinear = ylimits(1):spacing:ylimits(2);
where linspace makes a vector of values starting at the first one (xlimits(1)) and ending at the third one (xlimits(2)) and separated by spacing. Experiment with this and look at the results, you'll see how it works.
These two vectors specify the grid positions in each dimension. To make an actual meshgrid-style grid you then call meshgrid on them
[XQ, YQ] = meshgrid(xqlinear, yqlinear);
this will produce two matrices of points. XQ holds the x-coordinates of every points in the grid, arranged in the same grid. YQ holds the y-coordinates. The two need to go together. Again experiment with this and look at the results, you'll see how it works.
Then you can put them all together into the interpolation:
F = scatteredInterpolant(X(:), Y(:), Z(:));
ZQ = F(XQ, YQ);
to get the interpolated values ZQ at each of your grid points. You can then send those data to contourf
contourf(XQ, YQ, ZQ);
If the contour is too blocky you will probably need to make the spacing value smaller, which will create more points in your interpolant. If you have lots of data this might cause memory issues, so be aware of that.
If your goal is just to view the triangular mesh then you might find trimesh does what you want or, depending on how your data is already represented, scatter. These will both produce 3D plots with wireframes or point clouds though so if you need contours the interpolation is the way to go.
I am trying to make a simple plot (for this example doing a plot of y=x^2 will suffice) where I want to set the colors of the points based on their magnitude given some colormap.
Following along my simple example say I had:
x = 1:10;
y = x.^2;
Use gscatter(x,y,jet(10)); legend hide; colorbar which produces a plot with the points colored but the colorbar does not agree with the colored values. (Can't post picture as this is my first post). Using a caxis([1,100]) command gives the right range but the colors are still off.
So I have two questions:
(1) How can I fix the colors to fit to a colorbar given a range? In my real data, I am looking at values that range from -50 to 50 in some instances and have many more data points.
(2) I want to create a different plot with the same points (but on different axes) and I want the colors of each point on this new plot to have the same colors as their counterparts in the previous plot. How can I, programmatically, extract the color from each point so I can plot it on two different sets of axes?
I would just move the points into a matrix and do an imagesc() command but they aren't spaced as integers or equally so simple scaling wouldn't work either.
Thanks for any help!
Regarding you first question, you need to interpolate the y values into a linear index to the colormap. Something like:
x = 1:10;
y = x.^4;
csize = 128;
cmap = jet(csize);
ind = interp1(linspace(min(y),max(y),csize),1:csize,y,'nearest');
scatter(x,y,14,cmap(ind,:),'filled')
colorbar
caxis([min(y) max(y)])
Using interp1 in this case is an overkill; you could calculate it directly. However, I think in this way it is clearer.
I think it also answers your 2nd question, since you have the index of the color of each data point, so you can use it again in the same way.
I'm trying to plot several signals in one graph and i would like to restrict them and sort of minimize it so all my signals will be clear (more or less).
I have no idea how to do it. I'm adding an image so what i need to do will be clearer.
My data changes but in general it's the mean intensity of each column of a certain area in an intensity image.I tried to do it like with the same idea as you but i don't get the right plot as i wanted. A is the relevant matrix,b is the matrix with shifted values:
for i=1:20
b(i,:)=A(i,:)+(100*i);
plot(b(i,:))
hold on
end
I will also add 2 images: one is the plot of all the 20 signals that i get and the other one is the plot of only the first signal. I don't understand why do they look so different.
You can try something like that :
x = [1:100]; %Distance 1 to 100
y = F(x) % Your first function (signal)
y2 = 0.5*G(x) % Your second function (signal)
plot(x,y,x,y2); % plot both function in a single plot.
hleg1 = legend('Intensity t1,'Intensity t27');
So you have your signal at intensity t27 half cut for each value ( 0.5 ), so it shift down.
I have a 2D scatter plot in MATLAB. Is it possible to interpolate the scatter plot to create an area plot?
If you're simply trying to draw one large filled polygon around your entire set of scattered points, you can use the function CONVHULL to find the convex hull containing your points and the function PATCH to display the convex hull:
x = rand(1,20); %# 20 random x values
y = rand(1,20); %# 20 random y values
hullPoints = convhull(x,y); %# Find the points defining the convex hull
patch(x(hullPoints),y(hullPoints),'r'); %# Plot the convex hull in red
hold on; %# Add to the existing plot
scatter(x,y); %# Plot your scattered points (for comparison)
And here's the resulting figure:
Scatter is generally used to represent data where you can't use a line graph, i.e., where each x might have many different y values, so you can't convert directly to an area graph--it would be meaningless. If your data actually is representable as a line graph, then pass it to area directly.
So I'm not quite sure what you want, but here are some possibilities:
You could create a Voronoi diagram based on your points. This will show a region near your points showing which points are closer to a specific point: voronoi(x,y), or see the help.
You could bucket or quantize your data somehow, making it fit into a grid, and then plot the grid. This could also be considered a histogram, so read up on that.
You could just use larger scatter markers (scatter(x,y,scale) where scale is the same dimensions as x and y).