How can I distribute random points in some lines?

The follow code is a poisson line process code.

https://github.com/hpaulkeeler/posts/blob/master/PoissonLine/PoissonLine.m

I want to distibute the random points in the lines.

The point process is not specified. The point process is a unifrom random or a poisson point process.

Answer 1

[KSSV]

%% Striaght line 
L = rand(2,2) ; 
P1 = L(1,:) ; 
P2 = L(2,:) ; 
% Get slope and y intercept 
P = polyfit(L(:,1),L(:,2),1) ; 
m = P(1) ; 
c = P(2) ; 
% Get random points 
a = min(L(:,1)) ; b = max(L(:,1)) ; 
N = 20 ; 
x = (b-a)*rand(N,1)+a ;
y = m*x+c ; 

figure
hold on
plot(L(:,1),L(:,2),'r')
hold on
plot(x,y,'*k')