Reorganize vector elements without losing neighbor dependencies?

I have the following problem: I have a square mesh of which I know all points and all their neighbor points. Saved as y, z, P, PNorth, PEast, PSouth, PWest. Here is an example with just a few points:

Now I put a shape in this mesh but not all of the points are in this shape. So I want to delete the entries that are not inside the shape, but without losing the neighbor point dependencies.

I was thinking of some kind of substitution with numbers, is that possible?

%the neighbor point in the north of point number 4 is number 5
P       = [0, 0, 0, 4, 5, 0, 7, 0];
PNorth  = [0, 0, 0, 5, 0, 0, 0, 0];
%now i would like to delete the zero entries, without losing these
%dependencies. Point number 4 should have index 1 etc...
    old = [4,5,7];
    new = [1,2,3];
    subs(P,old,new); % (this does not worked, but it's like what it should do)
    subs(PNorth,old,new);
%and that's the result
P       = [1, 2, 3];
PNorth  = [2, 0, 0];

Any idea how that could work? It should work fast for larger amounts of points, so i can save memory.

Answer 1

[Jan]

P       = [0, 0, 0, 4, 5, 0, 7, 0];
PNorth  = [0, 0, 0, 5, 0, 0, 0, 0];

old = [4,5,7];
new = [1,2,3];

LUT(old + 1) = new;          % +1 to consider 0 elements

P       = LUT(P + 1);        % A look-up table
PNorth  = LUT(PNorth + 1);

% Maybe:
keep   = (P ~= 0 | PNorth ~= 0);
P      = P(keep)

P = 1×3

1 2 3

PNorth = PNorth(keep)

PNorth = 1×3

2 0 0