NAME

Math::PlanePath::HilbertMidpoint -- Hilbert curve midpoints

SYNOPSIS

 use Math::PlanePath::HilbertMidpoint;
 my $path = Math::PlanePath::HilbertMidpoint->new;
 my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

In progress ...

This is the midpoints of each segment of the HilbertCurve.

       |   \
    14 |    62          48----47          43----42
       |      \        /        \        /        \
    13 |       61    49          46    44          41
       |      /        \           \  /           /
    12 |    60          50          45          40
       |   /              \                    /
    11 | 59                51                39
       |  |                 |                  \
    10 |  |       55        |       33          38
       |  |      /  \       |      /  \           \
     9 | 58    56    54    52    32    34          37
       |   \  /        \  /       |      \        /
     8 |    57          53        |       35----36
       |                          |
     7 |                         31
       |                          |
     6 |     5           9        |       27----26
       |   /  \        /  \       |      /        \
     5 |  4     6     8    10    30    28          25
       |  |      \  /       |      \  /           /
     4 |  |        7        |       29          24
       |  |                 |                  /
     3 |  3                11                23
       |   \              /                    \
     2 |     2          12          17          22
       |      \        /           /  \           \
     1 |        1    13          16    18          21
       |      /        \        /        \        /
    Y=0|     0          14----15          19----20
       +----------------------------------------------
         X=0 1  2  3  4  5  6  7  8  9 10 11 12 13 14

The X,Y coordinates are kept as integers by doubling the segment lengths,

    *---5---*       *---9---*
    |       |       |       |
    4       6       8      10
    |       |       |       |
    *       *---7---*       *
    |                       |
    3                      11
    |                       |
    *---2---*       *--12---*
            |       |
            1      13
            |       |
    *---0---*       *--14---*--15--

The effect is to visit 1 of every 4 points in the first quadrant.

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.

$path = Math::PlanePath::HilbertMidpoint->new ()

Create and return a new path object.

($x,$y) = $path->n_to_xy ($n)

Return the X,Y coordinates of point number $n on the path. Points begin at 0 and if $n < 0 then the return is an empty list.

$n = $path->n_start()

Return 0, the first N in the path.

SEE ALSO

Math::PlanePath, Math::PlanePath::HilbertCurve, Math::PlanePath::DragonMidpoint

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

Copyright 2011, 2012 Kevin Ryde

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.