HILBERT(3) 3 (3/12/91) 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
Page 1 (printed 12/1/98)
