algorithm - Random points inside a parallelogram -

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i have 4 side convex polygon defined 4 points in 2d, , want able generate random points inside it.

if simplifies problem, can limit polygon parallelogram, more general answer preferred.

generating random points until 1 inside polygon wouldn't work because it's unpredictable time takes.

a. if can restrict input parallelogram, simple:

  1. take 2 random numbers between 0 , 1. we'll call u , v.

  2. if parallelogram defined points abcd such ab, bc, cd , da sides, take point being:

     p = + (u * ab) + (v * ad)

where ab vector b , ad vector d.

b. now, if cannot, can still use barycentric coordinates. barycentric coordinates correspond, quad, 4 coordinates (a,b,c,d) such a+b+c+d=1. then, point p within quad can described 4-uple such that:

p = a + b b + c c + d d

in case, can draw 4 random numbers , normalize them add 1. give point. note distribution of points not uniform in case.

c. can also, proposed elsewhere, decompose quad 2 triangles , use half-parallelogram method (i.e., parallelogram add condition u+v=1) or barycentric coordinates triangles. however, if want uniform distribution, probability of having point in 1 of triangle must equal area of triangle divided area of quad.


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