Re: CCL:Inside or outside of a polyhedron

 On Tue, 16 Apr 1996, Brian W. Beck wrote:
 > Alexander Golbraikh wrote:
 > :
 > :
 > :
 > : Take any ray beginning at the given point. Count the number of
 > : points of intersection of this ray with polyhedron surface. If it is
 > : even, then the point is outside the polyhedron, if it is odd, then
 inside.
 > : One precaution: the ray may slide on some edges of the polyhedron.
 > :
 > : Best regards,
 > : Alexander Golbraikh
 > :
 > :
 >        ^ /
 >        |/
 >        <     As you say, the ray may slide. The "o" point at
 the left is
 >        |\    outside the "polyhedron" yet passes through the
 polyhedron
 >        | \   surface only once if you send the ray only through the
 vertices
 >        o  \  defined by... say the Calphas of a protein.
 >
 > 	-Brian
 > --
 Thank you for your remark. I mean the point must be taken into
 account in case the ray crosses the surface of the polyhedron, i.e. when
 any whatever small segment of the ray containing this point
 contains also points both in the inside and in the outside of the
 polyhedron. Both cases could be easily discriminated. You may also ask
 what to do if the given point belongs to the polyhedron surface. In this
 case all depends on which polyhedron we consider: the closed or the open
 one. (If we consider that the border (the surface) of the polyhedron
 belongs to the polyhedron, it is closed). If it is closed, the point
 belongs to the polyhedron (but isn't its inner point), if it is open, the
 point doesn't belong to the polyhedron.
 Alexander
 +----------------------------------------------------------------------+
 +  Dr. Alexander Golbraikh                   Email: golb' at \`osi.lanet.lv  +
 +  Group of Molecular Biophysics                                       +
 +  Latvian Institute of Organic Synthesis    FAX:   + (371) 7-821-038  +
 +  21 Aizkraukles st.                                                  +
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 +  LATVIA                                                              +
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