.\" Copyright 1991, The Regents of the University of Michigan
.TH HILBERT 3 3/12/91 3
.UC 4
.SH NAME
hilbert_i2c, hilbert_c2i \- Compute points on a Hilbert curve.
.SH SYNOPSIS
.B
void hilbert_i2c( dim, bits, idx, coords )
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.B
int dim, bits;
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.B
long int idx;
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.B
int coords[];
.sp
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void hilbert_c2i( dim, bits, coords, idx )
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int dim, bits;
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int coords[];
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long int *idx;
.SH 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 \fIhilbert_i2c\fP
returns the coordinates of a point on the Hilbert curve, given an
index value representing its sequential position on the curve.  The
procedure \fIhilbert_c2i\fP reverses the process.  The arguments are:
.TP
.I dim
The dimensionality of the Hilbert curve.  For the usual planar curve
case, this would be 2.
.TP
.I bits
The resolution to which the Hilbert curve will be computed.  The space
is quantized to 2^\fIbits\fP values on each axis, so there are
2^(3*\fIbits\fP) points on the curve.  The product of
\fIdim\fP*\fIbits\fP should be less than or equal to the number of
bits in a long integer (typically 32), and \fIbits\fP should be less
than or equal to the number of bits in an integer.
.TP
.I idx
The sequential position of the point along the curve (starting from
0).  This is a 3*\fIbits\fP bit integer.
.TP
.I coords
The spatial coordinates of the point on the curve.  The array should
hold \fIdim\fP values.  Each is a \fIbits\fP bit integer.
.SH REFERENCE
A. R. Butz, "Alternative algorithm for Hilbert's space-filling
curve," \fIIEEE Trans. Comput.\fP, vol C-20, pp. 424-426, Apr. 1971.
.SH AUTHOR
Spencer W. Thomas