## Modern Geometric Computing for VisualizationTosiyasu L. Kunii, Yoshihisa Shinagawa This volume is on "modem geometric computing for visualization" which is at the forefront of multi-disciplinary advanced research areas. This area is attracting intensive research interest across many application fields: singularity in cosmology, turbulence in ocean engineering, high energy physics, molecular dynamics, environmental problems, modem mathe matics, computer graphics, and pattern recognition. Visualization re quires the computation of displayable shapes which are becoming more and more complex in proportion to the complexity of the objects and phenomena visualized. Fast computation requires information locality. Attaining information locality is achieved through characterizing the shapes in geometry and topology, and the large amount of computation required through the use of supercomputers. This volume contains the initial results of our efforts to satisfy these re quirements by inviting experts and selecting new research works through review processes. To be more specific, this book presents the proceedings of the International Workshop on Modem Geometric Computing for Visualization held at Kogakuin University, Tokyo, Japan, June 29-30, 1992 organized by the Computer Graphics Society, Japan Personal Com puter Software Association, Kogakuin University, and the Department of Information Science, Faculty of Science, The University of Tokyo. We received extremely high-quality papers for review from five different countries, one from Australia, one from Italy, four from Japan, one from Singapore and three from the United States, and we accepted eight papers and rejected two. |

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### Contents

3 | |

R A Earnshaw | 16 |

Polyhedral Surface Decomposition Based on Curvature Analysis | 57 |

The Conjugate Classification of the Kernel Form | 73 |

Motions of Flexible Objects | 91 |

Shape Description and Classification Based on Extremal Points | 121 |

Visualisation of Hyperobjects in HgramSpace by Computers | 141 |

Computation of Singularities for Engineering Design | 167 |

A Geographical Database System Based | 193 |

A Case Study for Building a Database | 207 |

Using Surface Coding to Detect Errors | 227 |

The Development of the Supercomputer System | 243 |

Workshop Organization | 265 |

### Other editions - View all

Modern Geometric Computing for Visualization Tosiyasu L Kunii,Yoshihisa Shinagawa No preview available - 1992 |

### Common terms and phrases

algorithm analysis applications Bézier called clusters complex Computer Graphics concave conjugate classification contour lines convex hull coordinates corresponding critical points crossing point curl value curvature regions curve defined described differential dimensional dp code edges engineering equations equivalent example extremal points Figure fractal geometric global Hamiltonian systems height function height relations hexagonal grid Hgram Hgram-space homotopy integrable Hamiltonian systems intersection Japan Kergosien kernel form knot diagram knot theory knotted surface Kunii linear loop manifold mapping mathematical mesh method Morse theory MTG sheet MTG-tree objects parallel parameter path Patrikalakis plane point geometry point set polygonal polynomial principal curvatures problem properties Reeb graph representation represented rotation saddle Scientific Visualization sequence shape Shinagawa singular points space stationary points structure Supercomputer surface reconstruction switching pair symmetries techniques Theorem topological toroidal graph triangles University of Tokyo variables vector vertex vertices