Provided by: libmath-planepath-perl_113-1_all 
NAME
Math::PlanePath::QuadricIslands -- quadric curve rings
SYNOPSIS
use Math::PlanePath::QuadricIslands;
my $path = Math::PlanePath::QuadricIslands->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION
This is concentric islands made from four sides of the "QuadricCurve",
27--26 3
| |
29--28 25 22--21 2
| | | |
30--31 24--23 20--19 1
| 4--3 |
34--33--32 | 16--17--18 <- Y=0
| 1--2 |
35--36 7---8 15--14 -1
| | |
5---6 9 12--13 -2
| |
55--56 10--11 -3
| |
... 53--54 57 60--61 -4
| | | |
52--51 58--59 62--63 -5
| |
48--49--50 66--65--64 -6
| |
39--40 47--46 67--68 -7
| | | |
37--38 41 44--45 69 -8
| | |
42--43 70--71 -9
|
74--73--72 -10
|
75--76 79--80 ... -11
| | | |
77--78 81 84--85 -12
| |
82--83 -13
^
-8 -7 -6 -5 -4 -3 -2 -1 X=0 1 2 3 4
The initial figure is the square N=1,2,3,4 then for the next level each straight side
expands to 4x longer and a zigzag like N=5 through N=13 and the further sides to N=36.
*---*
| |
*---* becomes *---* * *---*
| |
*---*
Level Ranges
Counting the innermost square as level 0, each ring is
length = 4 * 8^level many points
Nstart = 1 + length[0] + ... + length[level-1]
= (4*8^level + 3)/7
Xstart = - 4^level / 2
Ystart = - 4^level / 2
For example the lower partial ring shown above is level 2 starting N=(4*8^2+3)/7=37 at
X=-(4^2)/2=-8,Y=-8.
The innermost square N=1,2,3,4 is on 0.5 coordinates, for example N=1 at X=-0.5,Y=-0.5.
This is centred on the origin and consistent with the (4^level)/2. Points from N=5
onwards are integer X,Y.
4-------3 Y=+1/2
| |
| o |
|
1-------2 Y=-1/2
X=-1/2 X=+1/2
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
"$path = Math::PlanePath::QuadricIslands->new ()"
Create and return a new path object.
SEE ALSO
Math::PlanePath, Math::PlanePath::QuadricCurve, Math::PlanePath::KochSnowflakes,
Math::PlanePath::GosperIslands
HOME PAGE
<http://user42.tuxfamily.org/math-planepath/index.html>
LICENSE
Copyright 2011, 2012, 2013 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/>.