I am trying to interpolate data between points as shown in this
image. When I use the griddata function matlab, the interpolated data exceeds the boundary of the original data. The area of desired interpolation is highlighted by the boundary made in the figure. Is there any way around to this problem?
My code for interpolation an display
figure2 = figure;
[x , y] = meshgrid(min(Matrixmin(:,5)):0.01:max(Matrixmin(:,5)),min(Matrixmin(:,6)):0.01:max(Matrixmin(:,6)));%graduation des x et y.
[xi,yi,zi]=griddata(Matrixmin(:,5),Matrixmin(:,6),Matrixmin(:,10),x,y);
contourf(xi,yi,zi,'edgecolor','none','LevelStep',0.01);
h=colorbar('location','Eastout');colormap('jet');
I have also tried the interp2 function but the results are still the same.
You are creating query points [x, y] using meshgrid that are outside the boundary of your image. Then, griddata is estimating the zi values at those query points. Behavior of both meshgrid and griddata is as expected. If you do not want points outside the boundary of the image, use the inpolygon function to remove those points after creatingmeshgrid.
Related
Suppose we have quiver field i.e. we have a meshgrid and then we assign a vector to each point. Is it possible to plot only the quiver field within some polygon?
So in the figure below, we want everything outside the triangle to be cropped out.
Ideally the code will also be helpful for the next step of having multiple such polygons and cropping out everything on their complement.
Some approaches:
A direct way is to figure out the meshgrid for the particular polygon and then assign a vector to each point. But that will take a lot of time to figure out as polygons get more complicated. In other words, the regular meshgrid is the square polygon, so we must modify the meshgrid matrix depending on our polygon. A friend informed me of a mesh generator matlab code.
Use inpolygon. The input of inpolygon are points in (x,y). But in our case we only have the vector field assigned to a meshgrid. One idea is to solve the ode system to obtain concrete solution pairs (x,y) to plug into the polygon. But solving them takes a lot longer and the pictures are not as nice.
Here's some sample code which I think will generate the kind of plot you want. It uses inpolygon to "filter" out the points inside the polygon. The vector field is still evaluated at the original meshgrid points. It easily extends to multiple polygons too.
clear
clc
x = linspace(0, 1, 21);
[X,Y] = meshgrid(x,x);
U = -Y; %some velocity field
V = X;
hold off
quiver(X,Y,U,V); %quiver on all points
polygon = [0.2,0.2;
0.7,0.5;
0.5,0.8]; %polygon vertices
ind = inpolygon(X,Y,polygon(:,1),polygon(:,2)); %get indices of points inside polygon
hold on
quiver(X(ind),Y(ind),U(ind),V(ind)); %quiver of points inside polygon
I have this data with values on the edges of the matrix and other values at evenly spaced interval within the matrix. I want to predict the values of the zero positions from the original values and make a heat map of the new data. Through suggest, I use scatteredInterpolant, ndgrid and interpolant since the data is that interp2 (matlab functions) cannot be used to interpolate the zero elements. Now, this method doe not give me a smooth figure and I am want to know if someone can offer some help. I have attached the figure from my code, the data and the code to this post.Thank you.
[knownrows, knowncolumns, knownvalues] = find(DataGrid); %get location and value of all non-zero points
interpolant = scatteredInterpolant(knownrows, knowncolumns, knownvalues,'linear'); %create interpolant from known values
[queryrows, querycolumns] = ndgrid(1:1:size(DataGrid, 1), 1:1:size(DataGrid, 2)); %create grid of query points
interpolatedj = interpolant(queryrows, querycolumns);
HeatMap(interpolatedj)
https://www.mediafire.com/?pq40x1ljxk8h996
https://www.mediafire.com/?pq40x1ljxk8h996
To plot a smoothed matrix you can use pcolor and set the shading parameter to interp
pcolor(M); %where M is your 2D matrix
shading interp %set the shading to interp
Try
image(M) or imagesc(M) where M is a matrix. pcolor(M) also works. If your matrix is huge then you need to remove edges otherwise figure just looks like blank image.
Hope the title gave an adequate description of my problem. Basically, I am generating a contour plot in MATLAB using the contourf (x,y,z) function, where x and y are vectors of different lengths and z is a matrix of data with dimensions of x times y. The contourf plot is fine, however, I am looking to overlay this plot with the actual data points from the matrix z. I have tried using the scatter function, but I am getting an error message informing me that X and Y must be vectors of the same length - which they're not. Is there any other way to achieve this?
Thanks in advance for any help/suggestions!
I think meshgrid should help you.
z = peaks; %// example 49x49 z data
x = 1:20;
y = 1:49;
z = z(y,x); %// make dimensions not equal so length(x)~=length(y)
[c,h] = contourf(x,y,z);
clabel(c,h); colorbar;
[xx,yy]=meshgrid(x,y); %// this is what you need
hold on;
plot(xx,yy,'k.'); %// overlay points on contourf
Notice plot suffices instead of scatter. If you insist, scatter(xx(:),yy(:),10), for example, does the trick. Although my example isn't particularly interesting, this should hopefully get you started toward whatever you're going for aesthetically.
I've run simulations which have given me data points corresponding to X number of different radii, and Y number of angles each one was evaluated at. This means that I have X times Y data points which I need to plot.
I am currently plotting it in an non-ideal fashion: I am using the x and y axes as the r and theta axes. This means that my data appears as a sinusoidal trend which increases with radius on a Cartesian grid, not the circle which it physically represents. This is how I am currently plotting my data:
surf(r_val, th_val, v_val);
What I wish to do is plot my data on a cylindrical axis, such like that of the function polar(), but in R3 space. I would rather not download a toolbox, or modify the existing polar function; if there is no other solution then I will obviously end up doing this anyways.
Thanks for your help!
G.
Also, I am using Matlab 2012a
EDIT:
r_val = 1x8 vector containing unique radii
th_val = 1x16 vector containing unique angles
v_val = 8x16 matrix containing voltages corresponding to each position
NOTE: (after answered)
The truly ideal solution does not exist to this problem, as Matlab currently supports no true polar axes methods. Resource found here.
You should transform your coordinates to Cartesian coordinates before plotting them. MATLAB has builtin functions for perfroming coordiante transformations. See, for example pol2cart, which transforms polar or cylindrical coordinates to Cartesian coordinates. In your case you would simply use something like:
[x, y] = pol2cart(th_val, r_val);
surf(x, y, v_val);
Edit: Given that th_val and r_val are vectors of differing lengths it is necessary to first create a grid of points before calling pol2cart, along the lines of:
[R, T] = meshgrid(r_val, th_val);
[x, y] = pol2cart(T, R);
surf(x, y, v_val);
I know I can create a 3D surface plot in MATLAB by doing:
x = linspace(1,10,100);
y = linspace(10,20,100);
[X Y] = meshgrid(x,y);
Z = X * Y;
surf(X,Y,Z);
But this requires that all the nodes for the height map generated line up. I have a set of data which has arbitrary points (x,y) and a height (z). Is there a simple way to plot a graph which will generate a surface between the points in a similar fashion to surf?
Appologies, after some hunting I managed to answer my own question:
You can use the trisurf function:
tri = delaunay(x,y);
trisurf(tri,x,y,z);
If you have dense data you will want to do shading interp (or another value, check doc shading) so you don't get a black blob due to the grid.
It looks like you've found your answer by using DELAUNAY and TRISURF to generate and plot a triangulated surface.
As an alternative, you could also fit a regularly-spaced grid to your nonuniformly-spaced points in order to generate a surface that can be plotted with the SURF command. I discuss how this can be done using the TriScatteredInterp class (or the deprecated function GRIDDATA) in my answer to this other question on SO.