Non-rectangular meshgrids in MATLAB

Question

I want to create a non-rectangular meshgrid in matlab.

Basically I have a polygon shaped feasible set I need to make a grid of in order to interpolate 3D data points in this set. The function for interpolation is given and requires finite (x, y, z) inputs. Where x is nx1, y is 1xm and z is nxm. Right now I have the mesh set up with linspace and set all NaN (infeasible) values to 0 before using my function, which is wrong of course (third figure).

Is there a simple solution for this?

I added a picture illustrating what I'm currently doing: First plot is the feasible set, second plot are solved sample data points in this set and third plot is the interpolation (currently still with rectangular meshgrid and NaN = 0). What I need is a meshgrid looking like the first figure (red polygon) instead of a rectangular one. In the third plot you can see that the rectangular meshgrid in combination with setting NaN to 0 (=infeasible values, not included in the red polygon set) results in a wrong interpolation along the edges, because it includes infeasible regions.

Here is my code using a rectangular meshgrid:

figure (2) %sample data
plot3(X0(1,:), X0(2,:), U, 'x')
%X0(1,:) and X0(2,:) are vectors corresponding to the Z-Values (blue sample data)
%X0 and U are in the feasible set (red polygon)

xv = linspace(xLb(1), xUb(1), 100);
yv = linspace(xLb(2), xUb(2), 100); %xLb and xUb are upper and lower bounds for the rectangle mesh
[x1,x2] = meshgrid(xv, yv);
Z = griddata(X0(1,:), X0(2,:), U, x1, x2);
%This grid obviously includes values that are not in the feasible set (red polygon) by its rectangular nature

Z(isnan(Z))=0; %set infeasible values to 0, wrong of course
testMPC = someInterpolationFunction([0:length(Z)-1]',[0:length(Z)-1],Z);
testMPC.showInterpolation(20,20) 
%this shows figure 3 in the attached picture

Answer 1

Try something like this:

nRows = 100;
nCols = 200;

x1 = @(x) max(0, x-50);
x2 = @(x) min(nCols, nCols - 50 + x);

RR = zeros(nRows, nCols);
CC = zeros(nRows, nCols);

for iRow = 1:nRows
  c1 = x1(iRow);
  c2 = x2(iRow);
  
  colVec = linspace(c1, c2, nCols);
  
  RR(iRow, :) = iRow;
  CC(iRow, :) = colVec;
end

mesh(RR, CC, zeros(size(RR)))

You'd need to redefine the functions for x1 and x2 or course as well as the scaling, but this should give you an idea of how to get started.