NAME¶
Math::PlanePath::PixelRings -- pixellated concentric circles
SYNOPSIS¶
use Math::PlanePath::PixelRings;
my $path = Math::PlanePath::PixelRings->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION¶
This path puts points on the pixels of concentric circles using the midpoint
ellipse drawing algorithm.
63--62--61--60--59 5
/ \
64 . 40--39--38 . 58 4
/ / \ \
65 . 41 23--22--21 37 . 57 3
/ / / \ \ \
66 . 42 24 10-- 9-- 8 20 36 . 56 2
| / / / \ \ \ |
67 43 25 11 . 3 . 7 19 35 55 1
| | | | / \ | | | |
67 44 26 12 4 1 2 6 18 34 54 Y=0
| | | | \ /
68 45 27 13 . 5 . 17 33 53 80 -1
| \ \ \ / / / |
69 . 46 28 14--15--16 32 52 . 79 -2
\ \ \ / / /
70 . 47 29--30--31 51 . 78 -3
\ \ / /
71 . 48--49--50 . 77 -4
\ /
72--73--74--75--76 -5
-5 -4 -3 -2 -1 X=0 1 2 3 4 5
The way the algorithm works means the rings don't overlap. Each is 4 or 8 pixels
longer than the preceding. If the ring follows the preceding tightly then it's
4 longer, for example N=18 to N=33. If it goes wider then it's 8 longer, for
example N=54 to N=80 ring. The average extra is approximately 4*
sqrt(2).
The rings can be thought of as part-way between the diagonals like
"DiamondSpiral" and the corners like "SquareSpiral".
* ** *****
* * *
* * *
* * *
* * *
diagonal ring corner
5 points 6 points 9 points
For example the N=54 to N=80 ring has a vertical part N=54,55,56 like a corner
then a diagonal part N=56,57,58,59. In bigger rings the verticals are
intermingled with the diagonals but the principle is the same. The number of
vertical steps determines where it crosses the 45-degree line, which is at R*
sqrt(2) but rounded according to the midpoint algorithm.
FUNCTIONS¶
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
classes.
- "$path = Math::PlanePath::PixelRings->new ()"
- Create and return a new path object.
- "($x,$y) = $path->n_to_xy ($n)"
- For "$n < 1" the return is an empty list, it being considered
there are no negative points.
The behaviour for fractional $n is unspecified as yet.
- "$n = $path->xy_to_n ($x,$y)"
- Return an integer point number for coordinates "$x,$y". Each
integer N is considered the centre of a unit square and an
"$x,$y" within that square returns N.
Not every point of the plane is covered (like those marked by a
"." in the sample above). If "$x,$y" is not reached
then the return is "undef".
SEE ALSO¶
Math::PlanePath, Math::PlanePath::Hypot, Math::PlanePath::MultipleRings
HOME PAGE¶
<
http://user42.tuxfamily.org/math-planepath/index.html>
LICENSE¶
Copyright 2010, 2011, 2012, 2013, 2014 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/>.