How to generate uniform random points in the unit square

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Reference no: EM131353321

(a) Given a random number generator that produces values uniformly in the interval [0, 1], describe how to generate uniform random points in the unit square.

(b) If you generate the point (x, y) with x

(c) Let u = 1 - x, v = 1 - y, and w = 1 - (u + v). Show that applying this transformation to the results of part (b) generates points uniformly at random in barycentric coordinates on the triangle u + v + w = 1, 0 ≤ u, v,w, ≤ 1.

(d) Show that for any triangle PQR, the points uP + vQ + wR are distributed uniformly at random in the triangle, when uvw are generated according to part (c).

Reference no: EM131353321

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