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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::PixelRings \-\- pixellated concentric circles .SH "SYNOPSIS" .IX Header "SYNOPSIS" .Vb 3 \& use Math::PlanePath::PixelRings; \& my $path = Math::PlanePath::PixelRings\->new; \& my ($x, $y) = $path\->n_to_xy (123); .Ve .SH "DESCRIPTION" .IX Header "DESCRIPTION" This path puts points on the pixels of concentric circles using the midpoint ellipse drawing algorithm. .PP .Vb 10 \& 63\-\-62\-\-61\-\-60\-\-59 5 \& / \e \& 64 . 40\-\-39\-\-38 . 58 4 \& / / \e \e \& 65 . 41 23\-\-22\-\-21 37 . 57 3 \& / / / \e \e \e \& 66 . 42 24 10\-\- 9\-\- 8 20 36 . 56 2 \& | / / / \e \e \e | \& 67 43 25 11 . 3 . 7 19 35 55 1 \& | | | | / \e | | | | \& 67 44 26 12 4 1 2 6 18 34 54 Y=0 \& | | | | \e / \& 68 45 27 13 . 5 . 17 33 53 80 \-1 \& | \e \e \e / / / | \& 69 . 46 28 14\-\-15\-\-16 32 52 . 79 \-2 \& \e \e \e / / / \& 70 . 47 29\-\-30\-\-31 51 . 78 \-3 \& \e \e / / \& 71 . 48\-\-49\-\-50 . 77 \-4 \& \e / \& 72\-\-73\-\-74\-\-75\-\-76 \-5 \& \& \-5 \-4 \-3 \-2 \-1 X=0 1 2 3 4 5 .Ve .PP The way the algorithm works means the rings don't overlap. Each is 4 or 8 pixels longer than the preceding. If the ring follows the preceding tightly then it's 4 longer, for example N=18 to N=33. If it goes wider then it's 8 longer, for example N=54 to N=80 ring. The average extra is approximately 4*\fIsqrt\fR\|(2). .PP The rings can be thought of as part-way between the diagonals like \&\f(CW\*(C`DiamondSpiral\*(C'\fR and the corners like \f(CW\*(C`SquareSpiral\*(C'\fR. .PP .Vb 5 \& * ** ***** \& * * * \& * * * \& * * * \& * * * \& \& diagonal ring corner \& 5 points 6 points 9 points .Ve .PP For example the N=54 to N=80 ring has a vertical part N=54,55,56 like a corner then a diagonal part N=56,57,58,59. In bigger rings the verticals are intermingled with the diagonals but the principle is the same. The number of vertical steps determines where it crosses the 45\-degree line, which is at R*\fIsqrt\fR\|(2) but rounded according to the midpoint algorithm. .SH "FUNCTIONS" .IX Header "FUNCTIONS" See \*(L"\s-1FUNCTIONS\*(R"\s0 in Math::PlanePath for behaviour common to all path classes. .ie n .IP """$path = Math::PlanePath::PixelRings\->new ()""" 4 .el .IP "\f(CW$path = Math::PlanePath::PixelRings\->new ()\fR" 4 .IX Item "$path = Math::PlanePath::PixelRings->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)" For \f(CW\*(C`$n < 1\*(C'\fR the return is an empty list, it being considered there are no negative points. .Sp The behaviour for fractional \f(CW$n\fR is unspecified as yet. .ie n .IP """$n = $path\->xy_to_n ($x,$y)""" 4 .el .IP "\f(CW$n = $path\->xy_to_n ($x,$y)\fR" 4 .IX Item "$n = $path->xy_to_n ($x,$y)" Return an integer point number for coordinates \f(CW\*(C`$x,$y\*(C'\fR. Each integer N is considered the centre of a unit square and an \f(CW\*(C`$x,$y\*(C'\fR within that square returns N. .Sp Not every point of the plane is covered (like those marked by a \*(L".\*(R" in the sample above). If \f(CW\*(C`$x,$y\*(C'\fR is not reached then the return is \f(CW\*(C`undef\*(C'\fR. .SH "SEE ALSO" .IX Header "SEE ALSO" Math::PlanePath, Math::PlanePath::Hypot, Math::PlanePath::MultipleRings .SH "HOME PAGE" .IX Header "HOME PAGE" .SH "LICENSE" .IX Header "LICENSE" Copyright 2010, 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 .