NAME¶
Math::PlanePath::QuadricIslands -- quadric curve rings
SYNOPSIS¶
use Math::PlanePath::QuadricIslands;
my $path = Math::PlanePath::QuadricIslands->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION¶
This is concentric islands made from four sides of the "QuadricCurve",
27--26 3
| |
29--28 25 22--21 2
| | | |
30--31 24--23 20--19 1
| 4--3 |
34--33--32 | 16--17--18 <- Y=0
| 1--2 |
35--36 7---8 15--14 -1
| | |
5---6 9 12--13 -2
| |
10--11 -3
^
-3 -2 -1 X=0 1 2 3 4
The initial figure is the square N=1,2,3,4 then for the next level each straight
side expands to 4x longer and a zigzag like N=5 through N=13 and the further
sides to N=36.
*---*
| |
*---* becomes *---* * *---*
| |
*---*
* <------ *
| ^
| |
| |
v |
* ------> *
Level Ranges¶
Counting the innermost square as level 0, each ring is
length = 4 * 8^level many points
Nlevel = 1 + length[0] + ... + length[level-1]
= (4*8^level + 3)/7
Xstart = - 4^level / 2
Ystart = - 4^level / 2
For example the lower partial ring shown above is level 2 starting
N=(4*8^2+3)/7=37 at X=-(4^2)/2=-8,Y=-8.
The innermost square N=1,2,3,4 is on 0.5 coordinates, for example N=1 at
X=-0.5,Y=-0.5. This is centred on the origin and consistent with the
(4^level)/2. Points from N=5 onwards are integer X,Y.
4-------3 Y=+1/2
| |
| o |
|
1-------2 Y=-1/2
X=-1/2 X=+1/2
FUNCTIONS¶
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
classes.
- "$path = Math::PlanePath::QuadricIslands->new ()"
- Create and return a new path object.
Level Methods¶
- "($n_lo, $n_hi) = $path->level_to_n_range($level)"
- Return per "Level Ranges" above,
( ( 4 * 8**$level + 3) / 7,
(32 * 8**$level - 4) / 7 )
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, 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/>.