hilbert_i2c, hilbert_c2i - Compute points on a Hilbert curve.
void hilbert_i2c( dim, bits, idx, coords )
int dim, bits;
long int idx;
void hilbert_c2i( dim, bits, coords, idx )
int dim, bits;
long int *idx;
These procedures map the real line onto a Hilbert curve and vice versa.
(A Hilbert curve is a space filling curve similar to the Peano curve,
except it is not closed.) The procedure hilbert_i2c returns the coor‐
dinates of a point on the Hilbert curve, given an index value repre‐
senting its sequential position on the curve. The procedure
hilbert_c2i reverses the process. The arguments are:
dim The dimensionality of the Hilbert curve. For the usual planar
curve case, this would be 2.
bits The resolution to which the Hilbert curve will be computed. The
space is quantized to 2^bits values on each axis, so there are
2^(3*bits) points on the curve. The product of dim*bits should
be less than or equal to the number of bits in a long integer
(typically 32), and bits should be less than or equal to the
number of bits in an integer.
idx The sequential position of the point along the curve (starting
from 0). This is a 3*bits bit integer.
coords The spatial coordinates of the point on the curve. The array
should hold dim values. Each is a bits bit integer.
A. R. Butz, "Alternative algorithm for Hilbert's space-filling curve,"
IEEE Trans. Comput., vol C-20, pp. 424-426, Apr. 1971.
Spencer W. Thomas
4th Berkeley Distribution 3/12/91 HILBERT(3)