generate random point from within three points

if i have three points P1=(x1,y1),P2=(x2,y2),P3=(x3,y3). how can i generate a random point within them .

Thanks,

[Azzi Abdelmalek]

Do you mean inside a triangle?

[Hassan]

yes

Answer 1

[Image Analyst]

One way is to generate random coordinates within the x and y range - this would give a point in a rectangle. Then call inpolygon() to see if that point is inside the triangle. If it is, you're done. Otherwise, try another random point until you get one that is in side the polygon.

[Hassan]

i think this not a practical solution

[Image Analyst]

And why not? What's wrong with it? It's simple and fast. Anything else, such as using affine transforms, will be far more complicated. I believe even Roger Stafford was okay with the try-and-exclude method for getting random points in a circle, though he did come up with a better analytical method, but a circle is simpler than some arbitrary triangle.