I am trying to convert an image in polar to cartesian coordinates.
examples to convert image to polar coordinates do it explicitly - want a slick matrix method
I thought using the method used above would be a piece of cake but it really isn't!!
If anyone finds an error into my code please let me know!
phi=(0:.01:1)*2*pi;
r=0:.01:2;
psi=r<0.5;
psi_c=cos(phi).'*psi;
[P R z]=find(psi_c);
L=500;
X=R.*cos(P);
Y=R.*sin(P);
Xmin=min(X);Xmax=max(X);
Ymin=min(Y);Ymax=max(Y);
F=TriScatteredInterp(X,Y,z);
[Xi,Yi]=meshgrid(linspace(-Xmax,Xmax,L),linspace(-Ymax,Ymax,L));
Zi=F(Xi,Yi);
What I find very odd is the fact that when I change phi, it makes radical changes and not in the way I expect!
Cheers!
[X,Y] = pol2cart(THETA,RHO)
in case of conversion from polar grid to cartesian.
Likewise,
[X,Y] = pol2cart(THETA,RHO,Z)
to convert a cylindrical grid into the respective cartesian.
But I'm unsure those functions are what you need.
Related
Here is a sample dataset.
x = linspace(10,20,50);
y = linspace(10,20,50);
z = cos(linspace(0,2*pi,50));
time = linspace(1,60,50);
sci_temp = randi(100,50,1);
x,y,z is position, and sci_temp is temperature data.
I wonder how to draw trajectory over xyz position with sci_temp data.
I try interpolate data, so I get 2D interpolate time vs z with sci_temp plot.
S = TriScatteredInterp(time',z',sci_temp);
[t_mesh z_mesh] = meshgrid(time,z);
tz_mesh = S(t_mesh, z_mesh);
pcolor(t_mesh,z_mesh,tz_mesh)
What I want to get is a 2D (time vs sci_temp) section map on a xyz 3D plot. Like this image.
how to show trajectory over sci_temp in 3D plot?
Is there anyone can help me?
Thanks
First, you are doing your interpolation slightly wrong, you don't want to interpolate over the mesh created by
meshgrid(time,z);
Because it will duplicate values. You want to interpolate over the mesh created by
meshgrid(time,linspace(min(z),max(z),50));
Once you get the interpolated values like:
You can plot them in 3D space with the surface function, you just need to make sure to give x and y coordinates appropriately
surface(repmat(x,50,1),repmat(y,50,1),zmesh,tzmesh)
You can even have more complex paths, for example, same data but y=z
Edit: Also I forgot to mention, I'd suggest you to use scatteredInterpolant instead of TriScatteredInterp. It gives you more control over the interpolation
I want to graph different ellipses at different heights (z-coordinates).
My idea was to write the following code:
z=0:1/64:3/8;
t=linspace(-pi,pi,25);
[t,z]=meshgrid(t,z);
x=cos(-t);
y=cos(-t-4*pi*z);
I would like MATLAB to read my code like:
"Find x and y, and plot at the corresponding height (z). By doing so, join the points such that you'll form an ellipse at constant z".
I'm not sure what kind of function I could use here to do this and was hoping for someone to tell me if there exists such a function that will do the job or something similar.
In case you're wondering, I want to graph the polarization of light given two counterpropagating beams.
EDIT: While this is similar to the question draw ellipse and ellipsoid in MATLAB, that question doesn't address plotting 2D ellipses in 3D axes, which is what I am trying to do.
This can be solved by removing the meshgrid, and just using a plain old for-loop.
t = linspace(-pi,pi,25);
z = 0:1/64:3/8
f = figure;
hold on;
for i = 1:length(z)
x=cos(-t); y=cos(-t-4*pi*z(i));
plot3(x,y,z(i)*ones(length(z),1));
end
The problem in the original code is that you're trying build the ellipses all at once, but each ellipse only depends on a single z value, not the entire array of z values.
When I run this code, it produces the following plot:
I have to generate the mesh of the 3D-point cloud. So I used the delaunay function to perform the triangulation of points. The lidar data is a result of a human head scanning.
dt = delaunay(X,Y);
trisurf(dt,X,Y,Z);
When I used delaunay with two inputs it gives me output but not perfect. So I used three inputs (X,Y,Z)
dt = delaunay(X,Y,Z);
trisurf(dt,X,Y,Z);
But now the result comes out worse. I don't know what the problem is?
This is the full code that I have written:
load Head_cloud_point.txt;
data = Head_cloud_point;
for i = 1 : 3
X = data(:, 1);
end
for i = 1 : 3
Y = data(:, 2);
end
for i = 1 : 3
Z = data(:, 3);
end
[m n] = size(X);
[o p] = size(Y);
[r s] = size(Z);
[XI,YI]= meshgrid(X(m,n),Y(o,p));
ZI = interp2(X,Y,Z,XI,YI);
% dt = delaunay(X,Y);
% trisurf(dt,X,Y,ZI);
Head_cloud_point is the file with X,Y,Z coordinates. I have to generate the mesh using these coordinates.
Well, Delaunay is not going to do the trick directly here, neither the 2D nor the 3D version. The main reason is the way Delaunay is working. You can get some of the way, but the result is in general not going to be perfect.
You have not specified whether the poing cloud is the surface of the head, or the entire inner of the head (though another answer indicates the former).
First remember that Delaunay is going to triangulate the convex hull of the data, filling out any concavities, e.g. a C-like shape will have the inner part of the C triangulated (Ending like a mirrored D triangulation).
Assuming the point cloud is the surface of the head.
When using 2D Delaunay on all (X,Y), it can not distinguish between coordinates at the top of the head and at the bottom/neck, so it will mix those when generating the triangulation. Basically you can not have two layers of skin for the same (X,Y) coordinate.
One way to circumvent this is to split the data in a top and bottom part, probably around the height of the tip of the nose, triangulate them individually and merge the result. That could give something fairly nice to look at, though there are other places where there are similar issues, for example around the lips and ears. You may also have to connect the two triangulations, which is somewhat difficult to do.
Another alternative could be to transform the (X,Y,Z) to spherical coordinates (radius, theta, gamma) with origin in the center of the head and then using 2D Delaunay on (theta,gamma). That may not work well around the ear, where there can be several layers of skin at the same (theta,gamma) direction, where again Delaunay will mix those. Also, at the back of the head (at the coordinate discontinuity) some connections will be missing. But at the rest of the head, results are probably nice. The Delaunay triangulation in (theta, gamma) is not going to be a Delaunay triangulation in (X,Y,Z) (the circumcircle associated with each triangle may contain other point in its interior), but for visualization purposes, it is fine.
When using the 3D Delaunay using (X,Y,Z), then all concavities are filled out, especially around the tip of the nose and the eyes. In this case you will need to remove all elements/rows in the triangulation matrix that represents something "outside" the head. That seems difficult to do with the data at hand.
For the perfect result, you need another tool. Try search for something like:
meshing of surface point cloud
Since you have a cloud of raw data representing a 3D surface, you need to do a 3D surface interpolation to remove the noise. This will determine a function z=f(x,y) that best fits your data. To do that, you can use griddata, triscatteredinterp (deprecated) or interp2.
Note: From the context of your question, I assumed you use MATLAB.
[EDIT]
As you indicated that your data represents a head, the surface of a head which is a spheroid, it is not a function of the form z=f(x,y). See this post concerning possible solutions to visualizing spherical surfaces http://www.mathworks.com/matlabcentral/newsreader/view_thread/2287.
I have an array of normalized vectors (1538 of them) forming a sphere. Also I has an array of numbers of the same size 1538. I want to plot something like this:
I tried the sphere and surf functions but I can't find a way to use my vectors. I figured there should be some way to do this.
Thanks a lot.
I think you can use delaunay to create a triangulation and plot that using trimesh or trisurf.
Both trimesh as trisurf accepts a fourth argument to specify the color of each vertex, add the option 'facecolor','interp' to interpolate the color of each face between vertices.
edit: I experimented a bit further on it, and since it's a sphere, I think convhull is better suited.
Example:
[x,y,z]=sphere(25);
x=x(:);y=y(:);z=z(:);
tri = convhull([x y z]);
C = cos(y);
trisurf(tri,x,y,z,C,'facecolor','interp');
instead of C in the example you can use your own vector of values to specify the color
I am trying to plot a 3d view of a very large CT dataset. My data is in a 3d matrix of 2000x2000x1000 dimension. The object is surrounded by air, which is set to NaN in my matrix.
I would like to be able to see the greyscale value of the surface of the object (no isosurface) but I cannot quite work out how to do that in Matlab. Can anyone help me please?
Given that I a dealing with a huge matrix and I am only interested in the surface of the object, does anyone know a good trick how to reduce the size of my dataset?
The function surf(X,Y,Z) allows you to plot 3d data, where (X,Y) gives the coordinates in the x-y-plane while Z gives the z-coordinate and the surface color.
By default the function does not plot anything for the NaN entries, so you should be good to go with the surf function.
To set the surf-function to use a grayscale plotting use:
surf(matrix3d);
colormap(gray);
This plots the matrix in a surface plot and sets the colormap to grayscale.
In addition, as I understand your data, you might be able to eliminate entire plane-segments in your matrix. If for instance the plane A(1,1:2000,1:1000) is NaN in all entries you could eliminate all those entries (thus the entire Y,Z-plane in entry X=1). This will however require some heavy for loops, which might be over the top. This depends on how many data matrices you have compared to how many different plot you want for each matrix.
I will try to give you some ideas. I assume lack of a direct 3D "surface detector".
Since you have a 3D matrix where XY-planes are CT scan slices and each slice is an image, I would try to find edges of each slice say with edge. This would require some preprocessing like first thresholding each slice image. Then I can either use scatter3 to display the edge data as a 3D point cloud or delaunay3 to display the edge data as a surface.
I hope this will help you achieve what you are asking for.
I managed to get it working:
function [X,Y,Z,C] = extract_surface(file_name,slice_number,voxel_size)
LT = imread(file_name);%..READ THE 2D MAP
BW = im2bw(LT,1);%..THRESHOLD TO BINARY
B = bwboundaries(BW,8,'noholes');%..FIND THE OUTLINE OF THE IMAGE
X = B{1}(:,1);%..EXTRACT X AND Y COORDINATES
Y = B{1}(:,2);
indices = sub2ind(size(LT),X,Y);%..FIND THE CORRESPONDING LINEAR INDICES
C = LT(indices);%..NOW READ THE VALUES AT THE OUTLINE POSITION
Z = ones(size(X))*slice_number;
I can then plot this with
figure
scatter3(X,Y,Z,2,C)
Now the only thing I could improve is to have all these points in the scatter plot connected with a surface. #upperBound you suggested delaunay3 for this purpose - I cannot quite figure out how to do this. Do you have a tip?