## Hierarchical and Geometrical Methods in Scientific VisualizationGerald Farin, Bernd Hamann, Hans Hagen The nature of the physical Universe has been increasingly better understood in recent years, and cosmological concepts have undergone a rapid evolution (see, e.g., [11], [2],or [5]). Although there are alternate theories, it is generally believed that the large-scale relationships and homogeneities that we see can only be explainedby having the universe expand suddenlyin a very early “in?ationary” period. Subsequent evolution of the Universe is described by the Hubble expansion, the observation that the galaxies are ?ying away from each other. We can attribute di?erent rates of this expansion to domination of di?erent cosmological processes, beginning with radiation, evolving to matter domination, and, relatively recently, to vacuum domination (the Cosmological Constant term)[4]. We assume throughout that we will be relying as much as possible on observational data, with simulations used only for limited purposes, e.g., the appearance of the Milky Wayfrom nearbyintergalactic viewpoints. The visualization of large-scale astronomical data sets using?xed, non-interactive animations has a long history. Several books and ?lms exist, ranging from “Cosmic View: The Universe in Forty Jumps” [3] by Kees Boeke to “Powers of 10” [6,13] by Charles and Ray Eames, and the recent Imax ?lm “Cosmic Voyage” [15]. We have added our own contribution [9], “Cosmic Clock,” which is an animation based entirely on the concepts and implementation described in this paper. |

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### Contents

1 | |

Extraction of Crackfree Isosurfaces | 19 |

Efficient Error Calculation for Multiresolution TexturebasedT | 51 |

Multiresolution Representation of Datasets with Material Interfaces | 98 |

Approaches to Interactive Visualization of Largescale | 119 |

Data Structures for Multiresolution Representation | 143 |

41 | 169 |

Scaling the Topology of Symmetric SecondOrder Planar | 171 |

Mesh Fairing Based on Harmonic Mean Curvature Surfaces | 243 |

Georgios Stylianou and Gerald Farin | 268 |

Networkbased Rendering Techniques for Largescale | 283 |

A Data Model for Distributed Multiresolution Multisource | 296 |

89 | 316 |

AdaptiveSubdivisionSchemesforTriangularMeshes Ashish Amresh Gerald Farin and Anshuman Razdan | 319 |

99 | 327 |

Hierarchical Imagebased and Polygonbased Rendering | 328 |

SimplificationofNonconvexTetrahedralMeshes Martin Kraus and Thomas Ertl | 185 |

VirtualReality Based Interactive Exploration | 205 |

Hierarchical Indexing for OutofCore Access | 225 |

119 | 337 |

### Other editions - View all

Hierarchical and Geometrical Methods in Scientific Visualization Gerald Farin,Bernd Hamann,Hans Hagen No preview available - 2012 |

Hierarchical and Geometrical Methods in Scientific Visualization Gerald Farin,Bernd Hamann,Hans Hagen No preview available - 2011 |

### Common terms and phrases

adaptive adaptive mesh refinement AMR data AMR grids applied approximation boundary cell Center cluster coarse compression Computer Graphics connected convex hull coordinates crest lines crest point data model data set data structure datasource defined degenerate points discrete display domain edge collapses efficient error face Farin Figure function given Hamann hierarchy HMCSs implemented index space input interactive interpolation isosurface Kobbelt lath lattice level of resolution linear mapping material interfaces mean curvature method minimal multiresolution National Laboratory neighbors nodes nonconvex normal octree operations original mesh out-of-core performance polygonal principal curvatures problem query refinement regions remapping represent representation Research sample points scale Scientific Visualization shown in Fig SIGGRAPH simulation slice snav space filling curve step storage stored subdivision subsampling rate surface techniques tensor field tetrahedral tetrahedral meshes texture mapping tiles tion topology traversal triangle update values vector vertex vertices wavelet wavelet compression Z-order