**Single-strip triangulation of manifolds with arbitrary topology.**

D. Eppstein and M. Gopi.

13th Video Review of Computational Geometry, 2004.

*20th ACM Symp. Comp. Geom.,*Brooklyn, 2004, pp. 455–456 (abstract for video).

*25th Conf. Eur. Assoc. for Computer Graphics (EuroGraphics '04)*, Grenoble, 2004 (2nd best paper award).

*Eurographics Forum*23 (3): 371–379, 2004.

arXiv:cs.CG/0405036.We describe a new algorithm, based on graph matching, for subdividing a triangle mesh (without boundary) so that it has a Hamiltonian cycle of triangles, and prove that this subdivision process increases the total number of triangles in the mesh by at most a factor of 3/2. We also prove lower bounds on the increase needed for meshes with and without boundary.

(Graphics lab pubs page – Citations)

**Single triangle strip and loop on manifolds with boundaries.**

A. Bushan, P. Diaz-Gutierrez, D. Eppstein, and M. Gopi.

Tech. Rep. 05-11, UC Irvine, School of Information and Computer Science, 2005.

Proc. 19th Brazilian Symp. Computer Graphics and Image Processing (SIBGRAPI 2006), pp. 221–228.This follows on to our previous paper on using graph matching to cover a triangulated polyhedral model with a single triangle strip by extending the algorithms to models with boundaries. We provide two methods: one is based on using an algorithm for the Chinese Postman problem to find a small set of triangles to split in order to find a perfect matching in the dual mesh, while the other augments the model with virtual triangles to remove the boundaries and merges the strips formed by our previous algorithm on this augmented model. We implement the algorithms and report some preliminary experimental results.

**Curvature-aware fundamental cycles**.

P. Diaz-Gutierrez, D. Eppstein, and M. Gopi.

17th Pacific Conf. Computer Graphics and Applications, Jeju, Korea, 2009.

*Computer Graphics Forum*28 (7): 2015–2024, 2009.Considers heuristic modifications to the tree-cotree decomposition of my earlier paper Dynamic generators of topologically embedded graphs, to make the set of fundamental cycles found as part of the decomposition follow the contours of a given geometric model.

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

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