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[daisy <>]

Hi, 
    In my oppinion, you can have a try with the deviation. 
    Let *n* be a unit normal vector from the origin to the plane PI, and M
be a point in 3D space. Make a line segment MQ from the M to the plane PI,
and let MQ be perpendicular to PI at point Q. Then the projection from the
vector QM to the normal vector n is called deviation between M and PI.
http://cgal-discuss.949826.n4.nabble.com/file/n4548847/4.bmp 
Obviously, we can judge the M's position, on one side of the PI, or the
other. Especially, if we use the normalized plane equation, we can compute
the deviation easier.
   I am not sure if I can help you. Good luck.

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