I want to plot smooth contour plot from X Y Z matrix.
sf = fit([X Y] Z, 'poly23');
plot(sf);
I have not enought smooth curve..
What I need?
You can use the functions such as griddata and csaps. Together they will lead you to the result as smooth as you wish. The first function adds additional points to your data matrix set. The second one makes the result smoother. The example of the code is below. In the example smoothing is done first in X direction and then in Y direction. Try to play around with the resolution and smoothing_parameter (the current set of these parameters should be OK though).
x = min_x:step_x:max_x;
y = min_y:step_y:max_y;
resolution = 10;
xg = min_x:(step_x/resolution):max_x;
yg = min_y:(step_y/resolution):max_y;
[X,Y] = meshgrid(x,y);
[XG,YG] = meshgrid(xg,yg);
smoothing_parameter = 0.02;
fitted = griddata(X,Y,Z,XG,YG,'cubic');
fitted_smoothed_x = csaps(xg,fitted,smoothing_parameter,xg);
fitted_smoothed_xy = csaps(yg,fitted_smoothed_x',smoothing_parameter,yg);
surf(XG,YG,fitted_smoothed_xy');
EDIT: If you want to get just a contour plot, you can do, for example, as presented below. As I don't have the real data, I will use build-in function peaks to generate some.
[X,Y,Z] = peaks(30);
figure
surfc(X,Y,Z)
view([0 90])
zlim([-10 -8])
Here you just look at your contour plot from above being below the surface.
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
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
It seems to be very basic question, but I wonder when I plot x values against y values, what interpolation technique is used behind the scene to show me the discrete data as continuous? Consider the following example:
x = 0:pi/100:2*pi;
y = sin(x);
plot(x,y)
My guess is it is a Lagrangian interpolation?
No, it's just a linear interpolation. Your example uses a quite long dataset, so you can't tell the difference. Try plotting a short dataset and you'll see it.
MATLAB's plot performs simple linear interpolation. For finer resolution you'd have to supply more sample points or interpolate between the given x values.
For example taking the sinus from the answer of FamousBlueRaincoat, one can just create an x vector with more equidistant values. Note, that the linear interpolated values coincide with the original plot lines, as the original does use linear interpolation as well. Note also, that the x_ip vector does not include (all) of the original points. This is why the do not coincide at point (~0.8, ~0.7).
Code
x = 0:pi/4:2*pi;
y = sin(x);
x_ip = linspace(x(1),x(end),5*numel(x));
y_lin = interp1(x,y,x_ip,'linear');
y_pch = interp1(x,y,x_ip,'pchip');
y_v5c = interp1(x,y,x_ip,'v5cubic');
y_spl = interp1(x,y,x_ip,'spline');
plot(x,y,x_ip,y_lin,x_ip,y_pch,x_ip,y_v5c,x_ip,y_spl,'LineWidth',1.2)
set(gca,'xlim',[pi/5 pi/2],'ylim',[0.5 1],'FontSize',16)
hLeg = legend(...
'No Interpolation','Linear Interpolation',...
'PChip Interpolation','v5cubic Interpolation',...
'Spline Interpolation');
set(hLeg,'Location','south','Fontsize',16);
By the way..this does also apply to mesh and others
[X,Y] = meshgrid(-8:2:8);
R = sqrt(X.^2 + Y.^2) + eps;
Z = sin(R)./R;
figure
mesh(Z)
No, Lagrangian interpolation with 200 equally spaced points would be an incredibly bad idea. (See: Runge's phenomenon).
The plot command simply connects the given (x,y) points by straight lines, in the order given. To see this for yourself, use fewer points:
x = 0:pi/4:2*pi;
y = sin(x);
plot(x,y)
I'm trying to create a surface plot from (x,y,z) data on an irregular grid. The datasets are located along diagonal lines of positive gradient in the (x,y) plane. The method is illustrated below
xi = linspace (min(x), max(x), 1000);
yi = linspace (min(y), max(y), 1000);
zi = linspace (min(z), max(z), 400);
[XI YI]=meshgrid(xi,yi);
F = TriScatteredInterp (x,y,z);
Vi = F(XI,YI);
surf(Xi,Yi,Vi);
shading interp;
view(2)
An example result is shown below:
The data should be smooth in the x direction (so at y=860 there should be a single, continuous blue dip). I think the problem is that the interpolation is being carried out well along each dataset but poorly between them as the spacing between the datasets is far larger than between points within a dataset.
What would be the best way to deal with this?
i just started with my master thesis and i already am in trouble with my capability/understanding of matlab.
The thing is, i have a trajectory on a surface of a planet/moon whatever (a .mat with the time, and the coordinates. Then i have some .mat with time and the measurement at that time.
I am able to plot this as a color coded trajectory (using the measurement and the coordinates) in scatter(). This works awesomely nice.
However my problem is that i need something more sophisticated.
I now need to take the trajectory and instead of color-coding it, i am supposed to add the graph (value) of the measurement (which is given for each point) to the trajectory (which is not always a straight line). I will added a little sketch to explain what i want. The red arrow shows what i want to add to my plot and the green shows what i have.
You can always transform your data yourself: (using the same notation as #Shai)
x = 0:0.1:10;
y = x;
m = 10*sin(x);
So what you need is the vector normal to the curve at each datapoint:
dx = diff(x); % backward finite differences for 2:end points
dx = [dx(1) dx]; % forward finite difference for 1th point
dy = diff(y);
dy = [dy(1) dy];
curve_tang = [dx ; dy];
% rotate tangential vectors 90° counterclockwise
curve_norm = [-dy; dx];
% normalize the vectors:
nrm_cn = sqrt(sum(abs(curve_norm).^2,1));
curve_norm = curve_norm ./ repmat(sqrt(sum(abs(curve_norm).^2,1)),2,1);
Multiply that vector with the measurement (m), offset it with the datapoint coordinates and you're done:
mx = x + curve_norm(1,:).*m;
my = y + curve_norm(2,:).*m;
plot it with:
figure; hold on
axis equal;
scatter(x,y,[],m);
plot(mx,my)
which is imo exactly what you want. This example has just a straight line as coordinates, but this code can handle any curve just fine:
x=0:0.1:10;y=x.^2;m=sin(x);
t=0:pi/50:2*pi;x=5*cos(t);y=5*sin(t);m=sin(5*t);
If I understand your question correctly, what you need is to rotate your actual data around an origin point at a certain angle. This is pretty simple, as you only need to multiply the coordinates by a rotation matrix. You can then use hold on and plot to overlay your plot with the rotated points, as suggested in the comments.
Example
First, let's generate some data that resembles yours and create a scatter plot:
% # Generate some data
t = -20:0.1:20;
idx = (t ~= 0);
y = ones(size(t));
y(idx) = abs(sin(t(idx)) ./ t(idx)) .^ 0.25;
% # Create a scatter plot
x = 1:numel(y);
figure
scatter(x, x, 10, y, 'filled')
Now let's rotate the points (specified by the values of x and y) around (0, 0) at a 45° angle:
P = [x(:) * sqrt(2), y(:) * 100] * [1, 1; -1, 1] / sqrt(2);
and then plot them on top of the scatter plot:
hold on
axis square
plot(P(:, 1), P(:, 2))
Note the additional things have been done here for visualization purposes:
The final x-coordinates have been stretched (by sqrt(2)) to the appropriate length.
The final y-coordinates have been magnified (by 100) so that the rotated plot stands out.
The axes have been squared to avoid distortion.
This is what you should get:
It seems like you are interested in 3D plotting.
If I understand your question correctly, you have a 2D curve represented as [x(t), y(t)].
Additionally, you have some value m(t) for each point.
Thus we are looking at the plot of a 3D curve [x(t) y(t) m(t)].
you can easily achieve this using
plot3( x, y, m ); % assuming x,y, and m are sorted w.r.t t
alternatively, you can use the 3D version of scatter
scatter3( x, y, m );
pick your choice.
Nice plot BTW.
Good luck with your thesis.