1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
|
# Copyright 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/>.
package Math::PlanePath::NxN;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
# uncomment this to run the ### lines
#use Smart::Comments;
use constant n_start => 0;
use constant class_x_negative => 0;
use constant class_y_negative => 0;
sub n_to_xy {
my ($self, $n) = @_;
### NxN n_to_xy(): $n
if ($n < 0) { return; }
if (is_infinite($n)) { return ($n,$n); }
{
# fractions on straight line ?
my $int = int($n);
if ($n != $int) {
my $frac = $n - $int; # inherit possible BigFloat/BigRat
my ($x1,$y1) = $self->n_to_xy($int);
my ($x2,$y2) = $self->n_to_xy($int+1);
my $dx = $x2-$x1;
my $dy = $y2-$y1;
return ($frac*$dx + $x1, $frac*$dy + $y1);
}
$n = $int;
}
# d = [ 0, 1, 2, 3, 4 ]
# n = [ 0, 1, 3, 6, 10 ]
# N = (d+1)*d/2
# d = (-1 + sqrt(8*$n+1))/2
my $d = int((sqrt(8*$n+1) - 1) / 2);
$n -= $d*($d+1)/2;
### $d
### $n
my $x = $d-$n; # downwards
my $y = $n; # upwards
my $diff = $x-$y;
### diagonals xy: "$x, $y diff=$diff"
if ($diff <= 0) {
### non-pos diff, use x ...
return (2*$x + ($diff % 2),
2*$x + int((1-$diff)/2));
} else {
### pos diff, use y ...
return (2*($y+1) - 1 + int($diff/2),
2*$y + (($diff+1) % 2));
}
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### NxN xy_to_n(): "$x, $y"
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 0 || $y < 0) {
return undef;
}
if ($x <= $y) {
my $h = int($x/2);
($x,$y) = ($h,
$h + ($x%2) + 2*($y - 2*$h - ($x%2)));
} else {
my $h = int($y/2);
($x,$y) = (1 + $h + ($y%2) + 2*($x-1 - 2*$h - ($y%2)),
$h);
}
return (($x+$y)**2 + $x+3*$y)/2;
}
# not exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### NxN rect_to_n_range(): "$x1,$y1 $x2,$y2"
$x1 = round_nearest ($x1);
$y1 = round_nearest ($y1);
$x2 = round_nearest ($x2);
$y2 = round_nearest ($y2);
($x1,$x2) = ($x2,$x1) if $x1 > $x2;
($y1,$y2) = ($y2,$y1) if $y1 > $y2;
if ($x2 < 0 || $y2 < 0) {
### all outside first quadrant ...
return (1, 0);
}
if ($x1 < 0) { $x1 *= 0; }
if ($y1 < 0) { $y1 *= 0; }
return (0, $x2 * $y2);
}
1;
__END__
|
