图 书 馆
从仿射微分几何的角度看计算几何Computational Geometry from the Viewpoint of Affine Differential Geometry |
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| 课程网址: | http://videolectures.net/etvc08_matsuzoe_cgftv/ |
| 主讲教师: | Matsuzoe Hiroshi |
| 开课单位: | 名古屋工业大学 |
| 开课时间: | 2008-12-05 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Incidence relations (configurations of vertexes, edges, etc.) are important in computational geometry. Incidence relations are invariant under the group of affine transformations. On the other hand, affine differential geometry is to study hypersurfaces in an affine space that are invariant under the group of affine transformation. Therefore affine differential geometry gives a new sight in computational geometry. From the viewpoint of affine differential geometry, algorithms of geometric transformation and dual transformation are discussed. The Euclidean distance function is generalized by a divergence function in affine differential geometry. A divergence function is an asymmetric distance-like function on a manifold, and it is an important object in information geometry. For divergence functions, the upper envelope type theorems on statistical manifolds are given. Voronoi diagrams determined from divergence functions are also discussed. |
| 关 键 词: | 发生率关系; 仿射变换组; 仿射微分几何 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-04-14：lxf |
| 阅读次数: | 94 |