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HILBERT(3)            DragonFly Library Functions Manual            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

4th Berkeley Distribution           3/12/91                         HILBERT(3)