A hierarchical representation scheme for planar curves is proposed in this paper, which provides natural approximation and efficient localization. The scheme uses the iterative end-point fit algorithm (also known as the Douglas-Peucker algorithm [4]), but approximation errors are adjusted by force to eliminate unnatural approximations. The error adjusting is just making the approximation error of a node in a hierarchical tree to be less than or equal to those of its ancestor. A self- intersection resolving algorithm is also developed to remove self-intersections in all the possible approximations for a curve, which uses the cross-link technique to reduce computation time remarkably. In point of localization, the bounding area of a curve is represented us a minimum bounding octangle (MBO), which can enclose the curve compactly. The MB0 satisfies the hierarchical inclusion property, which is useful for hierarchical geometrical operations, such as the polygon intersection test and the point-inclusion test. Through several experiments, we found that the proposed scheme always generated curve approximations without self-intersections and provided more natural representations than the other hierarchical representation schemes such as the strip tree, the arc tree, and the HAL tree.