If I have a contour in Matlab obtained
[f, v] = isosurface(x, y, z, v, isovalue)
is there a clean way to apply a transformation to the surfaces and nicely plot the result as a smooth surface? The transformation T is nonlinear.
I tried to apply the transformation T to both f and vert and use patch but couldn't quite get it to work.
The trick is to apply the transformation on your vertices, but keep the same faces data. This way the faces always link the same points, regardless of their new positions.
Since there are no sample data I took the Matlab example as a starting point. This is coming from the Matlab isosurface page (very slightly modified for this example):
%// Generate an isosurface
[x,y,z,v] = flow;
fv = isosurface(x,y,z,v,-3) ;
figure(1);cla
p1 = patch(fv,'FaceColor','red','EdgeColor','none');
%// refine the view
grid off ; set(gca,'Color','none') ; daspect([1,1,1]) ; view(3) ; axis tight ; camlight ; lighting gouraud
This output:
Nothing original so far. Just note that I used the single structure output type fv instead of the 2 separate arrays [f,v]. It is not critical, just a choice to ease the next call to the patch object.
I need to retrieve the vertices coordinates:
%// Retrieve the vertices coordinates
X = fv.vertices(:,1) ;
Y = fv.vertices(:,2) ;
Z = fv.vertices(:,3) ;
You can then apply your transformation. I choose a simple one in this example, but any transformation function is valid.
%// Transform
X = -X.*Y.^2 ;
Y = Y.*X ;
Z = Z*2 ;
Then I rebuild a new structure for the patch which will display the transformed object.
This is the important bit:
%// create new patch structure
fvt.vertices = [X Y Z] ; %// with the new transformed 'vertices'
fvt.faces = fv.faces ; %// but we keep the same 'faces'
Then I display it the same way (well with a slightly different angle for a better view):
%// Plot the transformed isosurface
figure(2);cla
pt = patch( fvt ,'FaceColor','red','EdgeColor','none');
%// refine the view
grid off ; set(gca,'Color','none') ; daspect([1,1,1]) ; view(-3,4) ; axis tight ; camlight ; lighting gouraud
Which produces the figure:
(If you paste all the code snippet in one file it should run and give you the same output.)
Related
I have a set of n=8000 cartesian coordinates X,Y and Z as vectors and also a vector V of same size which I want to use as values to create a heatmap on a sphere.
I saw this link (visualization of scattered data over a sphere surface MATLAB), but I don't understand how I convert this set of data into a meshgrid for plotting using surf.
Almost every example I saw uses meshgrids.
Right now, I am doing by plotting a sphere and then use scatter3 to plot my points as big balls and try to smooth them later. I looks like this:
I would like to get the figure as the plotting of the example in that link, where he uses:
k = 5;
n = 2^k-1;
[x,y,z] = sphere(n);
c = hadamard(2^k);
surf(x,y,z,c);
colormap([1 1 0; 0 1 1])
axis equal
EDIT:
(Sorry for taking so long to reply, the corona crises kept away from work)
What I am actually doing is:
for i=1:numel(pop0n)
ori(i,:)=ori(i,:)/norm(ori(i,:));
end
x = ori(:,1);
y = ori(:,2);
z = ori(:,3);
%// plot
m=100;
[aa,bb,cc] = sphere(m);
surf(aa,bb,cc,ones(m+1,m+1)*min(pop0n))
hold on
colormap jet;
scatter3(x,y,z,400,pop0n/norm(pop0n),'filled');
colorbar
shading interp
The array 'ori' is 8000x3, and contains the x, y and z coordinates of the points I want to plot and pop0n is a 8000 sized vector with the intensities of each coordinate.
My main question is how do I transform my x, y, z and pop0n, that are vectors, into 2D arrays (meshgrid) to use surf?
Because I cannot simply do surf(x,y,z,pop0n) if they are vectors.
Thanks in advance
As David suggested, griddata does the job.
What I did was:
for i=1:numel(pop0n)
ori(i,:)=ori(i,:)/norm(ori(i,:));
end
x = ori(:,1);
y = ori(:,2);
z = ori(:,3);
%// plot
m=100;
[aa,bb,cc] = sphere(m);
v = griddata(x,y,z,pop0n,aa,bb,cc,'nearest');
surf(aa,bb,cc,v)
colormap jet;
colorbar
shading interp
I've found this answer, but I can't complete my work. I wanted to plot more precisely the functions I am studying, without overcoloring my function with black ink... meaning reducing the number of mesh lines. I precise that the functions are complex.
I tried to add to my already existing code the work written at the link above.
This is what I've done:
r = (0:0.35:15)'; % create a matrix of complex inputs
theta = pi*(-2:0.04:2);
z = r*exp(1i*theta);
w = z.^2;
figure('Name','Graphique complexe','units','normalized','outerposition',[0.08 0.1 0.8 0.55]);
s = surf(real(z),imag(z),imag(w),real(w)); % visualize the complex function using surf
s.EdgeColor = 'none';
x=s.XData;
y=s.YData;
z=s.ZData;
x=x(1,:);
y=y(:,1);
% Divide the lengths by the number of lines needed
xnumlines = 10; % 10 lines
ynumlines = 10; % 10 partitions
xspacing = round(length(x)/xnumlines);
yspacing = round(length(y)/ynumlines);
hold on
for i = 1:yspacing:length(y)
Y1 = y(i)*ones(size(x)); % a constant vector
Z1 = z(i,:);
plot3(x,Y1,Z1,'-k');
end
% Plotting lines in the Y-Z plane
for i = 1:xspacing:length(x)
X2 = x(i)*ones(size(y)); % a constant vector
Z2 = z(:,i);
plot3(X2,y,Z2,'-k');
end
hold off
But the problem is that the mesh is still invisible. How to fix this? Where is the problem?
And maybe, instead of drawing a grid, perhaps it is possible to draw circles and radiuses like originally on the graph?
I found an old script of mine where I did more or less what you're looking for. I adapted it to the radial plot you have here.
There are two tricks in this script:
The surface plot contains all the data, but because there is no mesh drawn, it is hard to see the details in this surface (your data is quite smooth, this is particularly true for a more bumpy surface, so I added some noise to the data to show this off). To improve the visibility, we use interpolation for the color, and add a light source.
The mesh drawn is a subsampled version of the original data. Because the original data is radial, the XData and YData properties are not a rectangular grid, and therefore one cannot just take the first row and column of these arrays. Instead, we use the full matrices, but subsample rows for drawing the circles and subsample columns for drawing the radii.
% create a matrix of complex inputs
% (similar to OP, but with more data points)
r = linspace(0,15,101).';
theta = linspace(-pi,pi,101);
z = r * exp(1i*theta);
w = z.^2;
figure, hold on
% visualize the complex function using surf
% (similar to OP, but with a little bit of noise added to Z)
s = surf(real(z),imag(z),imag(w)+5*rand(size(w)),real(w));
s.EdgeColor = 'none';
s.FaceColor = 'interp';
% get data back from figure
x = s.XData;
y = s.YData;
z = s.ZData;
% draw circles -- loop written to make sure the outer circle is drawn
for ii=size(x,1):-10:1
plot3(x(ii,:),y(ii,:),z(ii,:),'k-');
end
% draw radii
for ii=1:5:size(x,2)
plot3(x(:,ii),y(:,ii),z(:,ii),'k-');
end
% set axis properties for better 3D viewing of data
set(gca,'box','on','projection','perspective')
set(gca,'DataAspectRatio',[1,1,40])
view(-10,26)
% add lighting
h = camlight('left');
lighting gouraud
material dull
How about this approach?
[X,Y,Z] = peaks(500) ;
surf(X,Y,Z) ;
shading interp ;
colorbar
hold on
miss = 10 ; % enter the number of lines you want to miss
plot3(X(1:miss:end,1:miss:end),Y(1:miss:end,1:miss:end),Z(1:miss:end,1:miss:end),'k') ;
plot3(X(1:miss:end,1:miss:end)',Y(1:miss:end,1:miss:end)',Z(1:miss:end,1:miss:end)','k') ;
I have a number of 2d probability mass functions from 2 categories. I am trying to plot the contours to visualise them (for example at their half height, but doesn't really matter).
I don't want to use contourf to plot directly because I want to control the fill colour and opacity. So I am using contourc to generate xy coordinates, and am then using fill with these xy coordinates.
The problem is that the xy coordinates from the contourc function have strange numbers in them which cause the following strange vertices to be plotted.
At first I thought it was the odd contourmatrix format, but I don't think it is this as I am only asking for one value from contourc. For example...
contourmatrix = contourc(x, y, Z, [val, val]);
h = fill(contourmatrix(1,:), contourmatrix(2,:), 'r');
Does anyone know why the contourmatrix has these odd values in them when I am only asking for one contour?
UPDATE:
My problem seems might be a failure mode of contourc when the input 2D matrix is not 'smooth'. My source data is a large set of (x,y) points. Then I create a 2D matrix with some hist2d function. But when this is noisy the problem is exaggerated...
But when I use a 2d kernel density function to result in a much smoother 2D function, the problem is lessened...
The full process is
a) I have a set of (x,y) points which form samples from a distribution
b) I convert this into a 2D pmf
c) create a contourmatrix using contourc
d) plot using fill
Your graphic glitches are because of the way you use the data from the ContourMatrix. Even if you specify only one isolevel, this can result in several distinct filled area. So the ContourMatrix may contain data for several shapes.
simple example:
isolevel = 2 ;
[X,Y,Z] = peaks ;
[C,h] = contourf(X,Y,Z,[isolevel,isolevel]);
Produces:
Note that even if you specified only one isolevel to be drawn, this will result in 2 patches (2 shapes). Each has its own definition but they are both embedded in the ContourMatrix, so you have to parse it if you want to extract each shape coordinates individually.
To prove the point, if I simply throw the full contour matrix to the patch function (the fill function will create patch objects anyway so I prefer to use the low level function when practical). I get the same glitch lines as you do:
xc = X(1,:) ;
yc = Y(:,1) ;
c = contourc(xc,yc,Z,[isolevel,isolevel]);
hold on
hp = patch(c(1,1:end),c(2,1:end),'r','LineWidth',2) ;
produces the same kind of glitches that you have:
Now if you properly extract each shape coordinates without including the definition column, you get the proper shapes. The example below is one way to extract and draw each shape for inspiration but they are many ways to do it differently. You can certainly compact the code a lot but here I detailed the operations for clarity.
The key is to read and understand how the ContourMatrix is build.
parsed = false ;
iShape = 1 ;
while ~parsed
%// get coordinates for each isolevel profile
level = c(1,1) ; %// current isolevel
nPoints = c(2,1) ; %// number of coordinate points for this shape
idx = 2:nPoints+1 ; %// prepare the column indices of this shape coordinates
xp = c(1,idx) ; %// retrieve shape x-values
yp = c(2,idx) ; %// retrieve shape y-values
hp(iShape) = patch(xp,yp,'y','FaceAlpha',0.5) ; %// generate path object and save handle for future shape control.
if size(c,2) > (nPoints+1)
%// There is another shape to draw
c(:,1:nPoints+1) = [] ; %// remove processed points from the contour matrix
iShape = iShape+1 ; %// increment shape counter
else
%// we are done => exit while loop
parsed = true ;
end
end
grid on
This will produce:
MATLAB's surf command allows you to pass it optional X and Y data that specify non-cartesian x-y components. (they essentially change the basis vectors). I desire to pass similar arguments to a function that will draw a line.
How do I plot a line using a non-cartesian coordinate system?
My apologies if my terminology is a little off. This still might technically be a cartesian space but it wouldn't be square in the sense that one unit in the x-direction is orthogonal to one unit in the y-direction. If you can correct my terminology, I would really appreciate it!
EDIT:
Below better demonstrates what I mean:
The commands:
datA=1:10;
datB=1:10;
X=cosd(8*datA)'*datB;
Y=datA'*log10(datB*3);
Z=ones(size(datA'))*cosd(datB);
XX=X./(1+Z);
YY=Y./(1+Z);
surf(XX,YY,eye(10)); view([0 0 1])
produces the following graph:
Here, the X and Y dimensions are not orthogonal nor equi-spaced. One unit in x could correspond to 5 cm in the x direction but the next one unit in x could correspond to 2 cm in the x direction + 1 cm in the y direction. I desire to replicate this functionality but drawing a line instead of a surf For instance, I'm looking for a function where:
straightLine=[(1:10)' (1:10)'];
my_line(XX,YY,straightLine(:,1),straightLine(:,2))
would produce a line that traced the red squares on the surf graph.
I'm still not certain of what your input data are about, and what you want to plot. However, from how you want to plot it, I can help.
When you call
surf(XX,YY,eye(10)); view([0 0 1]);
and want to get only the "red parts", i.e. the maxima of the function, you are essentially selecting a subset of the XX, YY matrices using the diagonal matrix as indicator. So you could select those points manually, and use plot to plot them as a line:
Xplot = diag(XX);
Yplot = diag(YY);
plot(Xplot,Yplot,'r.-');
The call to diag(XX) will take the diagonal elements of the matrix XX, which is exactly where you'll get the red patches when you use surf with the z data according to eye().
Result:
Also, if you're just trying to do what your example states, then there's no need to use matrices just to take out the diagonal eventually. Here's the same result, using elementwise operations on your input vectors:
datA = 1:10;
datB = 1:10;
X2 = cosd(8*datA).*datB;
Y2 = datA.*log10(datB*3);
Z2 = cosd(datB);
XX2 = X2./(1+Z2);
YY2 = Y2./(1+Z2);
plot(Xplot,Yplot,'rs-',XX2,YY2,'bo--','linewidth',2,'markersize',10);
legend('original','vector')
Result:
Matlab has many built-in function to assist you.
In 2D the easiest way to do this is polar that allows you to make a graph using theta and rho vectors:
theta = linspace(0,2*pi,100);
r = sin(2*theta);
figure(1)
polar(theta, r), grid on
So, you would get this.
There also is pol2cart function that would convert your data into x and y format:
[x,y] = pol2cart(theta,r);
figure(2)
plot(x, y), grid on
This would look slightly different
Then, if we extend this to 3D, you are only left with plot3. So, If you have data like:
theta = linspace(0,10*pi,500);
r = ones(size(theta));
z = linspace(-10,10,500);
you need to use pol2cart with 3 arguments to produce this:
[x,y,z] = pol2cart(theta,r,z);
figure(3)
plot3(x,y,z),grid on
Finally, if you have spherical data, you have sph2cart:
theta = linspace(0,2*pi,100);
phi = linspace(-pi/2,pi/2,100);
rho = sin(2*theta - phi);
[x,y,z] = sph2cart(theta, phi, rho);
figure(4)
plot3(x,y,z),grid on
view([-150 70])
That would look this way
I have a 3D mesh like in this picture.
Now what I want to do is create a plane that will intersect the surface at a certain Z value. I would then want to get the x and y coordinates of this intersection and have matlab output them.
What I'm planning on doing is that this picture is a model of a lake. This lake will have water evaporating that will be removing a certain z value of water. I would then like to see what the new shoreline would look like by obtaining the x and y coordinates of this intersection.
This is my code for plotting that picture.
function plot(x,y,z)
Contour = xlsread('C:\Users\Joel\Copy\Contour','A2:D4757');
x = Contour(:,1);
y = Contour(:, 2);
z = Contour(:,3);
F = TriScatteredInterp(x,y,z);
[X,Y]=meshgrid(linspace(-600,600,300));
Z=F(X,Y);
surf(X,Y,Z);
end
You can do this by simply thresholding the interpolated Z values
inside = Z < seaLevel; % binary mask of points inside water
shoreline = bwmorph( inside, 'remove' ); % a mask with only shoreline pixels eq to 1
figure;
surf( X, Y, Z, 'EdgeColor', 'none', 'FaceColor', [210,180,140]/255, 'FaceAlpha', .5 );
hold on;
ii = find( shoreline );
plot3( X(ii), Y(ii), seaLevel*ones(size(ii)), 'b', 'LineWidth', 2 );
The contour3 will give nicer boundaries:
[h,c]=contour3(X,Y,Z,[seaLevel seaLevel]);
seaLevel is given twice: otherwise contour3 thinks seaLevel is the number of levels to automatically calibrate. And to nicely annotate with the numeric height of your seaLevel:
clabel(h,c);
you may modify c to print "sea level" instead of num2str(seaLevel).
If you don't have the MATLAB toolbox for image processing you can't use the function "bwmorph". As a solution you can replace line 2 of Shai's code with the following code which reimplements the bwmorph function for parameter 'remove'. (The reimplementation is probably neither very perfomrant nor an exact reimplementatin (the borders of the matrix aren't used) - but the solution should work as a first step. Feel free to improve).
shoreline= zeros(size(inside));
for i_row = 2:size(inside,1)-1
for i_col = 2:size(inside,2)-1
if(inside(i_row,i_col))
if (~( inside(i_row+1,i_col) && ...
inside(i_row-1,i_col) && ...
inside(i_row,i_col+1) && ...
inside(i_row,i_col-1)))
inside2(i_row,i_col) = 1;
end
end
end
end