Take the 2-minute tour ×  For a triangle $ABC$ in 3D (each point
has x, y, z coordinates) is it possible to generate uniform
random points on the triangle from only the following data:
Normal of the triangle plane $N = \vec{\text{AB}}\times
\vec{\text{AC}}$  Normal of the $AC$ edge plane $U =
\cfrac{\vec{AC} \times N}{| \text{N} |^2} $ and $d_u = -U.A$
Normal of the $AB$ edge plane $V = \cfrac{ N \times \vec{AB} }{|
\text{N} |^2} $ and $d_v = -V.A$  The two edge normals U and V
are calculated such that $\vec{U}.B + d_u = 1$ and $\vec{V}.C +
d_v = 1$ (As of yet I don't have the reputation to post an image
so of the arrangement but will as soon as I can).  If this
cannot be done with the available data what is the minimum
amount of extra data required to generate the uniform random
points (e.g. A, B, C)?  I am aware that the you can generate
uniform random points on a triangle using the vertex $A$ and
edges $\vec{AB} = B - A$ and $\vec{BC} = C-B$ as follows:  $S =
A +\sqrt{R_1}\vec{AB} + \sqrt{R_1}R_2\vec{BC}