NAME

       Math::PlanePath::CincoCurve -- 5x5 self-similar curve

SYNOPSIS

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

DESCRIPTION

       This is the 5x5 self-similar Cinco curve

           John Dennis, "Inverse Space-Filling Curve Partitioning of a Global Ocean Model", and
           source code from COSIM

           <http://www.cecs.uci.edu/~papers/ipdps07/pdfs/IPDPS-1569010963-paper-2.pdf>

           <http://oceans11.lanl.gov/trac/POP/browser/trunk/pop/source/spacecurve_mod.F90>,
           <http://oceans11.lanl.gov/svn/POP/trunk/pop/source/spacecurve_mod.F90>

       It makes a 5x5 self-similar traversal of the first quadrant X>0,Y>0.

                                                           |
             4  |  10--11  14--15--16  35--36  39--40--41  74  71--70  67--66
                |   |   |   |       |   |   |   |       |   |   |   |   |   |
             3  |   9  12--13  18--17  34  37--38  43--42  73--72  69--68  65
                |   |           |       |           |                       |
             2  |   8   5-- 4  19--20  33  30--29  44--45  52--53--54  63--64
                |   |   |   |       |   |   |   |       |   |       |   |
             1  |   7-- 6   3  22--21  32--31  28  47--46  51  56--55  62--61
                |           |   |               |   |       |   |           |
           Y=0  |   0-- 1-- 2  23--24--25--26--27  48--49--50  57--58--59--60
                |
                +--------------------------------------------------------------
                   X=0  1   2   3   4   5   6   7   8   9  10  11  12  13  14

       The base pattern is the N=0 to N=24 part.  It repeats transposed and rotated to make the
       ends join.  N=25 to N=49 is a repeat of the base, then N=50 to N=74 is a transpose to go
       upwards.  The sub-part arrangements are as follows.

           +------+------+------+------+------+
           |  10  |  11  |  14  |  15  |  16  |
           |      |      |      |      |      |
           |----->|----->|----->|----->|----->|
           +------+------+------+------+------+
           |^  9  |  12 ||^ 13  |  18 ||<-----|
           ||  T  |  T  |||  T  |  T  ||  17  |
           ||     |     v||     |     v|      |
           +------+------+------+------+------+
           |^  8  |  5  ||^  4  |  19 ||  20  |
           ||  T  |  T  |||  T  |  T  ||      |
           ||     |     v||     |     v|----->|
           +------+------+------+------+------+
           |<-----|<---- |^  3  |  22 ||<-----|
           |  7   |  6   ||  T  |  T  ||  21  |
           |      |      ||     |     v|      |
           +------+------+------+------+------+
           |  0   |  1   |^  2  |  23 ||  24  |
           |      |      ||  T  |  T  ||      |
           |----->|----->||     |     v|----->|
           +------+------+------+------+------+

       Parts such as 6 going left are the base rotated 180 degrees.  The verticals like 2 are a
       transpose of the base, ie. swap X,Y, and downward vertical like 23 is transpose plus
       rotate 180 (which is equivalent to a mirror across the anti-diagonal).  Notice the base
       shape fills its sub-part to the left side and the transpose instead fills on the right.

       The N values along the X axis are increasing, as are the values along the Y axis.  This
       occurs because the values along the sub-parts of the base are increasing along the X and Y
       axes, and the other two sides are increasing too when rotated or transposed for sub-parts
       such as 2 and 23, or 7, 8 and 9.

       Dennis conceives this for use in combination with 2x2 Hilbert and 3x3 meander shapes so
       that sizes which are products of 2, 3 and 5 can be used for partitioning.  Such mixed
       patterns can't be done with the code here, mainly since a mixture depends on having a top-
       level target size rather than the unlimited first quadrant here.

FUNCTIONS

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

       "$path = Math::PlanePath::CincoCurve->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.

   Level Methods
       "($n_lo, $n_hi) = $path->level_to_n_range($level)"
           Return "(0, 25**$level - 1)".

SEE ALSO

       Math::PlanePath, Math::PlanePath::PeanoCurve, Math::PlanePath::DekkingCentres

HOME PAGE

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

LICENSE

       Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde

       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/>.