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.IX Title "Math::PlanePath::WunderlichSerpentine 3pm"
.TH Math::PlanePath::WunderlichSerpentine 3pm "2014-08-30" "perl v5.20.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.nh
.SH "NAME"
Math::PlanePath::WunderlichSerpentine \-\- transpose parts of Peano curve, including coil order
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 3
\& use Math::PlanePath::WunderlichSerpentine;
\& my $path = Math::PlanePath::WunderlichSerpentine\->new (serpentine_type => \*(Aq111_000_111\*(Aq);
\& my ($x, $y) = $path\->n_to_xy (123);
\&
\& # or another radix digits ...
\& my $path5 = Math::PlanePath::WunderlichSerpentine\->new (radix => 5);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This is an integer version of Walter Wunderlich's
variations on the \f(CW\*(C`PeanoCurve\*(C'\fR. A \*(L"serpentine type\*(R" controls transposing
of selected 3x3 sub-parts. The default is \*(L"alternating\*(R" 010,101,010 which
transposes every second sub-part,
.IX Xref "Wunderlich, Walter"
.PP
.Vb 10
\& 8 | 60\-\-61\-\-62\-\-63 68\-\-69 78\-\-79\-\-80\-\-81
\& | | | | | | |
\& 7 | 59\-\-58\-\-57 64 67 70 77\-\-76\-\-75 ...
\& | | | | | |
\& 6 | 54\-\-55\-\-56 65\-\-66 71\-\-72\-\-73\-\-74
\& | |
\& 5 | 53 48\-\-47 38\-\-37\-\-36\-\-35 30\-\-29
\& | | | | | | | |
\& 4 | 52 49 46 39\-\-40\-\-41 34 31 28
\& | | | | | | | |
\& 3 | 51\-\-50 45\-\-44\-\-43\-\-42 33\-\-32 27
\& | |
\& 2 | 6\-\- 7\-\- 8\-\- 9 14\-\-15 24\-\-25\-\-26
\& | | | | | |
\& 1 | 5\-\- 4\-\- 3 10 13 16 23\-\-22\-\-21
\& | | | | | |
\& Y=0 | 0\-\- 1\-\- 2 11\-\-12 17\-\-18\-\-19\-\-20
\& |
\& +\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
\& X=0 1 2 3 4 5 6 7 8
.Ve
.PP
\&\f(CW\*(C`serpentine_type\*(C'\fR can be a string of 0s and 1s, with optional space, comma
or _ separators at each group of 3,
.PP
.Vb 4
\& "011111011" 0/1 string
\& "011,111,011"
\& "011_111_011"
\& "011 111 011"
.Ve
.PP
or special values
.PP
.Vb 3
\& "alternating" 01010101.. the default
\& "coil" 11111... all 1s described below
\& "Peano" 00000... all 0s, gives PeanoCurve
.Ve
.PP
Each \*(L"1\*(R" sub-part is transposed. The string is applied in order of the N
parts, irrespective of what net reversals and transposes are in force on a
particular part.
.PP
When no parts are transposed, which is a string of all 0s, the result is the
same as the \f(CW\*(C`PeanoCurve\*(C'\fR. The special \f(CW\*(C`serpentine_type => "Peano"\*(C'\fR
gives that.
.SS "Coil Order"
.IX Subsection "Coil Order"
\&\f(CW\*(C`serpentine_type => "coil"\*(C'\fR means \*(L"111 111 111\*(R" to transpose all parts.
The result is like a coil viewed side-on,
.PP
.Vb 10
\& 8 24\-\-25\-\-26\-\-27\-\-28\-\-29 78\-\-79\-\-80\-\-81\-\-...
\& | | |
\& 7 23\-\-22\-\-21 32\-\-31\-\-30 77\-\-76\-\-75
\& | | |
\& 6 18\-\-19\-\-20 33\-\-34\-\-35 72\-\-73\-\-74
\& | | |
\& 5 17\-\-16\-\-15 38\-\-37\-\-36 71\-\-70\-\-69
\& | | |
\& 4 12\-\-13\-\-14 39\-\-40\-\-41 66\-\-67\-\-68
\& | | |
\& 3 11\-\-10\-\- 9 44\-\-43\-\-42 65\-\-64\-\-63
\& | | |
\& 2 6\-\- 7\-\- 8 45\-\-46\-\-47 60\-\-61\-\-62
\& | | |
\& 1 5\-\- 4\-\- 3 50\-\-49\-\-48 59\-\-58\-\-57
\& | | |
\& Y=0 0\-\- 1\-\- 2 51\-\-52\-\-53\-\-54\-\-55\-\-56
\&
\& X=0 1 2 3 4 5 6 7 8
.Ve
.PP
Whenever \f(CW\*(C`serpentine_type\*(C'\fR begins with a \*(L"1\*(R" the initial sub-part is
transposed at each level. The first step N=0 to N=1 is kept fixed along the
X axis, then the higher levels are transposed. For example in the coil
above The N=9 to N=17 part is upwards, and then the N=81 to N=161 part is to
the right, and so on.
.SS "Radix"
.IX Subsection "Radix"
The optional \f(CW\*(C`radix\*(C'\fR parameter gives the size of the sub-parts, similar to
the \f(CW\*(C`PeanoCurve\*(C'\fR \f(CW\*(C`radix\*(C'\fR parameter (see
\&\*(L"Radix\*(R" in Math::PlanePath::PeanoCurve). For example radix 5 gives
.PP
.Vb 1
\& radix => 5
\&
\& 4 | 20\-21\-22\-23\-24\-25 34\-35 44\-45 70\-71\-72\-73\-74\-75 84\-85
\& | | | | | | | | | | |
\& 3 | 19\-18\-17\-16\-15 26 33 36 43 46 69\-68\-67\-66\-65 76 83 86
\& | | | | | | | | | | |
\& 2 | 10\-11\-12\-13\-14 27 32 37 42 47 60\-61\-62\-63\-64 77 82 87
\& | | | | | | | | | | |
\& 1 | 9\-\-8\-\-7\-\-6\-\-5 28 31 38 41 48 59\-58\-57\-56\-55 78 81 88
\& | | | | | | | | | | |
\& Y=0 | 0\-\-1\-\-2\-\-3\-\-4 29\-30 39\-40 49\-50\-51\-52\-53\-54 79\-80 89\-..
\& +\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
\& X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
.Ve
.PP
Like the \f(CW\*(C`PeanoCurve\*(C'\fR if the radix is even then the ends of each sub-part
don't join up. For example in radix 4 N=15 isn't next to N=16, nor N=31 to
N=32, etc.
.PP
.Vb 10
\& | |
\& 3 | 15\-\-14\-\-13\-\-12 16 23\-\-24 31 47\-\-46\-\-45\-\-44 48 55\-\-56 63
\& | | | | | | | | | | |
\& 2 | 8\-\- 9\-\-10\-\-11 17 22 25 30 40\-\-41\-\-42\-\-43 49 54 57 62
\& | | | | | | | | | | |
\& 1 | 7\-\- 6\-\- 5\-\- 4 18 21 26 29 39\-\-38\-\-37\-\-36 50 53 58 61
\& | | | | | | | | | | |
\& Y=0 | 0\-\- 1\-\- 2\-\- 3 19\-\-20 27\-\-28 32\-\-33\-\-34\-\-35 51\-\-52 59\-\-60
\& +\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
\& X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
.Ve
.PP
In the \f(CW\*(C`serpentine_type\*(C'\fR 0,1 form, any space, comma, etc, separators should
group \f(CW\*(C`radix\*(C'\fR many values, so for example
.PP
.Vb 1
\& serpentine_type => "00000_11111_00000_00000_11111"
.Ve
.PP
The intention is to do something friendly if the separators are not on such
boundaries, so that say 000_111_000 can have a sensible meaning in a radix
higher than 3. But exactly what is not settled, so always give a full
string of desired 0,1 for now.
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
See \*(L"\s-1FUNCTIONS\*(R"\s0 in Math::PlanePath for the behaviour common to all path
classes.
.ie n .IP """$path = Math::PlanePath::WunderlichSerpentine\->new ()""" 4
.el .IP "\f(CW$path = Math::PlanePath::WunderlichSerpentine\->new ()\fR" 4
.IX Item "$path = Math::PlanePath::WunderlichSerpentine->new ()"
.PD 0
.ie n .IP """$path = Math::PlanePath::WunderlichSerpentine\->new (serpentine_type => $str, radix => $r)""" 4
.el .IP "\f(CW$path = Math::PlanePath::WunderlichSerpentine\->new (serpentine_type => $str, radix => $r)\fR" 4
.IX Item "$path = Math::PlanePath::WunderlichSerpentine->new (serpentine_type => $str, radix => $r)"
.PD
Create and return a new path object.
.Sp
The optional \f(CW\*(C`radix\*(C'\fR parameter gives the base for digit splitting. The
default is ternary, radix 3. The radix should be an odd number, 3, 5, 7, 9
etc.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::PlanePath,
Math::PlanePath::PeanoCurve
.PP
Walter Wunderlich \*(L"Uber Peano-Kurven\*(R", Elemente der Mathematik, 28(1):1\-10,
1973.
.SH "HOME PAGE"
.IX Header "HOME PAGE"
.SH "LICENSE"
.IX Header "LICENSE"
Copyright 2011, 2012, 2013, 2014 Kevin Ryde
.PP
This file is part of Math-PlanePath.
.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 .