File Coverage

blib/lib/Math/PlanePath/HexSpiral.pm

Criterion	Covered	Total	%
statement	105	119	88.2
branch	22	30	73.3
condition	1	2	50.0
subroutine	21	27	77.7
pod	8	8	100.0
total	157	186	84.4

# Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 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 .



# Kanga "Number Mosaics" rotated to
#
#                ...-16---15
#                           \
#                  6----5   14
#                 /      \    \
#                7   1    4   13
#               /   /    /    /
#              8   2----3   12
#               \           /
#                9---10---11
#
#
# Could go pointy end with same loop/step, or point to the right
#
#                    13--12--11
#                   /         |
#                 14  4---3  10
#                /  /     |   |
#              15  5  1---2   9
#                \  \         |
#                 16  6---7---8
#                   \             |
#                    17--18--19--20
#


package Math::PlanePath::HexSpiral;
use 5.004;
use strict;
#use List::Util 'max';
*max = \&Math::PlanePath::_max;

use vars '$VERSION', '@ISA';
$VERSION = 128;
use Math::PlanePath;
*_sqrtint = \&Math::PlanePath::_sqrtint;
@ISA = ('Math::PlanePath');

use Math::PlanePath::Base::Generic
  'round_nearest',
  'xy_is_even';


# uncomment this to run the ### lines
#use Devel::Comments '###';


use Math::PlanePath::SquareSpiral;
*parameter_info_array = \&Math::PlanePath::SquareSpiral::parameter_info_array;

#      2w+3 --- 3w/2+3 -- w+4
#      /                     \
#    2w+4         0 -------- w+3  *
#      \                         /
#      2w+5 ----------------- 3w+7    w=2; 1+3*w+7=14
#                       ^
#                      X=0
sub x_negative_at_n {
  my ($self) = @_;
  return $self->n_start + ($self->{'wider'} ? 0 : 3);
}
sub y_negative_at_n {
  my ($self) = @_;
  return $self->n_start + 2*$self->{'wider'} + 5;
}
sub _UNDOCUMENTED__dxdy_list_at_n {
  my ($self) = @_;
  return $self->n_start + 3*$self->{'wider'} + 7;
}

sub rsquared_minimum {
  my ($self) = @_;
  return ($self->{'wider'} % 2
          ? 1   # odd "wider" minimum X=1,Y=0
          : 0); # even "wider" includes X=0,Y=0
}
*sumabsxy_minimum = \&rsquared_minimum;

use constant dx_minimum => -2;
use constant dx_maximum => 2;
use constant dy_minimum => -1;
use constant dy_maximum => 1;

*_UNDOCUMENTED__dxdy_list = \&Math::PlanePath::_UNDOCUMENTED__dxdy_list_six;

use constant absdx_minimum => 1;
*absdiffxy_minimum = \&rsquared_minimum;

use constant dsumxy_minimum => -2; # SW diagonal
use constant dsumxy_maximum => 2;  # dX=+2 and diagonal
use constant ddiffxy_minimum => -2; # NW diagonal
use constant ddiffxy_maximum => 2;  # SE diagonal
use constant dir_maximum_dxdy => (1,-1); # South-East

use constant turn_any_right => 0; # only left or straight
sub _UNDOCUMENTED__turn_any_left_at_n {
  my ($self) = @_;
  return $self->n_start + $self->{'wider'} + 1;
}


#------------------------------------------------------------------------------

sub new {
  my $self = shift->SUPER::new (@_);

  # parameters
  $self->{'wider'} ||= 0;  # default
  if (! defined $self->{'n_start'}) {
    $self->{'n_start'} = $self->default_n_start;
  }

  return $self;
}

# wider==0
# diagonal down and to the left
#   d = [ 0,  1,  2,  3 ]
#   N = [ 1,  6, 17,  34 ]
#   N = (3*$d**2 + 2*$d + 1)
#   d = -1/3 + sqrt(1/3 * $n + -2/9)
#     = (-1 + sqrt(3*$n - 2)) / 3
#
# wider==1
# diagonal down and to the left
#   d = [ 0,  1,  2,  3 ]
#   N = [ 1,  8, 21,  40 ]
#   N = (3*$d**2 + 4*$d + 1)
#   d = -2/3 + sqrt(1/3 * $n + 1/9)
#     = (-2 + sqrt(3*$n + 1)) / 3
#
# wider==2
# diagonal down and to the left
#   d = [ 0, 1,  2,  3,  4 ]
#   N = [ 1, 10, 25, 46, 73 ]
#   N = (3*$d**2 + 6*$d + 1)
#   d = -1 + sqrt(1/3 * $n + 2/3)
#     = (-3 + sqrt(3*$n + 6)) / 3
#
# N = 3*$d*$d + (2+2*$w)*$d + 1
#   = (3*$d + 2 + 2*$w)*$d + 1
# d = (-1-w + sqrt(3*$n + ($w+2)*$w - 2)) / 3
#   = (sqrt(3*$n + ($w+2)*$w - 2) -1-w) / 3

sub n_to_xy {
  my ($self, $n) = @_;
  #### n_to_xy: "$n   wider=$self->{'wider'}"

  $n = $n - $self->{'n_start'};  # N=0 basis
  if ($n < 0) { return; }
  my $w = $self->{'wider'};

  my $d = int((_sqrtint(3*$n + ($w+2)*$w + 1) - 1 - $w) / 3);
  #### d frac: ((_sqrtint(3*$n + ($w+2)*$w + 1) - 1 - $w) / 3)
  #### $d

  $n += 1; # N=1 basis

  $n -= (3*$d + 2 + 2*$w)*$d + 1;
  #### remainder: $n

  $d = $d + 1; # no warnings if $d==inf
  if ($n <= $d+$w) {
    #### bottom horizontal
    $d = -$d + 1;
    return (2*$n + $d - $w,
            $d);
  }
  $n -= $d+$w;
  if ($n <= $d-1) {
    #### right lower diagonal, being 1 shorter: $n
    return ($n + $d + 1 + $w,
            $n - $d + 1);
  }
  $n -= $d-1;
  if ($n <= $d) {
    #### right upper diagonal: $n
    return (-$n + 2*$d + $w,
            $n);
  }
  $n -= $d;
  if ($n <= $d+$w) {
    #### top horizontal
    return (-2*$n + $d + $w,
            $d);
  }
  $n -= $d+$w;
  if ($n <= $d) {
    #### left upper diagonal
    return (-$n - $d - $w,
            -$n + $d );
  }
  #### left lower diagonal
  $n -= $d;
  return ($n - 2*$d - $w,
          -$n);
}

sub xy_is_visited {
  my ($self, $x, $y) = @_;
  return xy_is_even($self,$x+$self->{'wider'},$y);
}

sub xy_to_n {
  my ($self, $x, $y) = @_;
  ### xy_to_n(): "$x, $y"

  $x = round_nearest ($x);
  $y = round_nearest ($y);
  my $w = $self->{'wider'};
  if (($x ^ $y ^ $w) & 1) {
    return undef;  # nothing on odd squares
  }

  my $ay = abs($y);
  my $ax = abs($x) - $w;
  if ($ax > $ay) {
    my $d = ($ax + $ay)/2;  # x+y is even

    if ($x > 0) {
      ### right ends
      ### $d
      return ((3*$d - 2 + 2*$w)*$d - $w  # horizontal to the right
              + $y                       # offset up or down
              + $self->{'n_start'});

    } else {
      ### left ends
      return ((3*$d + 1 + 2*$w)*$d    # horizontal to the left
              - $y                    # offset up or down
              + $self->{'n_start'});
    }

  } else {
    my $d = $ay;

    if ($y > 0) {
      ### top horizontal
      ### $d
      return ((3*$d + 2*$w)*$d      # diagonal up to the left
              + (-$d - $x-$w) / 2   # negative offset rightwards
              + $self->{'n_start'});
    } else {
      ### bottom horizontal, and centre horizontal
      ### $d
      ### offset: $d
      return ((3*$d + 2 + 2*$w)*$d   # diagonal down to the left
              + ($x + $w + $d)/2     # offset rightwards
              + $self->{'n_start'});
    }
  }
}

# not exact
sub rect_to_n_range {
  my ($self, $x1,$y1, $x2,$y2) = @_;
  ### HexSpiral rect_to_n_range(): $x1,$y1, $x2,$y2
  my $w = $self->{'wider'};

  # symmetric in +/-y, and biggest y is biggest n
  my $y = max (abs($y1), abs($y2));

  # symmetric in +/-x, and biggest x
  my $x = max (abs($x1), abs($x2));
  if ($x >= $w) {
    $x -= $w;
  }

  # in the middle horizontal path parts y determines the loop number
  # in the end parts diagonal distance, 2 apart
  my $d = ($y >= $x
           ? $y                 # middle
           : ($x + $y + 1)/2);  # ends
  $d = int($d) + 1;

  # diagonal downwards bottom left being the end of a revolution
  # s=0
  # s=1  n=7
  # s=2  n=19
  # s=3  n=37
  # s=4  n=61
  # n = 3*$d*$d + 3*$d + 1
  #
  # ### gives: "sum $d is " . (3*$d*$d + 3*$d + 1)

  # ENHANCE-ME: find actual minimum if rect doesn't cover 0,0
  return ($self->{'n_start'},
          (3*$d + 3 + 2*$w)*$d + $self->{'n_start'});
}

1;
__END__