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Plotting volumetric data in MATLAB
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I have given a 300x300x300 Matrix.
The first subscript represents the x-value, the second the y-value and the third the z-value.
To access a value of a specific point in the matrix i use:
matrix(x-val, y-val, z-val)
I want to create a 3D scatter plot where the color of the dots in the plot changes based on the values of the points in the matrix. All values are >=0
As i am pretty new to Matlab i have no idea where to start.
MathWorks has a page that summarizes types of MATLAB plots. I've referenced it on multiple occasions. The function you are looking for is scatter3(X,Y,Z,S,C). Walk through the function's example, it should help you out.
I'm not sure how you can have a 300x300x300 matrix for a point cloud in 3-D. I will assume you have a 300x300x3 matrix, i.e.:
x = matrix(:,:,1);
y = matrix(:,:,2);
z = matrix(:,:,3);
First of all, you probably want to rearrange points into a 2D matrix:
m = reshape(matrix, numel(matrix(:,:,1), 3);
n = size(m,1);
Your matrix is now arranged as a n-by-3 matrix, coloumn 1, 2 and 3 representing x-, y- and z-axis respectively, i.e.:
m = [ x1 y1 z1]
[ x2 y2 z2]
[ ... ]
[ xn yn zn]
Then you can create a basic 3D scatter plot:
scatter3(m(:,1), m(:,2), m(:,3))
However, this is not what you want, because points are in the same colour. To add colour based on your colouring logic, you should firstly create a color matrix using one of the MATLAB's built-in color maps. Here I use jet:
myc = jet(n);
You can also create your own colour map ofc. Elements in the colour matrix are simply normalised rgb values.
Now you will have to weight each points using your own logic:
weighting = myWeightingLogic(m);
weighting will be a n-by-1 vector and it should be normalised if it is not yet.
weighting = weighting/max(weighting);
Now you can colour your scatter plot:
scatter3(m(:,1), m(:,2), m(:,3)), [], myc(round(weighting*n),:));
The full code:
m = reshape(matrix, numel(matrix(:,:,1), 3);
n = size(m,1);
myc = jet(n);
weighting = myWeightingLogic(m);
weighting = weighting/max(weighting);
scatter3(m(:,1), m(:,2), m(:,3)), [], myc(round(weighting*n),:));
Related
I have three variables x, y and z. I have inequalities of the form
x >= a, y>= b, z>=c, x+y>=d, y+z>=e, x+z>=f, x+y+z>=g
where a to g are positive numbers. On a 3D plot with axes x, y and z, this is an open volume. I would like to fill the open side (i.e. away from 0) shape with color and show it in a plot. What is the way to do this on MATLAB?
I attempted to use fill3 and a mesh but the result was not very good
[x,y,z] = meshgrid(0:0.01:2,0:0.01:2,0:0.01:2);
ineq = (x>=1)& (y>0.5)&(z>=0.25)&(x+y>1.25)&(y+z>0.6)&(x+z>1.1)&(x+y+z>1.6);
fill3(x(:),y(:),z(:), 'r')
box on
grid on
Using plot3 also was not very good. Is there any other way to generate a nice 3D figure on MATLAB?
Mathematica does this using RegionPlot3D. I was hoping for a similar resultant image.
First of all, be careful when using 3D meshes, the one you defined contains 8M+ points.
Assuming your shape is convex, you can use convhull and trisurf:
Not that the option 'Simplify' is set as true to reduce the number of elements accounted for in the convex hull.
[x,y,z] = meshgrid(0:0.1:2,0:0.1:2,0:0.1:2);
ineq = (x>=1)& (y>0.5)&(z>=0.25)&(x+y>1.25)&(y+z>0.6)&(x+z>1.1)&(x+y+z>1.6);
figure;
x_ineq = x(ineq);
y_ineq = y(ineq);
z_ineq = z(ineq);
id_cvhl = convhull(x_ineq,y_ineq,z_ineq,'Simplify',true);
trisurf(id_cvhl,x_ineq,y_ineq,z_ineq,'FaceColor','cyan','edgecolor','none')
xlim([0 2])
ylim([0 2])
zlim([0 2])
In case you want the result to look a bit more than RegionPlot3D, don't use Simplify, and plot the edges (Be careful not too have a mesh with too many points!).
id_cvhl = convhull(x_ineq,y_ineq,z_ineq);
trisurf(id_cvhl,x_ineq,y_ineq,z_ineq,'Facecolor','yellow')
I have started to learn Machine Learning, and programming in matlab.
I want to plot a matrix sized m*d where d=3 and m are the number of points.
with y binary vector I'd like to color each point with blue/red.
and plot a plane which is described with the vertical vector to it w.
The problem I trying to solve is to give some kind of visual representation of the data and the linear predictor.
All I know is how to single points with plot3, but no any number of points.
Thanks.
Plot the points using scatter3()
scatter3(X(y,1),X(y,2),X(y,3),'filled','fillcolor','red');
hold on;
scatter3(X(~y,1),X(~y,2),X(~y,3),'filled','fillcolor','blue');
or using plot3()
plot(X(y,1),X(y,2),X(y,3),' o','MarkerEdgeColor','red','MarkerFaceColor','red');
hold on;
plot(X(~y,1),X(~y,2),X(~y,3),' o','MarkerEdgeColor','blue','MarkerFaceColor','blue');
There are a few ways to plot a plane. As long as w(3) isn't very close to 0 then the following will work okay. I'm assuming your plane is defined by x'*w+b=0 where b is a scalar and w and x are column vectors.
x1min = min(X(:,1)); x2min = min(X(:,2));
x1max = max(X(:,1)); x2max = max(X(:,2));
[x1,x2] = meshgrid(linspace(x1min,x1max,20), linspace(x2min, x2max, 20));
x3 = -(w(1)*x1 + w(2)*x2 + b)/w(3);
surf(x1,x2,x3,'FaceColor',[0.6,0.6,0.6],'FaceAlpha',0.7,'EdgeColor',[0.4,0.4,0.4],'EdgeAlpha',0.4);
xlabel('x_1'); ylabel('x_2'); zlabel('x_3'); axis('vis3d');
Resulting plot
I have a two columns of data. X = Model values of NOx concentrations and Y = Observations of NOx concentrations. Now, I want to scatter plot X, Y (markers varying with colors) as well as the colourbar which would show me the counts (i.e. number of data points in that range). X and Y are daily data for a year, i.e. 365 rows.
Please help me. Any help is greatly appreciated.
I have attached a sample image.
If I understand you correctly, the real problem is creating the color information, which is, creating a bivariate histogram. Luckily, MATLAB has a function, hist3, for that in the Statistics & Machine Learning Toolbox. The syntax is
[N,C] = hist3(X,nbins)
where X is a m-by-2 matrix containing the data, and nbins is a 1-by-2 vector containing the number of bins in each dimension. The return value N is a matrix of size nbins(1)-by-nbins(2), and contains the histogram data. C is a 1-by-2 cell array, containing the bin centers in both dimensions.
% Generate sample data
X = randn(10000, 1);
Y = X + rand(10000, 1);
% Generate histogram
[N,C] = hist3([X,Y], [100,100]);
% Plot
imagesc(C{1},C{2},N);
set(gca,'YDir','normal');
colormap(flipud(pink));
colorbar;
Result:
I'm working on MATLAB, where I have a vector which I need to split into two classes and then get a histogram of both resulting vectors (which have different sizes). The values represent height records so the interval is about 140-185.
How can I get a normalized histogram of both resulting vectors in different colors. I was able to get both normalized vectors in the same colour (which is indistiguible) and and also a histogram with different colours but not not normalized...
I hope you understand my question and will be able to help me.
Thanks in advance :)
Maybe this is what you need:
matrix = [155+10*randn(2000,1) 165+10*randn(2000,1)];
matrix(1:1100,1) = NaN;
matrix(1101:2000,2) = NaN; %// example data
[y x] = hist(matrix, 15); %// 15 is desired number of bins
y = bsxfun(#rdivide, y, sum(y)) / (x(2)-x(1)); %// normalize to area 1
bar(x,y) %// plots each column of y vs x. Automatically uses different colors
I'm trying to make a color plot in matlab using output data from another program. What I have are 3 vectors indicating the x-position, y-yposition (both in milliarcseconds, since this represents an image of the surroundings of a black hole), and value (which will be assigned a color) of every point in the desired image. I apparently can't use pcolor, because the values which indicate the color of each "pixel" are not in a matrix, and I don't know a way other than meshgrid to create a matrix out of the vectors, which didn't work due to the size of the vectors.
Thanks in advance for any help, I may not be able to reply immediately.
If we make no assumptions about the arrangement of the x,y coordinates (i.e. non-monotonic) and the sparsity of the data samples, the best way to get a nice image out of your vectors is to use TriScatteredInterp. Here is an example:
% samplesToGrid.m
function [vi,xi,yi] = samplesToGrid(x,y,v)
F = TriScatteredInterp(x,y,v);
[yi,xi] = ndgrid(min(y(:)):max(y(:)), min(x(:)):max(x(:)));
vi = F(xi,yi);
Here's an example of taking 500 "pixel" samples on a 100x100 grid and building a full image:
% exampleSparsePeakSamples.m
x = randi(100,[500 1]); y = randi(100,[500 1]);
v = exp(-(x-50).^2/50) .* exp(-(y-50).^2/50) + 1e-2*randn(size(x));
vi = samplesToGrid(x,y,v);
imagesc(vi); axis image
Gordon's answer will work if the coordinates are integer-valued, but the image will be spare.
You can assign your values to a matrix based on the x and y coordinates and then use imagesc (or a similar function).
% Assuming the X and Y coords start at 1
max_x = max(Xcoords);
max_y = max(Ycoords);
data = nan(max_y, max_x); % Note the order of y and x
indexes = sub2ind(size(data), max_y, max_x);
data(indexes) = Values;
imagesc(data); % note that NaN values will be colored with the minimum colormap value