Shifting points in fortran

Question

Hello I am trying to shift points which have been previously generated in the square area. I am having a trouble with some additional conditions how they should have been shifted.

xt=x(j)+2*rand()*shift - shift
yt=y(j)+2*rand()*shift - shift

Also I have more conditions to apply:

a) xt<0
b)xt>a
c)yt<0
d)yt>a
d) the distance (x(i)-xt)**2+(y(i)-yt)**2 <1 for i=1,2,...n; i/=j

where x(i) is a randomly generated number and shift is a parameter in the interval [0.1,1].x(j) is the randomly generated number again from the x(i) array. y(j) and y(i) is the same as x

I would like to know if the conditions are not being executed should I go back to the generating xt and yt positions or what would be other way to carry out with this problem?

Answer 1

In order to apply the last condition, I suggest you displace the points like so:

REAL, PARAMETER :: PI = 3.1415927
...
rt=shift*sqrt(rand())
tt=2.d0*PI*rand()
xt=x(j)+rt*cos(tt)
yt=y(j)+rt*sin(tt)

see here.

The easiest and quickest solution to constrain the new points to the interval $[0,a]^2$ is to impose some form of boundary condition. For example, periodic boundary conditions:

if(xt<0) xt=xt+a
else if(xt>a) xt=xt-a
same for yt...

Or you could reflect the points back across the boundary:

if(xt<0) xt=-xt
else if(xt>a) xt=2*a-xt
same for yt...