# Generate an equation of a 3D line from one point and two angles

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Matlab User on 21 Sep 2017
Answered: KSSV on 21 Sep 2017
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!

KSSV on 21 Sep 2017
P0 = [0 3000] ;
Z0 = 0 ; Z1 = 600 ;
P0 = [P0 Z0] ;
%%Top plane
x = linspace(-100,100,10) ;
y = linspace(-3000,3000,10) ;
[X,Y] = meshgrid(x,y) ;
Z = Z1*ones(size(X)) ;
figure
hold on
plot3(P0(1),P0(2),P0(3),'*r')
plot3(X,Y,Z,'.r')
for i = 1:size(X,1)
for j = 1:size(X,2)
plot3([P0(1) X(i,j)],[P0(2) Y(i,j)],[P0(3) Z(i,j)],'b')
drawnow
end
end
view(3)