  We introduce a new technique to create a mesh of convex polyhedra
representing the interior volume of a triangulated input surface. Our approach
is particularly tolerant to defects in the input, which is allowed to
self-intersect, to be non-manifold, disconnected, and to contain surface holes
and gaps. We guarantee that the input surface is exactly represented as the
union of polygonal facets of the output volume mesh. Thanks to our algorithm,
traditionally difficult solid modeling operations such as mesh booleans and
Minkowski sums become surprisingly robust and easy to implement, even if the
input has defects. Our technique leverages on the recent concept of indirect
geometric predicate to provide an unprecedented combination of guaranteed
robustness and speed, thus enabling the practical implementation of robust
though flexible solid modeling systems. We have extensively tested our method
on all the 10000 models of the Thingi10k dataset, and concluded that no
existing method provides comparable robustness, precision and performances.
