Question

I have to be able to set a random location for a waypoint for a flight sim. The maths challenge is straightforward:

“To find a single random location within a quadrangle, where there’s an equal chance of the point being at any location.”

Visually like this:

An example ABCD quadrangle is:
A:[21417.78 37105.97]
B:[38197.32 24009.74]
C:[1364.19 2455.54]
D:[1227.77 37378.81]

Thanks in advance for any help you can provide. 🙂

EDIT
Thanks all for your replies. I’ll be taking a look at this at the weekend and will award the accepted answer then. BTW I should have mentioned that the quadrangle can be CONVEX OR CONCAVE. Sry ’bout dat.

Answer 1

Split your quadrangle into two triangles and then use this excellent SO answer to quickly find a random point in one of them.

Update:

Borrowing this great link from Akusete on picking a random point in a triangle.

_{(from MathWorld – A Wolfram Web Resource: wolfram.com)}

Given a triangle with one vertex at
the origin and the others at positions v₁
and v₂, pick

_{(from MathWorld – A Wolfram Web Resource: wolfram.com)}
where A₁
and A₂ are uniform
variates in the interval [0,1] , which gives
points uniformly distributed in a
quadrilateral (left figure). The
points not in the triangle interior
can then either be discarded, or
transformed into the corresponding
point inside the triangle (right
figure).