I have a set of data points, x, y, and z contained in a matrix, record.
In record, each row is a data-point where the first value is the x-coordinate, the second is the y-coordinate, and the third is the z-coordinate. I would like to represent this as a surface plot. I tried:
surf([record(:,1), record(:,2)], record(:,3))
But the results were not what I expected. Any advice?
Try this code for instance.
[x,y,z]=sphere(n);
surf(x,y,z);
axis equal
This code plots with 3 parameters surf the surface of a sphere. As far as I understood from your code you want to utilize the 2 parameters surf for your application.
According to surf help when utilizing 2 parameters surf:
surf(Z) and surf(Z,C) use x = 1:n and y = 1:m. In this case,
the height, Z, is a single-valued function, defined over a
geometrically rectangular grid.
where:
The color scaling is determined
by the range of C
It just doesn't look like you want to utilize C as the color scaling parameter. For better understanding, can you send the contents of record for reference?
Related
I have a set of points in 3D in cartesian coordinates X,Y,Z. To every such point I associate a value which is stored in a vector C. I want to be able to colour the surface given by X,Y,Z with colors given by C. Alternatively, if possible, I would like to associate to each point a color from a finite number of given colors. In Matlab this is possible with surf(X,Y,Z,C), but X,Y must be in grid form (generated by meshgrid), not in general form, like in my case.
I managed to do this in the case of the sphere, but the procedure is not pretty, and it uses heavily the parametrization of the sphere. Here's an example of what I want to do (in the case of the sphere).
Is there a way to do this type of surface coloring in Matlab? (if it helps, I can also provide a triangulation of the surfaces in addition to the points X,Y,Z)
Is there another piece of software which can do similar things and can interface in some way with Matlab?
I based this off of Matlab's Representing Data as a Surface. Does this work?
xlin = linspace(min(x),max(x),33);
ylin = linspace(min(y),max(y),33);
[X,Y] = meshgrid(xlin,ylin);
f = scatteredInterpolant(x,y,z);
Z = f(X,Y);
g = scatteredInterpolant(x,y,c);
C = g(X,Y);
surf(X, Y, Z, C)
Thanks Ander Biguri for suggesting patch. Here's what I've come up with, and it seems to work fine.
function patch_color_plot(struc)
% struc is a structure containing at least the following:
% points - the coordinate of the points in a 3xN matrix
% t - the triangulation matrix
% x_0s - the point values
fac = struc.t;
vert = struc.points;
fvc = struc.x_0s;
p = patch('Faces',fac,'Vertices',vert,'FaceVertexCData',...
fvc,'FaceColor','interp');
set(p,'EdgeColor','none')
axis equal
axis off`
Here's a sample result:
and another one with a torus:
here's another example:
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 need to plot a 3D figure with each data point colored with the value of a 4th variable using a colormap. Lets say I have 4 variables X,Y,Z and W where W = f(X,Y,Z). I want a 3D plot with X, Y, and Z as the three axis. The statement scatter3(X,Y,Z,'filled','b') gives me a scatter plot in 3D but I want to incorporate the value of Z in the graph by representing the points as an extra parameter (either with different areas :bigger circles for data points with high value of Z and small circles for data points with low value of Z or by plotting the data points with different colors using a colormap). However, I am a novice in MATLAB and dont really know how to proceed. Any help will be highly appreciated.
Thanks in advance!
So just use z for the size vector (4th input) as well as the color vector (5th input):
z = 10*(1:pi/50:10*pi);
y = z.*sin(z/10);
x = z.*cos(z/10);
figure(1)
scatter3(x,y,z,z,z)
view(45,10)
colorbar
The size vector needs to be greater 0, so you may need to adjust your z accordingly.
You are already nearly there... simply use
scatter3(X,Y,Z,s,W);
where s is the point size (scalar, e.g. 3) and W is a vector with your W values.
You might also want to issue an
set(gcf, 'Renderer','OpenGL');
where gcf gets your current figure you are plotting in to significantly increase responsiveness when scattering a lot of data.
Usually, trisurf is used to plot nodal quantity on a triangular mesh. However, I would like to plot some element-wise quantity using the following command.
trisurf(t,p(:,1),p(:,2),elewise_quantity,'edgecolor','k','facecolor','interp');
Where elewise_quantiy should be of the same dimension as p(:,1) or p(:,2), so I create elewise_quantity by associating the element-wise quantity to each node of that element.
In this specific case, the 8 triangular element in the middle are associated with 1 and all other elements are 0-valued. There are 10*10 little squares and 10*10*2 little triangulars.
The problem is, as shown in the picture, trisurf can't produce the effect I want. What I expect is an "exact element-wise description", i.e sharp transition at the edge
Also notice that at each corner, the display is different, this's due to the specific orientation of the triangular, is there an elegant way to deal with it?
If you need sharp discontinuities across elements, I'd recommend not displaying nodal values. Calculate element values at internal integration points (e.g. element average at centroid) and assign that value to the element. Ask Matlab to color each element according to its centroidal or integration point value.
You can set per-triangle colors using this method:
%// Example data
X = rand(100,1);
Y = rand(100,1);
Z = X+Y;
T = delaunay(X,Y);
C = mean(Z(T),2);
%// Plot the data
hh = trisurf(T,X,Y,Z);
set(gca, 'CLim', [min(C), max(C)]);
set(hh,'FaceColor', 'flat', ...
'FaceVertexCData', C, ...
'CDataMapping', 'scaled');
If you also don't want the see the triangles that appear at the boundary, you won't get this behavior from a single call to trimesh. You would need to compute a per-triangle quantity and then drop those you don't want to plot according to the per-triangle quantity.
I have written a function in Matlab that gives me a vector at a position (x,y,z).
Now I am looking for the easiest way to make a colored map of this field on a grid and the color should be related to the norm of the vector.
What is the easiest way to define such a grid for $x \in [x_0,x_1],y \in [y_0,y_1], z \in [z_0,z_1]$? Probably linspace for each component would be possible, but maybe there is already a command that gives me the grid.
Now I need to evaluate my function. The problem is, that it actually gives me two vectors, but I am only interested in the first one. So when I first tried to do this I thought that $[A(i,j,k),~]=function(x(i),y(j),z(k))$ could work, but it did not(My goal was: Choose the first vector(A) and mark him with the reference(i,j,k), so that you later on know to which coordinates this vector belongs to).
So I am highly interested in any kind of ideas.
The function meshgrid might be what you are looking for to generate the x, y and z coordinates.
Instead of
[A(i,j,k),~]=function(x(i),y(j),z(k));
try
[A(i,j,k,:),~]=function(x(i),y(j),z(k));
so that you can fit the entire size of the 3-coordinate vector. Also, if you want to preallocate space use
A = zeros(Nx,Ny,Nz,3);
where Nx,... are the dims of your coordinate space. Then like #Moly explains, use meshgrid to generate a 3D grid,
[X Y Z] = meshgrid(x,y,z);
and loop or vectorize to resolve values of your function at points X(i,j,k),Y(i,j,k),Z(i,j,k), compute the norm and store it in 3D array C.
Edit
Representing a cube with mesh(X,Y,Z,C) is not possible but individual slices of the 3D cube can be visualized with mesh, setting the height Z equal to the result of the function C. Some additional work is then required to get coloring right.
Yet another alternative is to use pcolor or contourf. This is perhaps the easiest way to show the 4D data beyond creating a 3D isosurface.
code:
figure
colormap(jet)
for ii=1:9
subplot(3,3,ii)
pcolor(X(:,:,ii),Y(:,:,ii),F(:,:,ii))
axis('equal','square'), title(['Z=' num2str(ii)])
caxis([0 1])
end