Plotting a vectorial function over a meshgrid.

Dear MathWorks Community, I would like to plot a vectorial function called mysurface over a 2D area like [0,2]x[0,1]. Basically the function describes a deformation of [0,2]x[0,1] into 3D. When defining a meshgrid [X,Y] = meshgrid(0:0.1:2, 0:0.1:1) I can't simply write mysurface([X,Y]), since [X,Y] isn't a vector. How do I handle that? Also I would like to plot the resulting surface, but using surface[X,Y,Z] wouldn't make sense. I need something like p=mysurface([X,Y]) and plot with surface(p(1),p(2),p(3)) but over all points of the grid. Thank you in advance.

[Guillaume]

What is a vectorial function? What inputs does your function need?

[Philipp Tscherner]

With that i mean a function from R^2 to R^3. The function mysurface needs a 2D vector p in [0,2]x[0,1] and gives back a vector in R^3.

[Guillaume]

So does your function takes one 1x2 (or 2x1) input or two scalar inputs (dx, dy)? Is your function vectorised in that you can pass an array of vectors (so a Mx2 or 2xM array in the case of one input, or 2 Mx1 inputs for two inputs)?

whatever the answer it shouldn't be too hard to call your function with all the meshgrided vectors. How you'd display the result however, I have no idea. Maybe have 3 plots p(1) against (x, y), p(2) against (x, y), and p(3) against (x,y).

[KSSV]

Do you have specific input and pictorial example?

[Philipp Tscherner]

Input is a 2x1 vector and the function gives the 3x1 coordinates of the deformed 2D point. Visually it's referred to some plate bending problem. I now simply summed over all x and y in my mesh and created new matrizes Z1, Z2, Z3 and used surf(Z1, Z2, Z3). This seems to work pretty well, I can post the code later, if you are interested.

[Guillaume]

It sounds like your input was actually a 3D mesh with all points having Z=0 and your output was the resulting 3D mesh after deformation and you're just plotting that resulting 3D mesh.

In which case, yes it's fairly straightforward. However, I don't understand how summing the X and Y coordinates of the input mesh helps.

Please don't close questions that have an answer. Even if the answer is not what you were looking for.

[Philipp Tscherner]

Yes you could identify (x, y) = (x, y, 0). As already said I created 3 matrices Z1, Z2, Z3. Mysurface gets the 2D mesh point (x, y) and returns the deformed point p. Summing over all x, y (the indices i, j have to run accordingly) I can define my deformed surface by Z1, Z2, Z3 and finally plot the resutling surface. Although I know it works, I'm not sure if that's the prettiest way to solve the problem:

p = mysurface(x, y)
Zk(i, j) = p(k)
surf(Z1, Z2, Z3)

Answer 1

[KSSV]

V = [2 3] ;
L = V(1) ; % length of the plate 
B = V(2) ; % breadth of the plate 
N = 100 ;
x = linspace(0,L,N) ;
y = linspace(0,B,N) ;
[X,Y] = meshgrid(x,y) ;
mesh(X,Y)