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## Visualizing the Connection Among Convex Hull, Voronoi Diagram and Delaunay Triangulation

Citations: | 2 - 0 self |

### Citations

2031 |
Computational Geometry: An Introduction.
- Preparata, Shamos
- 1985
(Show Context)
Citation Context ...aduates, and there is no visualization tool available. Furthermore, textbooks that address these problems are written for beginning graduate courses (de Berg et al., 2000; O’Rourke and Goodman, 1997; =-=Preparata and Shamos, 1985-=-). To be able to understand the connection between these concepts as presented in a computational geometry textbook, students must already have a strong background in geometry. Hull2VD is a visualizat... |

1208 | Computational Geometry: Algorithms and Applications. - Berg, Kreveld, et al. - 1997 |

701 | The quick algorithm for convex hulls.
- Barber, David, et al.
- 1996
(Show Context)
Citation Context ...ta and Shamos, 1985). It is a fundamental concept in computational geometry, and many solutions have been proposed, such as Graham’s Scan (Graham, 1972), Jarvis’s March (Jarvis, 1973), and QuickHull (=-=Barber et al., 1996-=-).sFigure 1: The convex hull of a planar set of points The convex hull has been used in a multitude of scientific fields (especially computer graphics) for applications such as pattern matching (Soill... |

425 |
A sweepline algorithm for Voronoi diagrams,
- Fortune
- 1987
(Show Context)
Citation Context ...ata and Shamos, 1985). Many approaches have been proposed to compute the Voronoi diagram in optimal time such as randomized incremental, divide and conquer (Preparata and Shamos, 1985) and sweepline (=-=Fortune, 1987-=-). a b (b)s2.3 Delaunay Triangulation Triangulations of a planar point set are extremely important in computer graphics. Triangulation is essential in polygon-based rendering (used by APIs such as Ope... |

166 |
Shor Applications of random sampling
- Clarkson, W
(Show Context)
Citation Context ...(O’Rourke and Goodman, 1997) and randomized incremental (Seidel, 1991). The randomized incremental approach is of special note because the same method has been applied to calculating the convex hull (=-=Clarkson, 1987-=-). Not surprisingly, the algorithm’s runtime is bounded by O(n log n). This is in agreement with the runtime of the randomized incremental algorithms used in computing the convex hull and Voronoi diag... |

125 |
Automating spectral unmixing of AVIRIS data using convex geometry concepts
- Boardman
- 1994
(Show Context)
Citation Context ...titude of scientific fields (especially computer graphics) for applications such as pattern matching (Soille, 2000), finding bounding volumes (de Berg et al., 2000) and analysis of spectrometry data (=-=Boardman, 1993-=-). Many problems can be reduced to the convex hull problem, such as halfspace intersections, power diagrams, Voronoi diagram and Delaunay triangulation (de Berg et al., 2000). Students often learn one... |

112 | A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons,
- Seidel
- 1991
(Show Context)
Citation Context ...ding to each face in the triangulation. Many algorithms for computing the Delaunay triangulation exist, such as plane sweep, divideand-conquer (O’Rourke and Goodman, 1997) and randomized incremental (=-=Seidel, 1991-=-). The randomized incremental approach is of special note because the same method has been applied to calculating the convex hull (Clarkson, 1987). Not surprisingly, the algorithm’s runtime is bounded... |

102 |
On the identification of the convex hull of a finite set of points in the plane,”
- Jarvis
- 1973
(Show Context)
Citation Context ...s the points (Fig. 1) (Preparata and Shamos, 1985). It is a fundamental concept in computational geometry, and many solutions have been proposed, such as Graham’s Scan (Graham, 1972), Jarvis’s March (=-=Jarvis, 1973-=-), and QuickHull (Barber et al., 1996).sFigure 1: The convex hull of a planar set of points The convex hull has been used in a multitude of scientific fields (especially computer graphics) for applica... |

51 |
Measures of symmetry for convex sets
- Grünbaum
- 1961
(Show Context)
Citation Context ...mputational approaches that have been proposed (i.e., gift wrapping, divide and conquer, incremental). Hull2VD uses QuickHull, which is an incremental algorithm based on the Beneath-Beyond algorithm (=-=Grünbaum, 1993-=-). The QuickHull algorithm can be generalized and applied to any dimensionality; however in Hull2VD we are only concerned with finding the convex hull in three dimensions. Before any incremental conve... |

26 | Neural network design using voronoi diagrams,” - Bose, Garga - 1993 |

2 |
A program for convex hulls. Retrieved from http://www.netlib.org/voronoi/hull.html
- Clarkson
- 2009
(Show Context)
Citation Context ... available on Microsoft Windows, Sun Solaris, Mac OS X and Linux operating systems as part of the DesignMentor v2.0 package. The application was written using Ken Clarkson’s QuickHull implementation (=-=Clarkson, 1996-=-). Hull2VD displays the Voronoi diagram and Delaunay triangulation of planar point sets as well as the convex hull of a projected point set in space. All displays are updated in real time as the user ... |

2 |
An efficient algorithm for detemining the convex hull of a finite planar set
- Graham
- 1972
(Show Context)
Citation Context ...mallest convex set that contains the points (Fig. 1) (Preparata and Shamos, 1985). It is a fundamental concept in computational geometry, and many solutions have been proposed, such as Graham’s Scan (=-=Graham, 1972-=-), Jarvis’s March (Jarvis, 1973), and QuickHull (Barber et al., 1996).sFigure 1: The convex hull of a planar set of points The convex hull has been used in a multitude of scientific fields (especially... |

2 |
Voronoi diagrams to model forest dynamics
- Mercier, Baujard
- 1997
(Show Context)
Citation Context ...ound in part III of Descarte’s Principia Philosophiae, published in 1644 (de Berg et al., 2000). Voronoi diagrams have been used in a wide array of scientific fields such as modeling forest dynamics (=-=Mercier and Baujard, 1997-=-), animating lava flows (Stora et al., 1999) and neural network design (Bose and K.Garga, 1993). Because the Voronoi diagram can be applied to so many fields outside of geometric computing and compute... |

2 | From binary to grey scale convex hulls
- Soille
- 2000
(Show Context)
Citation Context ... 1996).sFigure 1: The convex hull of a planar set of points The convex hull has been used in a multitude of scientific fields (especially computer graphics) for applications such as pattern matching (=-=Soille, 2000-=-), finding bounding volumes (de Berg et al., 2000) and analysis of spectrometry data (Boardman, 1993). Many problems can be reduced to the convex hull problem, such as halfspace intersections, power d... |