Conventional geometric algorithms found in geometric modeling systems
work with fixed precision arithmetic and numerical approximation
schemes for computing intersections of curves and surfaces. That is
why their functionality is impaired by rounding and approximation
errors in (nearly) degenerate situations which frequently occur in
In contrast, this workshop emphasizes on exactness or certified
approximations, focusing on techniques guaranteeing correctness,
which are based on certified numerics and certified topology; the
attention is devoted to both algebraic objects and approximations
for more general objects.
The workshop areas contain, but are not restricted to, the following themes:
Algorithms and data structures for shape operations
in particular arrangements of curves and surfaces, meshing and boolean operations
for curved solids, optimization with quadratic constraints,...
Algebraic methods and certified numerics
in particular, algebraic numbers and dedicated solvers for a restricted
class of polynomial systems that are encountered in geometric
predicates and constructions.