HiRAMBO: a new hierarchical representation scheme for planar curves

This paper introduces a new hierarchical representation scheme for planar curves. The scheme approximates the curves by utilizing the approximation error information in splitting the curves and provides hierarchical bounding area information to support efficient set and search operation. While the approximation error is useful for deciding the abstraction level, its magnitude cannot be used to stand for the splitting order. An error adjusting method is proposed to keep the error magnitude in descending order according to the splitting order, thereby unnatural curve representation cannot occur. The minimum bounding octangle (MBO), a simple extension of the minimum bounding rectangle (MBR), is used to represent the bounding area information, which can localize curve segments effectively. Through several experiments, the authors found that approximation and localization of the proposed scheme were better than other hierarchical representation schemes such as strip tree, arc tree and HAL tree