**Dihedral bounds for mesh generation in high dimensions**.

M. Bern, L.P. Chew, D. Eppstein, and J. Ruppert.

*892nd Meeting Amer. Math. Soc.,*Brooklyn, 1994.

Abstract in*Abs. Amer. Math. Soc.*15, 1994, p. 366.

*6th ACM-SIAM Symp. Discrete Algorithms,*San Francisco, 1995, pp. 189–196.Any

*d*-dimensional point set can be triangulated with O(*n*^{ceil(d/2)}) simplices, none of which has an obtuse dihedral angle. No bound depending only on*n*is possible if we require the maximum dihedral angle to measure at most 90-epsilon degrees or the minimum dihedral to measure at least epsilon. Includes a classification of simplices in terms of their bad angles.(BibTeX – SODA paper – Citations – CiteSeer)

**Emerging challenges in computational topology**.

M. Bern, D. Eppstein, et al.

arXiv:cs.CG/9909001.

This is the report from the ACM Workshop on Computational Topology run by Marshall and myself in Miami Beach, June 1999. It details goals, current research, and recommendations in this emerging area of collaboration between computer science and mathematics.

(BibTeX – Citations – CiteSeer)

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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