Locality of Corner Transformation for Multidimensional Spatial Access Methods

The geometric structural complexity of spatial objects does not render an intuitive distance metric on the data space that measures spatial proximity. However, such a metric provides a formal basis for analytical work in transformation-based multidimensional spatial access methods, including locality preservation of the underlying transformation and distance-based spatial queries. We study the Hausdorff distance metric on the space of multidimensional polytopes, and prove a tight relationship between the metric on the original space of k-dimensional hyperrectangles and the standard p-normed metric on the transform space of 2k-dimensional points under the corner transformation, which justifies the effectiveness of the transformation-based technique in preserving spatial locality.