TY - JOUR
AU - SCHRACK, GÜNTHER
AB -  SUMMARY Explicit formulas are presented to generate the coordinates of a point on the two-dimensional Hilbert curve from its location code and vice versa. Execution-time assessments suggest that the proposed algorithms are faster than the ones published previously. KEY WORDS: space-filling curves ; Hilbert curve; Hilbert order INTRODUCTION Space-filling curves, and in particular the Hilbert curve, continue to attract much interest, as demonstrated by a steady stream of articles appearing in the literature. A space-filling curve, defined on an integer lattice, defines a corresponding order, e.g. the Hilbert order. By numbering the points visited sequentially on the curve, location codes are defined (see Figures 4,5,6, 1 1). For plotting purposes, several sequential algorithms for the Hilbert order (as well as other orders) have been proposed for generating the coordinates in sequence.'-' In recent years, applications from diverse fields that employ the Hilbert order have been described. For instance, it was reported recently that Hilbert curves may significantly improve For the performance of spatial data processing sy~terns.~, such applications, random-access algorithms are required, i.e. encoding and decoding without previous context or historical information. An encoding algorithm derives the location code from a given coordinate point, whereas a decoding algorithm 
TI - Encoding and Decoding the Hilbert Order
JF - Software: Practice and Experience
DO - 10.1002/(SICI)1097-024X(199612)26:12<1335::AID-SPE60>3.0.CO;2-A
DA - 1996-12-01
UR - https://www.deepdyve.com/lp/wiley/encoding-and-decoding-the-hilbert-order-AXFgN1EdXV
SP - 1335
EP - 1346
VL - 26
IS - 12
DP - DeepDyve
ER -