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What I have is a surface G(u,v) with parametric values u=[0,1] and v=[0,1]. Also, I have some discrete points on that surface which can be connected to form curves.

Is there an appropriate way to segment the surface G(u,v) given these discrete points on the surface?

Let's say I am given a surface G(u,v) and discrete points p0...pn on it that, if connected, form one single curve that divide the surface G(u,v) into two sections: A and B.

Now, I am given one point p(u,v) on the surface G(u,v). How can I know if the point p(u,v) lies on section A or B? Note that I am only given discrete points that create a section, and the region outside u=[0,1] and v=[0,1] should also be considered.

Thanks