Say I have a discrete vector field u(x,y) and v(x,y). I have another scalar field vort(x,y). x and y are a meshgrid style set of coordinates. I want to set a contour level of my scalar vort, and integrate the vector field around that closed contour. How can I do this when I have discrete data, not a function?
contour(x,y,vort,[0.5 0.5]); %for example
I can extract from this the data points at all locations on the contour, but how do I integrate the vector field onto this curve?
I sorted this by:
use contourc to find the coordinates of the points in the loop
use improfile to interpolate to find the u and v values at a specified number of points around the loop
Find the angle (a) of the loop at each point
Integrate u * cos(a) - v * sin(a) using trapz
Related
I'm trying to interpolate a 3D vector field. For every (x,y,z) position we have a vector (u,v,w). I have another set of points let's call them (xq,yq,zq) in which I don't have vector information (uq,vq,wq). I would like to interpolate my data to find the vectors at the points (xq,yq,zq).
I've tried to interpolate using several functions like griddata, by interpolating each vector component individually.
uq = griddata(x,y,z,u,xq,yq,zq);
vq = griddata(x,y,z,v,xq,yq,zq);
wq = griddata(x,y,z,w,xq,yq,zq);
I expect to obtain the vectors at the locations I specified, but the message I get is:
"Warning: The underlying triangulation is empty - the points may be
coplanar or collinear."
Is there a better way to interpolate a vector field?
For example, I got 3 pairs of 1-D loglog curves and additionally their associated cartesian coordinate points (x,y,z) of one of their ends A, B and C over a mesh surface S (z is positive downwards and linear but coincides in direction with the log(y)-axis from the curves). Is it possible to respresent in a single figure such system of plots in matlab?
Moreover, obtain an interpolated slice from A,B and C?
The images from the question of user3281667 gives an insight of what we are trying to do here:
https://gis.stackexchange.com/questions/252939/interpolating-xyz-data-in-arcgis-3d-analyst
Thanks.
Kind of solved. First we need to know in which format is our data, this case scattered.
I concatenated a nx4 matrix with the preprocessed data A=[X Y Z C].
Then use the right tools, to plot use scatter3: scatter3(A(:,1), A(:,2), A(:,3),30, A(:,4), 'filled' )
Now to interpolate, fisrt generate a grid refinement with meshgrid: [Xm, Ym, Zm] = meshgrid(min(X):2:max(X), min(Y):2:max(Y), min(Z):2:max(Z)) next interpolate using griddata Cm = griddata(X,Y,Z,C,Xm,Ym,Zm);and last plot again.
figure
scatter3(Xm(:), Ym(:), Zm(:), 30, Cm(:), 'filled' )
Thanks to user7431005
I want to determine a point in space by geometry and I have math computations that gives me several theta values. After evaluating the theta values, I could get N 1 x 3 dimension matrix where N is the number of theta evaluated. Since I have my targeted point, I only need to decide which of the matrices is closest to the target with adequate focus on the three coordinates (x,y,z).
Take a view of the analysis in the figure below:
Fig 1: Determining Closest Point with all points having minimal error
It can easily be seen that the third matrix is closest using sum(abs(Matrix[x,y,z])). However, if the method is applied on another figure given below, obviously, the result is wrong.
Fig 2: One Point has closest values with 2-axes of the reference point
Looking at point B, it is closer to the reference point on y-,z- axes but just that it strayed greatly on x-axis.
So how can I evaluate the matrices and select the closest one to point of reference and adequate emphasis will be on error differences in all coordinates (x,y,z)?
If your results is in terms of (x,y,z), why don't evaluate the euclidean distance of each matrix you have obtained from the reference point?
Sort of matlab code:
Ref_point = [48.98, 20.56, -1.44];
Curr_point = [x,y,z];
Xd = (x-Ref_point(1))^2 ;
Yd = (y-Ref_point(2))^2 ;
Zd = (z-Ref_point(3))^2 ;
distance = sqrt(Xd + Yd + Zd);
%find the minimum distance
I have plotted a piece-wise defined continuous linear function comprising of several oblique straight lines joined end-to-end:-
x=[0,1/4,1/2,3/4,1];
oo=[1.23 2.31 1.34 5.69 7] % edit
y=[oo(1),oo(2),oo(3),oo(4),oo(5)];
plot(x,y,'g--')
I now wish to sample points from this plot itself, say i want the y corresponding to x=0.89. How to achieve that using Matlab? Is there a special function in-built in Matlab?
Yes, there's a built-in function for that: interp1:
vq = interp1(x,v,xq) returns interpolated values of a 1-D function at specific query points using linear interpolation. Vector x contains the sample points, and v contains the corresponding values, v(x). Vector xq contains the coordinates of the query points.
[...]
See the linked documentation for further options. For example, you can specify the interpolation method (default is linear), or whether you want to extrapolate (i.e. allow for xq values to lie outside the original x range).
I have a 25000x3-matrix, with each row containing a x-, a y- and a z-value. Now I wanted to do a graphical plot out of these. But for using for example surf(Z) I have to use a mxn-matrix as Z with m equal the size of x and n equal the size of y. How can I reshape the matrix I have to the needed mxn-matrix? The problem is that my x- and y-values are no ints, but floats, so I assume that I have to do a interpolation first. Is that true? My data plotted with plot3 looks like:
The fact that your x- and y- values are not integers is not a problem at all. The real question is: are your (x,y) points forming a grid, or not ?
If your points are forming a grid, then you have to reshape your columns to form m-by-n arrays. You may need to sort your data according to the first, then second column and then use the reshape function.
If your points are not forming a grid, then you will have to make an interpolation. By chance the scatterinterpolant class can nicely help you in doing so.
As you can see, the data you are providing is neither given in a gridded way, nor is the point cloud clean. You could however try to do the following:
Project the point cloud onto the x-y plane
Triangulate those points
Give the points their original z-coordinate back.
Plot the surface using trisurf
Here is a MATLAB code that does this:
%// Generate some points P
[X,Y] = ndgrid(0:30);
P = [X(:), Y(:), X(:).^2+Y(:)];
%%// Here the actual computation starts
[~,I] = unique(P(:,1:2),'rows'); %// Remove points with duplicate (x,y)-coords
P = P(I,:);
T = delaunay(P(:,1),P(:,2)); %// Triangulate the 2D-projection
surface = triangulation(T, P(:,1), P(:,2), P(:,3)); %// Project back to 3D
trisurf(surface); %// Plot
You may want to remove stray points first, though.