## random numbers inside a rectangle at an angle

### VASISTAKRISHNA (view profile)

on 21 Mar 2014
Latest activity Answered by Roger Stafford

### Roger Stafford (view profile)

on 21 Mar 2014
Accepted Answer by Roger Stafford

### Roger Stafford (view profile)

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

Azzi Abdelmalek

on 21 Mar 2014

What angle?

### Roger Stafford (view profile)

Answer by Roger Stafford

### Roger Stafford (view profile)

on 21 Mar 2014

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```