Recent advances of computer performance and network infrastructure have increased the opportunities for various users to treat spatial data, such as figures and images. Compared to textual data, spatial data contains more abundant information and provides a representation that is easy to understand. But since spatial data are generally stored and processed as numerical data, their processing requires more memory and time. Therefore, an efficient mechanism for spatial data processing is desired. The more refined the data used are, the clearer and more precise the figure is. However, refined data are not always necessary unless a clear, precise figure is required. It is sometimes sufficient to know the number of objects or the positional relationships of the objects in a figure depending on a user's purpose.
Consider the following problem.