Re: CCL:Inside or outside of a polyhedron

[Harry Johnson <Harry_Johnson at.at avanticorp.com>]

 >>>>> "Rui" == Rui Luo <rui at.at
 iris6.carb.nist.gov> writes:
     Rui> Second look at the sign of the transformed coordinates of all
     Rui> vertices.  If all xi's, where i=1,...,N, have the same sign,
     Rui> the point is outside of the polyhedron. The statement holds
     Rui> for all yi's or all zi's. So if any one of the three
     Rui> conditions holds, the point will be outside. Otherwise if
     Rui> none of the conditions hold, it's inside.
 Your last statement is incorrect.  Consider the 2D case:
     ----
    /   /
  +/   /
  /   /
 /   /
 ---
 If the point '+' is the origin, then all of the Xi's do not have the
 same sign, nor do all of the Yi's, so none of the above conditions
 hold, yet the point is still outside the polygon.  Your method is
 another implementation of a bounding box.  Usually, however, it is
 done by simply finding the maximum and minimum value of each
 coordinate, x, y, and z, and checking to see whether the point's
 coordinates lie within the extrema of the polyhedrons coordinates.  If
 most of the points of interest likely lie outside the polyhedron this
 is a quick initial screening method.
 -Harry
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