Hi,
I have been other thinking this and think I am missing a very simple solution.
The problem: I have a 3D space in which x-y [0 3000] and z[0 600]. I want to generate random "lines" specified by points. For this, I generate seed points, within the xyz plane between the given limits. I also generate Phi [0 pi] and Theta[0 2*pi] such that I have a random initial start and random angular information. Using this information alone, is it possible to generate a set of points within the xyz space limits based upon random Theta and Phi?
I've attached some prelim code that may help.
SizeSimulated_xy= 3000;
SizeSimulated_z=600;
Boundries_xy=[0 SizeSimulated_xy];
Boundries_z=[0 SizeSimulated_z];
xmin=Boundries_xy(1);
xmax=Boundries_xy(2);
xmin_z=Boundries_z(1);
xmax_z=Boundries_z(2);
Phi=rand(1,1)*pi;
Theta=rand(1,1)*2*pi;
xyRand = xmin+rand(1,2)*(xmax-xmin);
zRand=xmin_z+(xmax_z-xmin_z)*rand(1,1);
r=sqrt(xyRand(1,1).^2+xyRand(1,2).^2+zRand.^2);
x_dir=r*cos(Phi)*sin(Theta);
y_dir=r*cos(Phi)*cos(Theta);
z_dir=r*sin(Phi);
direction=[x_dir;y_dir;z_dir];
a=direction(1,1);
b=direction(2,1);
c=direction(3,1);
x0=xyRand(1,1);
y0=xyRand(1,2);
z0=zRand;
Although here is my problem:
z=z0+(c/a)*(x-x0);
x=z0+(a/c)*(z-z0);
y=y0+(b/c)*(z-z0);
Thanks!
