Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets
Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets
复制标题
确保扩展欧拉图最多 8 组的可绘制性
DOI：
10.1007/978-3-540-25931-2_13
复制
发表时间：
2004
期刊：
影响因子：
2.1
通讯作者：
M. Viaud
中科院分区：
文献类型：
--
作者：
Anne Verroust;M. Viaud
本文通过构造性方法证明了对于任何集合 X 1,...,X n , n<9 的集合，存在一种称为扩展欧拉图的图解表示。这些图适用于表示集合包含和交集：每个集合 X i 和 X 1,...,X n 的子集合的每个非空交集由平面的唯一连接区域表示。从图的抽象描述开始，我们定义对偶图 G 并利用该图的属性进行推理，以构建 X 1,...,X n 的平面表示。这些图表将用于可视化任何索引视频数据库上的复杂请求的结果。事实上，这样的表示允许用户同时感知其查询的结果以及根据查询的数据库的相关性。
This paper shows by a constructive method the existence of a diagrammatic representation called extended Euler diagrams for any collection of sets X 1,...,X n , n<9. These diagrams are adapted for representing sets inclusions and intersections: each set X i and each non empty intersection of a subcollection of X 1,...,X n is represented by a unique connected region of the plane. Starting with an abstract description of the diagram, we define the dual graph G and reason with the properties of this graph to build a planar representation of the X 1,...,X n . These diagrams will be used to visualize the results of a complex request on any indexed video databases. In fact, such a representation allows the user to perceive simultaneously the results of his query and the relevance of the database according to the query.