CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

On 02/03/2012 02:04 PM, Sandeep Dey wrote:
> Hi,
>
> If we consider that segment lies completely inside polygon means: that
> end point of segment is also inside polygon and not on the boundary then
> the query can be answered by writing a similar function bounded_side_2.
> Actually if the 1st end point of the segment is inside the polygon then
> shooting the ray directing towards other end point of the segment can
> answer the query,
>   In case there is any intersection before reaching the other end point,
> then for sure the segment is not inside the polygon.
> And if there is no intersection then the segment is inside the polygon.
>
> Now if we want to consider a point on the boundary of polygon to be
> inside the polygon, we need one extra check for the special case as
> shown in your figure:
> We can do the following:
> The case when both the end points are on the boundary of polygon , and
> no other intersection taken place between two end points,
> we need to do one more check, take any point in the line segment say
> mean of the two end points, then if this point lies outside polygon then
> the segment also lies outside polygon,
> else the whole segment is inside the polygon.
In that case it is not sufficient, (the midpoint can be inside the 
polygon but not the segment itself). In that case, I think you need to 
check if each polygon segments is intersected in its interior by the
query segment.

Sebastien.

> Regards,
>
> Sandeep.
>
>
>
>
>
> On Fri, Feb 3, 2012 at 11:03 AM, pgiitu 
> <
> <mailto:>>
>  wrote:
>
>     Hello Sandeep,
>
>     Thanks for the help but I would like to emphasize that point inside a
>     polygon and line segment inside a polygon are two very different
>     problems.
>     Even after counting the no. of intersections it is not possible to tell
>     whether the whole line segment is inside the polygon or not.
>
>     For Ex consider the following image in the file
>
>     http://cgal-discuss.949826.n4.nabble.com/file/n4354159/imagepdf.pdf
>     imagepdf.pdf
>
>
>     For the two red line segments the no of intersections are the same
>     in every
>     case. so The no of intersections thing will not work.
>
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