I have a cloud of points scattered in a rectangle and some data in this points, a bit like this $$ x(:)=[x(1), x(2), ..., x(N)] \\ y(:)=[y(1), y(2), ..., y(N)] \\ u(:)=[u(1), u(2), ..., u(N)] $$ Here, I am looking for plotting a contour of the $u$ data on matlab. I tried several function on matlab; contour, contourf, contourc,... etc but in vain.
Any help please
In essence, what you want to do is interpolate data: You want to find a function $U(x,y)$ so that $U(x_i,y_i)=u_i$. This is then the function for which you'd like to do draw isocontours.
You should take a look at books on numerical methods and search for "two-dimensional interpolation". Among the methods you will find is to triangulate your points $(x_i,y_i)$ to form a mesh, on which you can then define $U(x,y)$ as a piecewise linear function. But I think a better approach -- unless your data is pretty evenly distributed -- is to use something like the Radial Basis Function (RBF) method.
The only way I know of to visualise such data is to first triangulate it. Matlab can do the triangulation. See the Matlab functions 'delaunay', 'trisurf', 'pdecont'. This works if the domain is convex. If not then you need to construct the triangulation by accounting for the domain boundaries. Maybe Matlab has methods to do this, I am not very much familiar with Matlab. You may also want to look at Shewchuk's Triangle program https://www.cs.cmu.edu/~quake/triangle.html which may help in case of non-convex domains.
Also see this post: Plot a surface from data sets in MATLAB
