Is there a way to parametrize an irregular surface (say in terms of (u,v) such that any point inside the area can be given as p(u,v)? (The boundary is defined by a series of straight line segments which form a closed area)
I have attached a very simple example of an a boundary. I have already parametrized the boundary in terms of the variable "t" where 0<t<1. I now need to do something similar for the area.
The reason I am doing this is because I am using MATLAB's optimization toolbox to optimize the connectivity of certain structures inside a particular region. So far I have just used rectangular areas which are simple to work with as all you need to do is set the upper and lower bounds for x and y. I thought if I could map an area to (u,v) I could do something similar for u and v rather than working with cartesian co-ordinates.
My apologies if this does not belong here, I thouhght this would be my best chance in the hopes that someone else has worked with irregular boundaries in computer programs before.
Code for attached figure:
x = [0 5 4 5 1 0]'; y = [0 0 1 2 2 0]';
dx = x(2:length(x))-x(1:length(x)-1);
dy = y(2:length(x))-y(1:length(x)-1);
LENS = sqrt(dx.^2+dy.^2);
TOTAL_LEN = sum(LENS);
dt = LENS/TOTAL_LEN;
t = [0;cumsum(dt)];
title 'Boundary Geometry'
title('Parameterized Boundry Position')