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[Arun Ramasamy <>]

Thanks Sebastien. I think there may be some inaccuracies w.r.to the the points being exactly on the plane. I'll try the 2d-projection method for now.
thanks arun

---

From: Sebastien Loriot (GeometryFactory) <>
To:
Sent: Thu, January 6, 2011 11:37:50 AM
Subject: Re: [cgal-discuss] 3D-Point inside a 3D Polyhedron facet query

Arun Ramasamy wrote:
> HI,
> I've to determine if a given 3D point is inside a 3D facet of a polyhedron. The facet is guaranteed to be a convex polygon and point is guaranteed to be in the same plane as the facet. Currently I'm planning to either
> 1. rotate everything to the X-Y plane and do a 2D evaluation using sign of angles and such or
> 2. Remove the least varying component from the facet and point coordinates (say Z) and do a 2D evaluation.
>
> Is there any better way to do this, where I don't have to reduce this to a 2D operation. Is that query supported in CGAL ?
>
> Please let me know if anything is not clear.
> thanks arun
>
>
You can use function coplanar_orientation with consecutive segments of
the facet:

http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_23_ref/Function_coplanar_orientation.html#Index_anchor_428

Note that the point has to be in the plane (not almost in the plane).
If your point is not exactly in the plane, using a projection along x,y
or z axis should be a better solution (check the normal vector of the
plane to choose which one).

FYI, in the next release, they will probably be something called
Projection_traits that allows to use to 2D algorithms on 3D points
by considering them as 2D points projected onto a plane (xy, yx or
zx). With this traits used together with Polygon_2::bounded_side
(http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Polygon_ref/Class_Polygon_2.html)
you could also have the answer.

S.

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