CGAL users discussion list

["Bart Janssens" <>]

On 8/27/07, Peter Hachenberger 
<>
 wrote:
> you found the main problem---the facets must be coplanar. I guess it's
> not an option for you to first convert the coordinates to exact
> coordinates and then do the rotation? That's easier than doing the
> triangulation.

The rotation is just an example, in fact. Multiplying the
transformation could be done in exact math, but the source mesh itself
could contain non-planar polygons, like i.e. a sphere primitive
represented by quads. In theory, these quads should be coplanar, but
here the rounding errors occur during the primitive construction
itself.

> BTW, why are you using the Extended_homogeneous kernel? This kernel is
> very slow. Do you need to represent halfspaces? Otherwise, you should
> use another kernel.

Just part of some experimenting, to see if it changed anything. I had
tried with a Cartesian kernel first, but then switched to Homogeneous
because of the conversion to exact points that use an integer number
type.

I am currently trying a new approach. I am implementing a number type
based on double, but with comparison operators that use certain
threshold "epsilon". The equality test then returns true if the
difference between both numbers is smaller than epsilon. I am hoping
that this will trick the operations in the Nef construction and
boolean calculation into seeing approximatly coplanar points as
coplanar. I know the result won't be exact, but this is not required
in our application, where all we aim for is visually pleasing results
:)

regards,

-- 
Bart