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Hello Sebastien,

thanks for the reply! My original misconception was that
Plane_3(1,0,0,1) constrcuct an YZ-plane with distance 1 in x-direction
from the origin. In fact it is -1:

  Plane_3(1, 0, 0, 1).has_on(Point_3(1, 0, 0))) # delivers False
  Plane_3(1, 0, 0, 1).has_on(Point_3(-1, 0, 0))) # delivers True

The documentation
(https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Plane__3.html )
states that the coefficients of Plane_3(a,b,c,d) correspond to the
coefficients of the equation ax + bx + cx + d = 0, if filled with these
coefficients above it would result in x = -1.

So everyting is fine, and makes sense.

Am Dienstag, dem 01.02.2022 um 14:10 +0100 schrieb Sebastien Loriot:
> Welcome on the mailing list!
> 
> As documented here:
> https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Plane__3.html#ad8f355a87bd5ca0fec2d423dbf5909d7
> 
> `returns a point q, such that to_2d( to_3d( p )) is equal to p.`
> 
> Since (-1,0,0) and (1,0,0) are both converted by to_2d() to (0,0),
> there is no way to guarantee that to_3d(to_2d(p3)) == p3 (it is
> not a bijection).
> 
> Best regards,
> 
> 
> Sebastien.
> 
> 
> 
> 
> On 1/31/22 5:46 PM,  wrote:
> > Hello!
> > 
> > First time writing on the mailing list, so I hope it is the right
> > place
> > to discuss, since I'm not super convinced, whether my finding is a
> > bug
> > or not. I transform a 3d point into 2D using a plane and transform
> > it
> > back. I would have expected approximately the same point.
> > 
> > I'm using CGAL with Python SWIG bindings in the newest version
> > (commit
> > 2479e35) on Arch Linux. I took a look at the bindings code and
> > could
> > not find much code, that could do something wrong. Therefore I
> > suspect
> > the error being somewhere in the C++ part.
> > 
> > Here is my example:
> > ```python
> > from CGAL.CGAL_Kernel import Plane_3, Point_3
> > 
> > # plane with distance 1 in x-direction
> > plane_3d_x = Plane_3(1, 0, 0, 1)
> > 
> > # this point obviously lies on the plane
> > point_3d_unit_x = Point_3(1, 0, 0)
> > 
> > # results into a (0,0)
> > point_2d = plane_3d_x.to_2d(point_3d_unit_x)
> > 
> > print(str(point_2d))
> > 
> > assert point_2d.x() == 0
> > assert point_2d.y() == 0
> > 
> > # i would have expected the same point (except for minor numerical
> > errors)
> > point_3d_retransformed = plane_3d_x.to_3d(point_2d)
> > 
> > print(str(point_3d_retransformed))
> > 
> > # this assertion fails, since x == -1
> > assert point_3d_retransformed.x() == 1
> > assert point_3d_retransformed.y() == 0
> > assert point_3d_retransformed.z() == 0```
> > 
> > Can anyone tell, if this is a bug or explain to me, why this is
> > correct?
> > 
> > Thanks in advance!
> > 
>