CGAL users discussion list

[Camille Wormser <>]

 wrote:
> Though I am a bit puzzled why shifting the vertices should change the 
> triangulation, as I shifted them by an integer...
>   

By the way, this is a good example of the differences between the two 
kinds of kernels:

- the exact_predicates_inexact_constructions_kernel guarantees that the 
algorithm -- does not crash and -- computes exactly the Delaunay 
triangulation of the input points. However, if you translate your 
dataset, the algorithm computes a different triangulation. The reason is 
not any bug or imprecision in the algorithm, but simply the fact that 
the double precision number type is not able to represent the exact 
translation of the data. Your data are slightly different, and the 
_exact_ Delaunay triangulation is _different_.

- the exact_predicates_exact_constructions_kernel gives you the same 
guarantees in terms of correctness of the output, and also allows to 
obtain consistent results upon construction of new data. The reason is 
that it uses an exact number type, i.e. a number type which guarantees 
the consistency of mathematical operations, so that, for example, a = [b 
+ c]/2  <=> a+x = [(b+x) + (c+x)]/2 for any x. And aligned points are 
still aligned after any affine transformation, which is not the case 
with double precision floating point numbers, even with the simplest 
transformations.

Hope this gives a clearer view of the properties of each kernel...
--
Camille