Geodesic
Dirichlet cells in the shortest-path metric
Matematičeskoe modelirovanie, Tome 15 (2003) no. 5, pp. 71-79

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We present a new approach to the problems of construction of constrained Delaunay triangulations and Dirichlet cells for arbitrary constraint configurations. A metric equal to the length of the shortest boundary-conforming path between two points is introduced. Dirichlet cells in the new metric resemble classical cells, while taking into account point visibility through the constraints. We prove statements that precisely describe the form of these cells. 
@article{MM_2003_15_5_a8,
     author = {K. L. Bogomolov and V. F. Tishkin},
     title = {Dirichlet cells in the shortest-path metric},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {71--79},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_5_a8/}
}
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K. L. Bogomolov; V. F. Tishkin. Dirichlet cells in the shortest-path metric. Matematičeskoe modelirovanie, Tome 15 (2003) no. 5, pp. 71-79. http://geodesic.mathdoc.fr/item/MM_2003_15_5_a8/