14-2. Coordinates from Distance along the Hilbert Curve
To find the (x, y) coordinates of a point located at a distance s along the order n Hilbert curve, observe that the most significant two bits of the 2n-bit integer s determine which major quadrant the point is in. This is because the Hilbert curve of any order follows the overall pattern of the order 1 curve. If the most significant two bits of s are 00, the point is somewhere in the lower left quadrant, if 01 it is in the upper left quadrant, if 10 it is in the upper right quadrant, and if 11 it is in the lower right quadrant. Thus, the most significant two bits of s determine the most significant bits of the n-bit integers x and y, as follows:
| Most significant two bits of s | Most significant ... |
|---|
Get Hacker's Delight now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
