HILBERT(3)

NAME
hilbert_i2c, hilbert_c2i - Compute points on a Hilbert curve.

SYNOPSIS
void hilbert_i2c( dim, bits, idx, coords )
int dim, bits;
long int idx;
int coords[];

void hilbert_c2i( dim, bits, coords, idx )
int dim, bits;
int coords[];
long int *idx;

DESCRIPTION
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 coordinates of a point on the Hilbert curve, given an index value representing 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.

REFERENCE
A. R. Butz, "Alternative algorithm for Hilbert's space-filling curve," IEEE Trans. Comput., vol C-20, pp. 424-426, Apr. 1971.

AUTHOR
Spencer W. Thomas