CGAL users discussion list

[Louis Lavery <>]

Marko Kukovec wrote:
> Hello!
>
> About a week ago I put a question on this mailing list about
> offsetting/insetting 2D polygons in CGAL. I have a problem as I have a
> polygons with arcs and lines so I can't directly feed the
> offsetting/insetting algorithm. I got an answer from Fernando Cacciola
> and he suggested I should polygonize all arcs prior to feeding the
> offsetting algorithm. He even pointed out this algorithm
> http://www.worldserver.com/turk/computergraphics/CircularArcSubdivision.pdf .

If you have an arc not more than 90 degrees, of radius r,
centred on the origin with start point s and end point e
then the point m = (s+e)/2 is mid way between s and e
and its distance from the arc is r-length(m).

So it should be possible to adapt this...

OutIter varc(Vector const s,Vector const e,double const r,
double const delta,OutIter res)
{
    Vector m = (s+e)/2;

    double const l = length(m);

    if (r-l > delta)
    {
        m *= r/l;

        res = varc(s,m,r,delta,res);

        *res = m;
        ++res;

        res = varc(m,e,r,delta,res);
    }

    return res;
}

...to vector a general arc.

HTH, Louis.