http://qs321.pair.com?node_id=681969
Category: Fun Stuff
Author/Contact Info
Description:

One of my friends teaches math to 7th-8th graders and came up with a little puzzle game to help demonstrate elementary geometry (coordinate systems, transform/translation of shapes). It consists a series of puzzles cut out of cardboard that the students assemble to form a perfect square.

He was showing it to me and mentioned that it was getting unwieldy to keep all the individual puzzles sorted out and in their proper envelopes. A lightbulb went on and I whipped up this script for him.

This is a simple puzzle game. Each puzzle has 2 or more pieces that you can drag and/or rotate to fit together to form a perfect square. Every vertex of each piece falls exactly on a 4 X 4 unit square grid, so each piece is described by its whole number verticies on a 0 .. 4 by 0 .. 4 cartesion grid.

Many of the puzzles are simple, some are tricky, all have at least one solution.

Works under Windows and Linux (and probably others but haven't tested).

Update: Added smoothing suggested by zentara

 
#!/usr/bin/perl

use strict;
use warnings;
use Tk;
use Tk::BrowseEntry;
use Tk::Zinc;

use constant OS_Win => $^O =~ /Win/;

my $current;      # currently selected shape
my @currentxy;    # coordinates of pointer when button clicked
my %objects;      # hash of piece IDs => vertex coordinates for each p
+uzzle
my @vertices;     # array of the coordinates of all the shapes for sna
+pping
my @puzzles;      # array of puzzles read in from DATA file
my $color;        # default color of objects
my $block    = 50;               # puzzle square is 4 x 4 $block pixel
+ blocks
my $screen   = 15;               # default screen size - in blocks squ
+are
my $selected = 'yellow';         # color of selected object
my $pi4      = atan2( 1, 1 );    # constant pi/4
my $which    = 0;                # currently loaded puzzle
my $detent   = 16;               # 'Stops' in a 90 degree rotation
my @colors   = qw/bisque cyan green magenta pink red tan/;

{
    local $/ = '@@';
    while (<DATA>) {
        chomp;
        s/#.+\n//;
        push @puzzles, [ split / *\r?\n/, $_ ] if /\w/;
    }
}

my $mw = MainWindow->new();

{ # scale window to fit screen
    my $width  = $mw->screenwidth;
    my $height = $mw->screenheight;
    my $square = $height - $width > 0 ? $width : $height;
    $block = int( $square * .8 / $screen );
    my $dim = $block * $screen;
    $mw->geometry( $dim . 'x' . $dim );
}

$mw->Label(
    -text => "Fit the pieces together to form a perfect square.\n".
      'Left drag to move selected; Mouse Wheel to rotate selected.' )
  ->pack;

my $zinc = $mw->Zinc(
    -borderwidth => 3,
    -relief      => 'sunken'
  )->pack(
    -expand => 1,
    -fill   => 'both',
  );

my $buttonbar = $mw->Frame->pack;

my $index = $buttonbar->BrowseEntry(
    -label     => 'Puzzle #',
    -variable  => \$which,
    -width     => 6,
    -browsecmd => sub {
        del();
        load($which);
    }
  )->grid(
    -row    => 1,
    -column => 1,
    -padx   => 2,
  );

$index->insert( 'end', 0 .. $#puzzles );

$buttonbar->Button(
    -text    => 'Next',
    -width   => 10,
    -command => sub {
        del();
        $which++ if $which < $#puzzles;
        load($which);
    }
  )->grid(
    -row    => 1,
    -column => 2,
    -padx   => 2,
  );

$buttonbar->Button(
    -text    => 'Random',
    -width   => 10,
    -command => sub {
        del();
        $which = int rand @puzzles;
        load($which);
    }
  )->grid(
    -row    => 1,
    -column => 3,
    -padx   => 2,
  );

my $colorsel = $buttonbar->BrowseEntry(
    -label     => 'Color',
    -variable  => \$color,
    -width     => 10,
    -browsecmd => sub {
        for ( keys %objects ) {
            $zinc->itemconfigure( $_, -fillcolor => $color );
            $index->focus;
        }
    }
  )->grid(
    -row    => 1,
    -column => 4,
    -padx   => 5,
  );

$colorsel->insert( 'end', @colors );

$mw->update;

load(0);

$mw->repeat( 100, \&snap );

MainLoop;

sub load {
    my $which = shift;
    $color = $colors[ int rand @colors ];
    my $pattern = $puzzles[$which];
    for ( @{$pattern} ) {
        my @points;
        my ( $repeat, @shape ) = split /\D/, $_;
        while ($repeat) {
            my $x = int rand($block) + $mw->width / 2;
            my $y = int rand($block) + $mw->height / 2;
            while (@shape) {
                push @points, $x - $block * pop @shape,
                  $y - $block * pop @shape;
            }
            $current = $zinc->add(
                'curve', 1, [@points],
                -closed    => 1,
                -visible   => 1,
                -filled    => 1,
                -fillcolor => $color,
                -smoothrelief => 1
            );
            add_bindings($current);
            @currentxy = ( $x, $y );
            rotate( ( int rand 32 ) / 4 + 1 );
            update_vertices();
            $repeat--;
        }
    }
}

sub del {
    $zinc->remove($_) for keys %objects;
    %objects = ();
}

sub add_bindings {
    my $object = shift;
    $zinc->bind( $object, '<Enter>' => sub { choose($object) } );
    $zinc->bind( $object, '<Leave>' => sub { unchoose() } );

    $zinc->bind( $object, '<1>'         => \&click );
    $zinc->bind( $object, '<B1-Motion>' => \&mousemove );
}

sub mousemove {
    my $ev = $zinc->XEvent();
    move( $ev->x - $currentxy[0], $ev->y - $currentxy[1] );
}

sub move {
    my ( $x, $y ) = @_;
    $zinc->translate( $current, $x, $y );
    $currentxy[0] += $x;
    $currentxy[1] += $y;
    update_vertices();
}

sub update_vertices {
    $objects{$current} = '';
    $objects{$current} .= "$_->[0],$_->[1] "
      for $zinc->transform( $current, 'device', [ $zinc->coords($curre
+nt) ] );
}

sub choose {
    $current = shift;
    $zinc->itemconfigure( $current, -fillcolor => $selected );
    $zinc->raise($current);
    update_vertices();
    if (OS_Win) {
        $mw->bind(
            '<MouseWheel>' => [
                sub {
                    click();
                    rotate( $_[1] / 120 / $detent );
                },
                Ev('D')
            ]
        );
    }
    else {
        $mw->bind( '<4>' => sub { click(); rotate( 1 / $detent ) } );
        $mw->bind( '<5>' => sub { click(); rotate( -1 / $detent ) } );
    }
}

sub unchoose {
    $zinc->itemconfigure( $current, -fillcolor => $color );
    if (OS_Win) {
        $mw->bind( '<MouseWheel>' => sub { } );
    }
    else {
        $mw->bind( '<4>' => sub { } );
        $mw->bind( '<5>' => sub { } );
    }
}

sub click {
    my $ev = $zinc->XEvent();
    @currentxy = ( $ev->x, $ev->y );
}

sub rotate {
    my $angle = shift;
    $zinc->rotate( $current, $angle * $pi4 * 2, @currentxy );
    update_vertices();
}

sub snap {
    my ( @points, $done );
    for ( keys %objects ) {
        next if $_ eq $current;
        push @points, split ' ', $objects{$_};
    }
    for ( split ' ', $objects{$current} ) {
        my ( $x1, $y1 ) = split /,/, $_;
        for my $vertex (@points) {
            my ( $x2, $y2 ) = split /,/, $vertex;
            if ( abs( $x2 - $x1 ) < 8 and abs( $y2 - $y1 ) < 8 ) {
                move( $x2 - $x1, $y2 - $y1 );
                $done++;
            }
            last if $done;
        }
        last if $done;
    }
}

# Shapes for puzzles laid out on a 5 x 5 cartesian
# map. Pieces may be slid and rotated as needed.
# Each line represents a shape in the puzzle.
# The first number is the number of times the shape
# appears in the puzzle, the remaining numbers are
# x,y coordinate pairs of each vertex in the shape.
# The 'x' and comma delineators are not critical, any
# non-number separator will work.

__DATA__
#0
2x0,0,4,0,4,4
@@
#1
2x0,0,3,0,3,4,2,4
@@
#2
2x0,0,2,2,0,4
1x0,0,4,0,4,4
@@
#3
2x0,0,2,0,2,2,0,2
1x0,0,4,0,4,2,0,2
@@
#4
1x0,0,4,0,0,2
1x0,0,4,0,4,2
1x0,0,4,2,0,4
@@
#5
4x0,0,4,0,2,2
@@
#6
4x0,0,3,0,2,2,0,1
@@
#7
2x0,0,1,0,1,1,0,1
2x0,0,2,0,2,1,0,1
2x0,0,3,0,3,1,0,1
1x0,0,4,0,4,1,0,1
@@
#8
4x0,0,2,0,0,2
1x2,0,4,2,2,4,0,2
@@
#9
2x0,0,1,0,0,1
2x0,0,3,0,0,3
1x1,0,4,3,3,4,0,1
@@
#10
2x0,0,1,0,0,1
1x0,0,2,0,0,2
1x0,0,2,0,1,1
1x0,0,4,0,2,2
1x0,0,4,4,0,4
@@
#11
2x0,0,2,0,0,1
2x0,0,3,0,0,2
2x2,0,2,4,0,1
@@
#12
4x0,0,1,0,0,1
4x0,0,2,0,1,1
2x1,0,2,1,1,2,0,1
1x1,0,4,3,3,4,0,1
@@
#13
2x0,0,2,0,0,2
4x0,0,2,0,1,1
2x0,2,2,0,3,1,1,3
@@
#14
4x0,0,2,0,0,2
2x0,1,1,0,2,1,1,2
1x0,1,1,0,3,2,2,3
@@
#15
4x0,0,1,0,0,1
4x0,0,2,0,1,1
5x0,1,1,0,2,1,1,2
@@
#16
1x0,0,2,0,2,2,0,2
4x0,0,3,0,3,1,0,1
@@
#17
1x0,0,4,0,0,1
1x0,0,4,0,4,1
3x0,0,4,1,0,2
@@
#18
2x0,0,2,0,0,1
2x0,0,2,0,2,1
2x0,0,2,1,0,2
2x0,1,2,0,4,1,2,2
@@
#19
4x0,0,3,0,3,1
1x0,3,1,0,4,1,3,4
@@
#20
4x0,0,1,0,2,1,0,3
1x0,1,1,0,2,1,1,2
@@
#21
4x0,0,3,0,3,1,1,1,1,2,0,2
@@
#22
4x0,0,3,0,3,1,2,1,2,2,1,2,1,1,0,1
@@
#23
2x0,0,2,0,1,1
1x0,0,2,0,2,2
1x0,0,2,0,3,1,1,1
2x0,0,2,2,0,4
1x0,1,1,0,2,1,1,2
@@
#24
1x0,0,1,0,0,1
3x0,0,1,0,0,2
1x0,0,2,1,2,2,0,1
1x0,0,3,0,2,1
1x0,1,1,0,1,2
1x0,2,1,0,2,1,1,3
1x0,2,1,0,3,1,2,3
@@
#25
2x0,0,1,0,0,2
2x0,0,1,0,2,1,1,1
2x0,0,2,0,2,2
1x0,2,1,0,2,0,1,2
2x0,2,1,0,2,1,1,3
@@
#26
2x0,0,1,0,0,1
1x0,0,1,0,0,3
1x0,0,1,0,1,3
1x0,0,2,0,1,1
1x0,0,2,0,1,3
1x0,1,1,0,2,3,1,4
1x0,3,1,0,2,1,1,4
@@
#27
4x0,0,1,0,3,1,2,2
4x0,0,1,1,0,3
@@
#28
4x0,0,0,1,4,1,4,0
@@
#29
2x0,0,1,2,0,4
4x0,0,2,0,1,2
1x0,2,1,0,2,2,1,4
@@
#30
2x0,0,2,0,0,4
1x0,4,2,0,4,0,2,4
@@
#31
4x0,0,1,0,0,2
2x0,2,1,0,4,0,3,2
@@
#32
2x0,0,1,0,0,2
2x0,0,1,0,1,2
1x0,2,1,0,3,0,4,2,3,4,1,4
@@
#33
2x0,0,1,0,0,2
2x0,4,0,2,1,0,2,0
1x0,4,2,0,4,0,2,4
@@
#34
2x0,0,1,0,0,2
2x0,0,2,0,0,3
1x0,3,2,0,4,1,2,4
@@
#35
2x0,0,1,0,1,1
1x0,0,1,0,1,2,0,2
3x0,0,1,1,0,2
2x0,0,2,0,2,2
1x0,0,3,0,2,1
1x0,1,1,0,2,1,1,2
1x0,1,1,0,3,2,2,2
@@
#36
2x0,0,1,0,0,1
2x0,0,1,0,2,1,0,3
2x0,0,2,0,3,1,1,1
1x0,2,2,0,4,0,2,2
@@
#37
2x0,0,1,0,0,1
3x0,0,1,1,0,2
1x0,0,1,1,1,2,0,1
1x0,0,4,0,2,2
1x0,1,1,0,1,1,0,2
1x0,1,1,0,2,1,1,2
1x0,1,1,0,2,1,2,2,1,3,0,2
@@
#38
1x0,0,1,0,1,1,0,1
1x0,0,1,0,1,2,0,2
1x0,0,1,0,1,3,0,3
1x0,0,2,0,2,2,0,2
1x0,0,2,0,2,3,0,3
@@
#39
1x0,0,1,1,0,2
2x0,0,2,0,2,2
1x0,0,2,0,4,2,2,2
1x0,0,2,2,1,2,0,1
1x0,1,1,0,2,0,0,2
1x0,2,2,0,4,0,2,2
@@
#40
2x0,0,1,0,0,1
2x0,0,1,1,1,2,0,3
2x0,0,3,0,2,1
2x0,1,1,0,3,1,1,2
1x0,1,2,0,2,1,0,2
@@
#41
2x0,0,1,0,1,1
3x0,0,1,1,0,2
1x0,0,3,0,1,1
1x0,0,3,0,2,1
3x0,1,1,0,3,1,1,2
@@
#42
1x0,0,1,0,2,1,1,2,0,2
1x0,0,1,0,2,1,2,2,1,2,0,1
1x0,0,1,1,1,2,0,2
1x0,0,2,0,2,1,1,1
1x0,0,2,0,2,1,1,2,0,1
2x0,0,3,0,2,1,1,1
@@
#43
4x0,0,1,0,2,1,2,2,1,2,0,1
4x0,0,1,1,0,2
@@
#44
1x0,0,0,2,2,2,2,0
4x0,0,1,1,0,2
4x0,0,2,0,0,2
@@
#45
4x0,0,1,1,0,2
1x0,0,2,0,0,2
2x0,0,2,0,3,1,2,2
1x1,0,3,2,2,3,0,1
@@
#46
1x0,0,1,0,2,1,1,2,0,2
2x0,0,1,1,0,2
2x0,0,2,0,1,1,0,1
2x0,0,2,0,2,1,1,1
2x0,1,1,0,2,1,2,2,1,2
@@
#47
1x0,0,0,2,1,3,2,2,2,0
1x0,0,1,0,1,1,0,1
1x0,0,1,0,2,1,0,1
1x0,0,1,0,2,1,1,2,0,1
2x0,0,2,0,1,1,0,1
1x0,0,2,0,2,1,1,2,0,1
@@
#48
1x0,0,1,0,0,1
1x0,0,1,0,1,1,0,1
1x0,0,1,0,1,1,0,2
1x0,0,1,0,1,2,0,3
1x0,0,1,0,1,3,0,4
1x0,0,1,1,0,2
1x0,0,2,0,0,2
1x0,0,2,2,0,4
@@
#49
1x0,0,1,0,1,1,0,1
1x0,0,1,0,1,1,0,2
1x0,0,1,0,1,2,0,1
1x0,0,2,0,0,2
4x0,1,1,2,2,1,2,0,1,0
@@
#50
1x0,0,3,0,0,3
1x0,3,3,0,3,3
1x0,3,3,0,4,0,0,4
1x0,4,4,0,4,1,1,4
@@
#51
2x0,0,0,1,1,0
1x0,3,3,0,4,0,0,4
1x0,4,4,0,4,1,1,4
2x1,0,2,0,0,2,0,1
2x2,0,3,0,0,3,0,2
@@
#52
1x2,0,3,2,0,2,0,1
1x0,0,4,0,2,2
1x0,0,2,0,2,2,1,2
1x0,0,2,2,0,3
1x2,0,2,2,0,2
@@
#53
2x0,0,1,1,1,3,0,4
2x0,0,3,0,2,1,1,1
2x0,0,1,0,0,1
1x0,2,0,3,1,3,3,1,3,0,2,0
@@
#54
2x0,0,2,0,2,1,1,1,1,2,0,2
2x0,0,2,0,2,1,1,1,1,4,0,4
@@
#55
2x0,0,2,0,2,1,1,1,1,2,0,2
1x0,0,2,0,2,1,1,1,1,4,0,4
1x0,0,3,0,3,1,1,1,1,3,0,3
@@
#56
1x0,0,4,0,4,1
1x0,0,4,1,4,2
1x0,0,4,2,4,3
1x0,0,4,3,4,4,3,4
1x0,0,3,4,0,1
1x0,0,3,3,0,1
1x0,0,3,2,0,1
1x0,0,3,1,0,1
@@
#57
2x0,0,1,0,3,2,1,2,0,1
2x0,0,3,0,3,1,1,1
2x0,0,2,0,2,2
@@
#58
1x0,0,0,3,3,0
2x0,0,0,1,1,2,2,1,1,0
2x0,0,1,1,2,0
1x0,0,1,1,1,0
1x0,0,0,1,1,1,1,0
1x0,1,2,3,2,2,3,2,1,0,1,1
@@
#59
2x0,0,0,1,1,2,1,0
2x0,0,0,1,1,0
4x0,0,1,1,2,1,3,0
2x0,0,0,2,2,2
@@
#60
1x0,0,2,0,2,1,1,1
1x0,0,2,0,1,1,0,1
1x0,0,1,0,2,1,1,1,1,2,0,1
1x0,0,1,0,2,1,2,2,1,2,0,1
4x0,0,3,0,2,1,1,1
@@
#61
1x0,0,1,0,3,2,1,2,0,1
1x0,0,3,0,3,1,2,2
1x0,0,2,0,1,1
1x0,0,1,0,2,1,2,2,1,2,0,1
1x0,0,3,0,2,1,1,1
1x0,0,3,0,2,1,2,2,1,2,1,1
@@
#62
1x0,0,4,0,4,1,1,1
1x0,0,1,1,2,1,2,2,1,2,0,3
1x0,0,1,0,1,1
1x0,0,2,0,2,2
2x0,0,3,0,3,1,2,2
@@
#63
1x0,0,2,0,1,1
1x0,0,1,1,1,2,0,1
1x0,0,2,0,3,1,1,1
1x0,0,1,0,2,1,2,2,1,2,0,1
3x0,0,1,1,2,1,2,2,1,2,0,3
@@
#64
2x0,0,1,0,0,1
2x0,0,2,0,1,1
2x0,0,2,0,2,1,1,1
4x0,0,1,0,2,1,1,1
6x0,0,1,1,1,2,0,1
@@
#65
2x0,0,1,0,0,1
1x0,0,1,1,0,2
1x1,0,3,2,1,4,0,3,1,2,0,1
2x0,0,3,0,2,1,1,1
1x0,0,2,0,2,1,1,2,1,1
1x0,0,2,0,1,1,1,2,0,1
@@
#66
1x0,0,4,0,4,1,3,2,2,1,1,1
2x0,0,2,0,1,1,1,2,0,1
1x0,0,2,0,2,1,1,2,1,1
1x0,0,1,0,1,2,0,1
1x1,0,1,1,2,2,1,3,1,2,0,1
1x1,0,2,1,2,2,1,1,1,2,0,1
@@
#67
1x0,0,2,0,2,1,4,3,2,3,2,2
1x0,0,1,1,0,2
1x0,0,2,2,2,3,0,1
1x0,0,2,0,2,2
1x0,0,1,1,1,2,0,1
1x1,0,1,1,2,2,1,3,1,2,0,1
1x0,0,2,0,1,1,0,1
1x0,0,3,0,2,1,0,1
@@
#68
1x0,0,1,0,1,1
2x0,0,2,0,2,2,1,1,0,2
3x1,0,2,1,1,1,1,2,0,1
1x0,0,2,0,2,2,1,2,1,1
1x0,0,2,0,1,1,1,2,0,2
@@
#69
1x0,0,1,0,0,1
1x0,0,2,0,1,2,0,1
1x0,0,2,0,2,2,0,1
1x0,0,2,0,2,2,1,1,0,2
1x0,0,1,0,1,2,0,2
1x0,0,2,0,0,2
1x1,0,1,1,3,3,2,4,2,3,0,1
@@
#70
1x0,0,1,0,1,1
1x1,0,2,1,1,2,0,1
1x0,0,3,0,1,1
2x0,0,3,0,2,1
2x0,0,2,1,0,2
1x0,0,2,0,0,3
1x0,0,2,0,3,2
@@
#71
2x0,0,2,0,1,2
2x0,0,4,0,2,1
4x0,0,3,2,1,2
@@
#72
1x0,0,2,0,0,4
1x0,0,2,0,1,2
1x0,0,4,0,2,1
1x0,0,4,0,3,2
1x0,0,3,2,2,4
@@
#73
1x0,0,2,0,3,1,1,1
2x0,0,2,0,1,1,1,2,0,1
2x0,0,2,0,2,1,1,2,1,1
1x0,0,1,0,1,2,0,1
1x1,0,1,1,2,2,1,3,1,2,0,1

1x1,0,2,1,2,2,1,1,1,2,0,1
1x0,0,1,0,0,1
@@
#74
1x0,0,2,0,1,1,1,2,0,1
4x0,0,2,0,2,1,1,2,1,1
1x0,0,1,0,0,1
1x1,0,2,1,3,1,2,2,1,1,0,1
1x0,0,1,0,1,1,0,1
1x0,0,2,0,1,1,0,1
1x0,0,1,1,1,2,0,1
@@
#75
1x0,0,1,0,0,1
1x1,0,2,1,3,1,2,2,1,1,0,1
1x0,0,2,0,2,1,1,1
1x0,0,2,0,2,2,1,1,0,1
1x0,0,2,0,0,2
1x0,0,4,0,4,1,2,1,2,2
1x0,0,2,0,2,1,1,2,0,2
@@
#76
1x0,0,1,0,1,2
1x0,0,1,2,0,3
1x0,0,3,0,0,1
1x0,0,2,0,1,3
1x0,0,2,0,0,2
1x0,0,1,2,1,3
1x0,0,2,0,1,2
1x0,0,1,0,2,1
1x1,0,3,2,0,3
@@
#77
2x0,0,1,0,2,1,2,2,1,2,1,1
2x0,0,1,0,2,1,2,2,1,1,0,1
1x0,0,3,0,2,1,1,1
1x0,0,1,0,2,1,1,1
1x0,0,1,0,1,1,0,1
1x1,0,2,0,0,2,0,1
1x0,0,2,0,0,2
1x0,0,1,0,0,1
@@
#78
1x0,0,2,0,1,1,1,2,0,3
1x0,0,2,0,2,1,1,1,1,2,0,1
1x0,0,2,0,2,2,1,1,0,1
1x0,0,1,0,1,2
1x0,0,1,2,1,3,0,2
1x0,0,1,0,1,1,2,2,1,2,0,1
1x0,0,1,1,2,1,1,2,0,1
1x1,0,1,1,2,2,1,3,1,2,0,1
@@
#79
2x0,0,2,0,2,2,1,1,0,1
2x0,0,2,0,2,1,1,1,0,2
1x0,0,1,0,1,1,0,1
1x0,0,3,0,3,1,2,2,2,1,1,1
1x0,0,1,1,1,3,0,2
@@
#80
1x0,0,4,0,2,2
1x0,0,2,0,2,2
1x0,0,4,0,3,1,1,1
1x0,0,2,0,2,2,1,3,1,1
2x0,0,1,1,1,3,0,2
@@
#81
2x0,0,2,0,3,1,2,2
1x1,0,3,0,1,2,0,1
2x0,0,2,0,1,1,2,2,0,2
1x0,0,2,0,1,1
@@

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