CGAL users discussion list

[Tapadi <>]

Hi everyone,

I am manipulating arrangements of Bezier curves, using
Arr_Bezier_curve_traits_2. 

I need an explicit representation (4 control points) of edges. However, they
are stored as X-monotone curves. Only implicit geometry is available then :
parent curve, plus approximated parameter interval.

I implemented De Casteljau's algorithm in order to "cut" the parent curve at
these parameter values and retreive an approximated, explicit representation
of the edge's geometry.

The problem is : my resulting curves don't start and finish at real
intersection points. I mean, the approximation is clearly visible. For the
following image "input 1" :

<http://cgal-discuss.949826.n4.nabble.com/file/n4657965/input1.png> 

I get this vertex and edge set :

<http://cgal-discuss.949826.n4.nabble.com/file/n4657965/output1.png> 

For this second input :

<http://cgal-discuss.949826.n4.nabble.com/file/n4657965/input2.png> 

I get this vertex and edge set :

<http://cgal-discuss.949826.n4.nabble.com/file/n4657965/output2.png> 

Not that curves' endpoints do not match vertices' approximations given by
Point_2::approximate().
I have the following questions:
- What is the precision of approximations on parameter intervals in
x-monotones Bezier subcurves ?
- Is there any other way to go from implicit x-monotone representation to
explicit Curve_2 representation (clamp to rational coordinates, etc)?
- ... Does anyone have an idea for solving this problem?

Thanks in advance!
Hugo Loi
PhD student at Inria - Maverick Team



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