## Hierarchical and Geometrical Methods in Scientific VisualizationThe 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

Dataflow and Remapping for Wavelet Compression and Viewdependent Optimization of Billiontriangle Isosurfaces | 1 |

Extraction of Crackfree Isosurfaces from Adaptive Mesh Refinement Data | 19 |

A Simple Technique for Representing and Compressing Triangulated Surfaces | 41 |

Efficient Error Calculation for Multiresolution Texturebased Volume Visualization | 51 |

Hierarchical Spline Approximations | 63 |

Terrain Modeling Using Voronoi Hierarchies | 89 |

Multiresolution Representation of Datasets with Material Interfaces | 99 |

Approaches to Interactive Visualization of Largescale Dynamic Astrophysical Environments | 119 |

A Framework for Visualizing Hierarchical Computations | 197 |

VirtualReality Based Interactive Exploration of Multiresolution Data | 205 |

Hierarchical Indexing for OutofCore Access to MultiResolution Data | 225 |

Mesh Fairing Based on Harmonic Mean Curvature Surfaces | 243 |

Shape Feature Extraction | 269 |

Networkbased Rendering Techniques for Largescale Volume Data Sets | 283 |

A Data Model for Distributed Multiresolution Multisource Scientific Data | 297 |

Adaptive Subdivision Schemes for Triangular Meshes | 319 |

Data Structures for Multiresolution Representation of Unstructured Meshes | 143 |

Scaling the Topology of Symmetric SecondOrder Planar Tensor Fields | 171 |

Simplification of Nonconvex Tetrahedral Meshes | 185 |

Hierarchical Imagebased and Polygonbased Rendering for LargeScale Visualizations | 329 |

Color Plates | 347 |

### 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 algorithm AMR data AMR grids applied approximation binary boundary cell Center clockwise cluster coarse grid Computer Graphics connected convex hull coordinates crest lines data model data set data structure datasource decompression defined Delaunay triangulation discrete domain dual edge collapses efficient elements error face Figure geometry ghost value Given a lath half-edge image-based implemented input interactive interpolation isosurface lath lattice level of resolution linear loop mapping material interfaces mean curvature method multiresolution National Laboratory nodes normal octree operations original mesh out-of-core performance polygonal problem query refinement remapping rendering represent representation Research sample points scalar scale scheme Scientific shown in Fig SIGGRAPH simplified simulation slice snav spline split-edge step stored subdivision surface techniques tensor field tetrahedral tetrahedral mesh texture tiles tion topology traversal triangle meshes unstructured update vector vertex vertices Visualization Voronoi Voronoi diagram voxel wavelet compression