Geodesic
The Lifting Projection of Convex Polyhedra for Finding Delaunay Triangulations
Journal of convex analysis, Tome 29 (2022) no. 1, pp. 143-156
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D. Walkup and R. J-B Wets's lifting projection of convex polyhedra in 1969 is used for finding the Delaunay triangulation of a finite planar point set. In concrete, the finite planar point set is lifted on the surface of a paraboloid in R3 with center outside the convex hull of the set. To find quickly the lower convex hull of these points on the paraboloid a restricted region is proposed, thereby eliminating a large number of points to be calculated. The numerical experiments also show that our new version algorithm significantly reduces the running time.
Classification : 52A15, 52B55, 52A30, 52B10, 68U05
Mots-clés : Computing science, convex hull, Delaunay triangulation, extreme edge, gift-wrapping algorithm, lifting projection, lower convex hull, pattern recognition, restricted region, Voronoi diagram 
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     author = {P. T. An and N. D. Hoang and N. K. Linh},
     title = {The {Lifting} {Projection} of {Convex} {Polyhedra} for {Finding} {Delaunay} {Triangulations}},
     journal = {Journal of convex analysis},
     pages = {143--156},
     year = {2022},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a7/}
}
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P. T. An; N. D. Hoang; N. K. Linh. The Lifting Projection of Convex Polyhedra for Finding Delaunay Triangulations. Journal of convex analysis, Tome 29 (2022) no. 1, pp. 143-156. http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a7/