We present an algorithm that produces high quality tetrahedral meshes conforming with input polyhedra. Our meshing algorithm is based on Ruppert's Delaunay refinement where convergence is guaranteed thanks to a novel chamfering approach that removes all acute angles from the input. On such a modified input Delaunay refinement produces a Delaunay tetrahedrization where all the faces have bounded angles. The input portions that were removed by the chamfering are re-inserted in this tetrahedrization to achieve exact conformance at the cost of a small number of bad-shaped tetrahedra near the formerly acute input angles. Numerical robustness is guaranteed along all the phases thanks to a clever use of modern indirect geometric predicates and the definition of a new type of implicit point to represent Steiner vertices on the input faces. In practice, our prototype implementation produces meshes having a quality comparable to the state-of-the-art tetgen software: while tetgen fails on 37% of the 3942 valid models in the Thingi10k dataset, our method succeeds on all of them.

We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the underlying theory of the well-known tetgen software, but use a floating-point implementation based on indirect geometric predicates to implicitly represent Steiner points: this new approach dramatically simplifies the implementation, removing the need for ad-hoc tolerances in geometric operations. Our approach leads to a robust and parameter-free implementation, with an empirically manageable number of added Steiner points. Furthermore, our algorithm addresses a major gap in tetgen's theory which may lead to algorithmic failure on valid models, even when assuming perfect precision in the calculations. Our output tetrahedrization conforms with the input geometry without approximations. We can further round our output to floating-point coordinates for downstream applications, which almost always results in valid floating-point meshes unless the input triangulation is very close to being degenerate.

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.