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Paramtrize irregular area in MATLAB.

Hi,

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.

Regards Elbarto

Code for attached figure:

Code:

`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)];

subplot(2,1,1)

plot(x,y)

xlabel x

ylabel y

title 'Boundary Geometry'

subplot(2,1,2)

plot(t,x,'-',t,y,'-')

xlabel t

legend('x','y')

title('Parameterized Boundry Position')