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Future Work

The directions of future work are mainly focused on the implementation aspects. This is first of all robustness and computational efficiency, including handling of round-off errors related to various frequently used computational evaluations, as empty-circumsphere property, point visibility, etc. One possible solution may be the use of robust predicates [42] based on precise floating point arithmetic. The next issue worth dealing with is the removal of slivers, especially near the boundary composed of constraining faces, where the freedom to perform topological and geometrical transformations is rather limited. This can be solved for example by creating a new tetrahedron, newly created faces of which (added to the set of constraining faces) will prevent the sliver to be created. A more preferred solution is to form such a tetrahedron that allows to remove the sliver from the final mesh by a simple topological transformation. The appearance of this tetrahedron in the final constrained Delaunay triangulation may be enforced with the help of a protective sphere (circumscribed to that tetrahedron) which will not allow any inserted point to fall into it. Another aspect is related to the procedure of inserting internal points. It may be beneficial to replace it by another one based on the advancing front approach [27]. This may further improve the mesh quality near the boundary. And finally, it is desirable to extend the proposed algorithm to handle also constraining faces defining internal boundary of a computational domain and constraining edges inside the domain.



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Daniel Rypl
2005-11-06