How can I efficiently mesh 2D lines in MATLAB

I have created a 2D mesher (for lack of a better word?). Its useage is as follows:

xmin = -pi/2;
xmax = +pi/2;
numx = 8; % desired number of points for output distribution
funx = @(x) sin(x); % example function to mesh

xq = varspace(funx,xmin,xmax,numx); % optimally sampled domain

xq =

     -1.5708   -1.2809   -0.9157   -0.5130    0.5028    0.9363    1.2368    1.5708

plot(xq,funx(xq,'rs-')) % plot of sin(x) with variable spacing

I like this example because it illustrates how sin(x) is very linear at x=0 so there is no need to sample this region as much as near the endpoints in the domain.

For the time being, I've accomplished this method of variably sampling x by generating a relative spacing array and tweaking with :

dx = fminsearch(@(m) err(m),ones(1,numx)); diff(xq) == dx

so as to minimize the error between the original @funx and an interpolated interp1(xq,funx(xq),...).

In 2D, this procedure doesn't take forever but I'm wondering if there are resources to accomplishing this task in a more deterministic way. Computing f''(x) and sampling based on this proportion seems like a reasonable solution but I'm betting this question has been answered before, I just can't find the correct phrase to describe it.

[Alexander Laut]

I have attached my contribution to the FileExchange to better illustrate my strategy.

[RobF]

Hello Alexander,

could you please be a little more specific on what you want to achieve? Additionally, I cannot find the command "varspace" in the documentation - is this a special function?

[Jan]

@RobF: "varspace" must be downloaded from the FileExchange: https://www.mathworks.com/matlabcentral/fileexchange/65808-varspace-funx-xmin-xmax-numx-varargin-