How to Segment a Parametric Surface with Discrete Points?

[hiroman]

Hi! I am trying to segment a parametric surface into different sections.

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

 

[pat_connell]

for your help! One way to approach this problem is by using a technique called ray tracing. With ray tracing, you can trace a ray from the point p(u,v) to an infinite line outside the surface G(u,v). Then, you can count the number of times the ray intersects with the curves that divide the surface, and determine which section the point p(u,v) belongs to.