random numbers inside a rectangle at an angle

How to I generate random numbers inside a rectangle at an angle?

[Azzi Abdelmalek]

What angle?

Answer 1

[Roger Stafford]

Let (x0,y0) be coordinates of one of the rectangle's corners, and let one of its sides stretching from this corner to another corner be of length a and making an angle of theta radians with respect to the x-axis. Let another side be of length b stretching from (x0,y0) at a counterclockwise right angle to the first side. Finally suppose you want n random points within that rectangle. Then do this:

 X = a*rand(n,1);
 Y = b*rand(n,1);
 x = x0 + X*cos(theta) - Y*sin(theta);
 y = y0 + X*sin(theta) + Y*cos(theta);
 plot(x,y,'y.')
 axis equal   % <-- Keep the x and y axes scale factors equal