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Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .SH "NAME" Math::PlanePath::CincoCurve \-\- 5x5 self\-similar curve .SH "SYNOPSIS" .IX Header "SYNOPSIS" .Vb 3 \& use Math::PlanePath::CincoCurve; \& my $path = Math::PlanePath::CincoCurve\->new; \& my ($x, $y) = $path\->n_to_xy (123); .Ve .SH "DESCRIPTION" .IX Header "DESCRIPTION" This is the 5x5 self-similar Cinco curve by John Dennis, .IX Xref "Dennis, John" .PP .Vb 10 \& | \& 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 .Ve .PP 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. .PP .Vb 10 \& +\-\-\-\-\-\-+\-\-\-\-\-\-+\-\-\-\-\-\-+\-\-\-\-\-\-+\-\-\-\-\-\-+ \& | 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|\-\-\-\-\->| \& +\-\-\-\-\-\-+\-\-\-\-\-\-+\-\-\-\-\-\-+\-\-\-\-\-\-+\-\-\-\-\-\-+ .Ve .PP 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. .PP 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. .PP John Dennis conceived 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 target top-level size rather than the unlimited size here. .SH "FUNCTIONS" .IX Header "FUNCTIONS" See \*(L"\s-1FUNCTIONS\*(R"\s0 in Math::PlanePath for behaviour common to all path classes. .ie n .IP """$path = Math::PlanePath::CincoCurve\->new ()""" 4 .el .IP "\f(CW$path = Math::PlanePath::CincoCurve\->new ()\fR" 4 .IX Item "$path = Math::PlanePath::CincoCurve->new ()" Create and return a new path object. .ie n .IP """($x,$y) = $path\->n_to_xy ($n)""" 4 .el .IP "\f(CW($x,$y) = $path\->n_to_xy ($n)\fR" 4 .IX Item "($x,$y) = $path->n_to_xy ($n)" Return the X,Y coordinates of point number \f(CW$n\fR on the path. Points begin at 0 and if \f(CW\*(C`$n < 0\*(C'\fR then the return is an empty list. .SS "Level Methods" .IX Subsection "Level Methods" .ie n .IP """($n_lo, $n_hi) = $path\->level_to_n_range($level)""" 4 .el .IP "\f(CW($n_lo, $n_hi) = $path\->level_to_n_range($level)\fR" 4 .IX Item "($n_lo, $n_hi) = $path->level_to_n_range($level)" Return \f(CW\*(C`(0, 25**$level \- 1)\*(C'\fR. .SH "SEE ALSO" .IX Header "SEE ALSO" Math::PlanePath, Math::PlanePath::PeanoCurve, Math::PlanePath::DekkingCurve .PP John Dennis \*(L"Inverse Space-Filling Curve Partitioning of a Global Ocean Model\*(R", and source code from \s-1COSIM\s0 .Sp .RS 4 .Sp .RE .SH "HOME PAGE" .IX Header "HOME PAGE" .SH "LICENSE" .IX Header "LICENSE" Copyright 2011, 2012, 2013, 2014 Kevin Ryde .PP Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the \s-1GNU\s0 General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. .PP Math-PlanePath is distributed in the hope that it will be useful, but \&\s-1WITHOUT ANY WARRANTY\s0; without even the implied warranty of \s-1MERCHANTABILITY\s0 or \s-1FITNESS FOR A PARTICULAR PURPOSE. \s0 See the \s-1GNU\s0 General Public License for more details. .PP You should have received a copy of the \s-1GNU\s0 General Public License along with Math-PlanePath. If not, see .