=head1 NAME
Geo::Google::PolylineEncoder - encode lat/lons to Google Maps Polylines
=head1 SYNOPSIS
use Geo::Google::PolylineEncoder;
my $points = [
# can also take points as [lat, lon]
{ lat => 38.5, lon => -120.2 },
{ lat => 40.7, lon => -120.95 },
{ lat => 43.252, lon => -126.453 },
];
my $encoder = Geo::Google::PolylineEncoder->new;
my $eline = $encoder->encode( $points );
print $eline->{num_levels}; # 18
print $eline->{zoom_factor}; # 2
print $eline->{points}; # _p~iF~ps|U_ulLnnqC_mqNvxq`@
print $eline->{levels}; # POP
# in Javascript, assuming eline was encoded as JSON:
# ... load GMap2 ...
var opts = {
points: eline.points,
levels: eline.levels,
numLevels: eline.num_levels,
zoomFactor: eline.zoom_factor,
};
var line = GPolyline.fromEncoded( opts );
=cut
package Geo::Google::PolylineEncoder;
use strict;
use warnings;
use accessors qw(num_levels zoom_factor visible_threshold force_endpoints
zoom_level_breaks escape_encoded_points lons_first
points dists max_dist encoded_points encoded_levels );
use constant defaults => {
num_levels => 18,
zoom_factor => 2,
force_endpoints => 1,
escape_encoded_points => 0,
visible_threshold => 0.00001,
lons_first => 0,
};
our $VERSION = 0.06;
# The constructor
sub new {
my $class = shift;
my $self = bless {}, $class;
$self->init(@_);
return $self;
}
sub init {
my ($self, %args) = @_;
foreach my $attr (keys %{ $self->defaults }) {
$self->$attr($self->defaults->{$attr});
}
foreach my $attr (keys %args) {
$self->$attr($args{$attr});
}
}
sub init_zoom_level_breaks {
my $self = shift;
# Cache for performance:
my $num_levels = $self->num_levels;
my @zoom_level_breaks;
for my $i (1 .. $num_levels) {
push @zoom_level_breaks,
$self->visible_threshold * $self->zoom_factor ** ($num_levels - $i);
}
$self->zoom_level_breaks(\@zoom_level_breaks);
}
sub reset_encoder {
my $self = shift;
$self->points([])->dists([])->max_dist(0)->encoded_points('')->encoded_levels('');
# Note: calculate zoom level breaks here in case num_levels, etc. have
# changed between encodes:
$self->init_zoom_level_breaks;
}
sub set_points {
my ($self, $points) = @_;
die "points must be an arrayref!" unless UNIVERSAL::isa( $points, 'ARRAY' );
# Internally, points are stored as [lat, lon]. Although this is less
# readable, it is more efficient than using a hash.
# Make a copy of the points we were given
my @points;
if (UNIVERSAL::isa($points->[0], 'HASH')) {
my @keys = keys %{ $points->[0] };
my ($lat_key) = grep( /^lat$/i, @keys );
my ($lon_key) = grep( /^(?:lon)|(?:lng)$/i, @keys );
@points = map { [$_->{$lat_key}, $_->{$lon_key}] } @$points;
} elsif (UNIVERSAL::isa($points->[0], 'ARRAY')) {
if ($self->lons_first) {
@points = map {[ $_->[1], $_->[0] ]} @$points;
} else {
@points = map {[ $_->[0], $_->[1] ]} @$points;
}
} else {
die "don't know how to handle points = $points";
}
return $self->points( \@points );
return $self;
}
# The main entry point
sub encode {
my ($self, $points) = @_;
$self->reset_encoder
->set_points( $points )
->calculate_distances
->encode_points
->encode_levels;
my $eline = {
points => $self->encoded_points,
levels => $self->encoded_levels,
num_levels => $self->num_levels,
zoom_factor => $self->zoom_factor,
};
if ($self->escape_encoded_points) {
# create string literals:
$eline->{points} =~ s/\\/\\\\/g;
}
return $eline;
}
# The main function. Essentially the Douglas-Peucker algorithm, adapted for
# encoding. Rather than simply eliminating points, we record their distance
# from the segment which occurs at that recursive step. These distances are
# then easily converted to zoom levels.
#
# Note: this function has been optimized and is quite long, sorry.
# Any further optimizations should probably be done in XS.
sub calculate_distances {
my $self = shift;
my $points = $self->points;
my @dists;
my $max_dist = 0;
if (@$points <= 2) {
# no point doing distance calcs:
return $self->dists( \@dists )->max_dist( $max_dist );
}
# cache commonly used vars:
my $visible_threshold = $self->visible_threshold;
# Iterate through all the points, and calculate their dists
# Each stack element contains the index of two points representing a line
# seg that we calculate distances from. Start off with the first & last pt:
my @stack = ([0, @$points - 1]);
while (@stack > 0) {
my $current = pop @stack;
# cache to save array lookups:
my $current_0 = $current->[0];
my $current_1 = $current->[1];
# Get the two points, $A & $B:
my ($A, $B) = ($points->[$current_0], $points->[$current_1]);
# Cache their lon/lats to avoid unneccessary array lookups.
# Note: we use X/Y because it's shorter, and more math-y
my ($Ax, $Ay, $Bx, $By) = ($A->[1], $A->[0], $B->[1], $B->[0]);
# Create a line segment between $A & $B and calculate its length
# Note: cache the square of the seg length for use in calcs later...
my $seg_length_squared = (($Bx - $Ax) ** 2 + ($By - $Ay) ** 2);
my $seg_length = sqrt($seg_length_squared);
my $seg_length_is_0 = $seg_length == 0; # cache
# Cache the deltas in x/y for calcs later:
my ($Bx_minus_Ax, $By_minus_Ay) = ($Bx - $Ax, $By - $Ay);
my $current_max_dist = 0;
my $current_max_dist_idx;
for (my $i = $current_0 + 1; $i < $current_1; $i++) {
# Get the current point:
my $P = $points->[$i];
# Cache its lon/lat to avoid unneccessary hash lookups.
# Note: we use X/Y because it's shorter, and more math-y
my ($Py, $Px) = ($P->[0], $P->[1]);
# Compute the distance between point $P and line segment [$A, $B].
# Maths borrowed from Philip Nicoletti (see below).
#
# Note: we approximate distance using flat (Euclidian) geometry,
# rather than trying to bring the curvature of the earth into it.
# This greatly simplifies things, and makes the calcs faster...
#
# Note: distance calculations have been brought in-line as the
# majority of encoding time was spent calling the 'distance'
# method. This way we can avoid passing lots of data by value,
# setting up the sub stack, and we can also cache some values.
#my $dist = $self->distance($points->[$i], $A, $B, $seg_length, $seg_length_squared);
my $dist;
if ($seg_length_is_0) {
# The line is really just a point, so calc dist between it and $P:
$dist = sqrt(($By - $Py) ** 2 + ($Bx - $Px) ** 2);
} else {
# Thanks to Philip Nicoletti's explanation:
# http://www.codeguru.com/forum/printthread.php?t=194400
#
# So, to find out how far the line segment (AB) is from the point (P),
# let 'I' be the point of perpendicular projection of P on AB. The
# parameter 'r' indicates I's position along AB, and is computed by
# the dot product of AP and AB divided by the square of the length
# of AB:
#
# AP . AB (Px-Ax)(Bx-Ax) + (Py-Ay)(By-Ay)
# r = -------- = -------------------------------
# ||AB||^2 L^2
#
# r can be interpreded ala:
#
# r=0 I = A
# r=1 I = B
# r<0 I is on the backward extension of A-B
# r>1 I is on the forward extension of A-B
# 00 P is right of AB
# s=0 P is on AB
#
# Compute s as follows:
#
# (Ay-Py)(Bx-Ax) - (Ax-Px)(By-Ay)
# s = -------------------------------
# L^2
#
# Then the distance from P to I = |s|*L.
my $r = (($Px - $Ax) * ($Bx - $Ax) +
($Py - $Ay) * ($By - $Ay)) / $seg_length_squared;
if ($r <= 0.0) {
# Either I = A, or I is on the backward extension of A-B,
# so find dist between $P & $A:
$dist = sqrt(($Ay - $Py) ** 2 + ($Ax - $Px) ** 2);
} elsif ($r >= 1.0) {
# Either I = B, or I is on the forward extension of A-B,
# so find dist between $P & $B:
$dist = sqrt(($By - $Py) ** 2 + ($Bx - $Px) ** 2);
} else {
# I is interior to A-B, so find $s, and use it to find the
# dist between $P and A-B:
my $s = (($Ay - $Py) * $Bx_minus_Ax -
($Ax - $Px) * $By_minus_Ay) / $seg_length_squared;
$dist = abs($s) * $seg_length;
}
# warn "\t$Px\t$Py\t$Ax\t$Ay\t$Bx\t$By\t$r\t$dist\n";
}
# See if this distance is the greatest for this segment so far:
if ($dist > $current_max_dist) {
$current_max_dist = $dist;
$current_max_dist_idx = $i;
if ($current_max_dist > $max_dist) {
$max_dist = $current_max_dist;
}
}
}
# If the point that had the greatest distance from the line seg is
# also greater than our threshold, process again using it as a new
# start/end point for the line.
if ($current_max_dist > $visible_threshold) {
# store this distance - we'll use it later when creating zoom values
$dists[$current_max_dist_idx] = $current_max_dist;
push @stack, [$current_0, $current_max_dist_idx];
push @stack, [$current_max_dist_idx, $current_1];
}
}
$self->dists( \@dists )->max_dist( $max_dist );
} # calculate_distances
# The encode_points function is very similar to Google's
# http://www.google.com/apis/maps/documentation/polyline.js
# The key difference is that not all points are encoded,
# since some were eliminated by Douglas-Peucker.
sub encode_points {
my $self = shift;
my $points = $self->points;
my $dists = $self->dists;
my $encoded_points = "";
my $oldencoded_points = "";
my ($last_lat, $last_lon) = (0.0, 0.0);
for (my $i = 0; $i < @$points; $i++) {
my $point = $points->[$i];
my $lat = $point->[0];
my $lon = $point->[1];
if (defined($dists->[$i]) || $i == 0 || $i == @$points - 1) {
# compute deltas, rounded to 5 decimal places:
my $lat_e5 = sprintf('%.5f', $lat)+0; # round()
my $lon_e5 = sprintf('%.5f', $lon)+0; # round()
my $delta_lat = sprintf('%.5f', $lat_e5 - $last_lat)+0;
my $delta_lon = sprintf('%.5f', $lon_e5 - $last_lon)+0;
($last_lat, $last_lon) = ($lat_e5, $lon_e5);
$encoded_points .=
$self->encode_signed_number($delta_lat) .
$self->encode_signed_number($delta_lon);
} else {
# warn "skipping point: $lat, $lon";
}
}
$self->encoded_points( $encoded_points );
}
# Use compute_level to march down the list of points and encode the levels.
# Like encode_points, we ignore points whose distance (in dists) is undefined.
# See http://code.google.com/apis/maps/documentation/polylinealgorithm.html
sub encode_levels {
my $self = shift;
my $points = $self->points;
my $dists = $self->dists;
my $max_dist = $self->max_dist;
# Cache for performance:
my $num_levels = $self->num_levels;
my $num_levels_minus_1 = $num_levels - 1;
my $visible_threshold = $self->visible_threshold;
my $zoom_level_breaks = $self->zoom_level_breaks;
my $encoded_levels = "";
if ($self->force_endpoints) {
$encoded_levels .= $self->encode_number($num_levels_minus_1);
} else {
$encoded_levels .= $self->encode_number($num_levels_minus_1 - $self->compute_level($max_dist));
}
# Note: skip the first & last point:
for my $i (1 .. scalar(@$points) - 2) {
my $dist = $dists->[$i];
if (defined $dist) {
# Note: brought compute_level in-line as it was performing *really* slowly
#
# This computes the appropriate zoom level of a point in terms of it's
# distance from the relevant segment in the DP algorithm. Could be done
# in terms of a logarithm, but this approach makes it a bit easier to
# ensure that the level is not too large.
#my $level = $self->compute_level($dist);
my $level = 0;
if ($dist > $visible_threshold) {
while ($dist < $zoom_level_breaks->[$level]) {
$level++;
}
}
$encoded_levels .= $self->encode_number($num_levels_minus_1 - $level);
}
}
if ($self->force_endpoints) {
$encoded_levels .= $self->encode_number($num_levels_minus_1);
} else {
$encoded_levels .= $self->encode_number($num_levels_minus_1 - $self->compute_level($max_dist));
}
$self->encoded_levels( $encoded_levels );
}
# This computes the appropriate zoom level of a point in terms of it's
# distance from the relevant segment in the DP algorithm. Could be done
# in terms of a logarithm, but this approach makes it a bit easier to
# ensure that the level is not too large.
sub compute_level {
my ($self, $dist) = @_;
# Cache for performance:
my $zoom_level_breaks = $self->zoom_level_breaks;
my $level;
if ($dist > $self->visible_threshold) {
$level = 0;
while ($dist < $zoom_level_breaks->[$level]) {
$level++;
}
}
return $level;
}
# Based on the official google example
# http://code.google.com/apis/maps/documentation/include/polyline.js
sub encode_signed_number {
my ($self, $orig_num) = @_;
# 1. Take the initial signed value:
# 2. Take the decimal value and multiply it by 1e5, rounding the result:
# Note 1: we limit the number to 5 decimal places with sprintf to avoid
# perl's rounding errors (they can throw the line off by a big margin sometimes)
# From Geo::Google: use the correct floating point precision or else
# 34.06694 - 34.06698 will give you -3.999999999999999057E-5 which doesn't
# encode properly. -4E-5 encodes properly.
# Note 2: we use sprintf(%.0f ...) rather than int() for similar reasons
# (see perldoc -f int), though there's not much in it and the sprintf approach
# ends up doing more of a round() than a floor() in some cases:
# floor = -30 num=-30 *int=-29 1e5=-30 %3.5f=-0.00030 orig=-0.000300000000009959
# floor = 119 *num=120 int=119 1e5=120 %3.5f=0.00120 orig=0.0011999999999972
# Note 3: We don't use floor() to avoid a dependency on POSIX. And it
# doesn't round() anyway.
# do this in a series of steps so we can see what's going on in the debugger:
my $num3_5 = sprintf('%.5f', $orig_num)+0; # round at 5 decimal places
my $num_1e5 = $num3_5 * 1e5;
my $num = sprintf('%.0f', $num_1e5)+0; # think int(...)
# RT 49327: the signedness has to be determined *after* rounding
my $is_negative = $num < 0;
{
# 3. Convert the decimal value to binary. Note that a negative value
# must be calculated using its two's complement by inverting the
# binary value and adding one to the result.
# Note: perl ints are already binary, but bitwise operators work on
# the assumption they are unsigned, ie ~$num => one's complement.
# if we 'use integer' bitwise operands are treated as signed:
use integer; # force 2's complement
# 4. Left-shift the binary value one bit:
$num = $num << 1;
# 5. If the original decimal value is negative, invert this encoding:
# (see note on RT 49327 above)
if ($is_negative) {
$num = ~$num;
}
}
return $self->encode_number($num);
}
# Based on the official google example
# http://code.google.com/apis/maps/documentation/include/polyline.js
sub encode_number {
my ($self, $num) = @_;
no integer; # treat bitwise operands as unsigned
# 6. Break the binary value out into 5-bit chunks (starting from the right hand side):
# 7. Place the 5-bit chunks into reverse order:
# 8. OR each value with 0x20 if another bit chunk follows:
# 9. Convert each value to decimal:
# 10. Add 63 to each value:
my $encodeString = "";
while ($num >= 0x20) {
my $nextValue = (0x20 | ($num & 0x1f)) + 63;
$encodeString .= chr( $nextValue );
$num >>= 5;
}
my $finalValue = $num + 63;
$encodeString .= chr( $finalValue );
return $encodeString;
}
# Superficial validation of encoded points. Note that decode_points
# does not check that points are validated before decoding.
sub validate_encoded_points {
my ($class, $encoded) = @_;
return unless (defined $encoded && $encoded ne "");
my @ords = unpack "c*", $encoded;
my @out = grep { $_ < 63 || $_ > 127 } @ords;
return if @out;
return 1;
}
# Decode an encoded polyline into a list of lat/lng tuples.
# adapted from http://code.google.com/apis/maps/documentation/include/polyline.js
sub decode_points {
my ($class, $encoded) = @_;
my $len = length( $encoded );
my @array;
my $index = 0;
my $lat = 0;
my $lon = 0;
while ($index < $len) {
{
my $b;
my $shift = 0;
my $result = 0;
do {
$b = ord( substr( $encoded, $index++, 1 ) ) - 63;
$result |= ($b & 0x1f) << $shift;
$shift += 5;
} while ($b >= 0x20);
my $dlat = $result >> 1;
if ($result & 1) {
use integer; # force 2's complement
$dlat = ~$dlat;
}
$lat += $dlat;
# cut-n-paste to improve performance?
$shift = 0;
$result = 0;
do {
$b = ord( substr( $encoded, $index++, 1 ) ) - 63;
$result |= ($b & 0x1f) << $shift;
$shift += 5;
} while ($b >= 0x20);
my $dlon = $result >> 1;
if ($result & 1) {
use integer; # force 2's complement
$dlon = ~$dlon;
}
$lon += $dlon;
}
push @array, { lat => $lat * 1e-5, lon => $lon * 1e-5 };
}
return \@array;
}
# Decode an encoded levels string into a list of levels.
# adapted from http://code.google.com/apis/maps/documentation/include/polyline.js
sub decode_levels {
my ($class, $encoded) = @_;
my $len = length( $encoded );
my @levels;
for (my $index = 0; $index < $len; $index++) {
my $level = ord( substr( $encoded, $index, 1 ) ) - 63;
push @levels, $level;
}
return \@levels;
}
1;
__END__
=head1 DESCRIPTION
This module encodes a list of lat/lon points representing a polyline into a
format for use with Google Maps. This format is described here:
L
The module is a port of Mark McClure's C with some tweaks.
The original can be found here:
L
=head1 CONSTRUCTOR & ACCESSORS
=over 4
=item new( [%args] )
Create a new encoder. Arguments are optional and correspond to the accessor
with the same name: L, L, L,
L, etc...
Note: there's nothing stopping you from setting these properties each time you
L a polyline.
=item num_levels
How many different levels of magnification the polyline has.
Default: 18.
=item zoom_factor
The change in magnification between those levels (see L).
Default: 2.
=item visible_threshold
Indicates the length of a barely visible object at the highest zoom level.
Default: 0.00001. err.. units.
=item force_endpoints
Indicates whether or not the endpoints should be visible at all zoom levels.
force_endpoints is. Probably should stay true regardless.
Default: 1=true.
=item escape_encoded_points
Indicates whether or not the encoded points should have escape characters
escaped, eg:
$points =~ s/\\/\\\\/g;
This is useful if you'll be evalling the resulting strings, or copying them into
a static document.
B don't turn this on if you'll be passing the encoded points straight
on to your application, or you'll get unexpected results (ie: lines that start
out right, but end up horribly wrong). It may even crash your browser.
Default: 0=false.
=item lons_first
Specifies the order in which coordinates passed as arrayrefs to L should be
interpreted:
# false: lat, lon
$encoder->encode([
[ 38.5, -120.2 ],
[ 40.7, -120.95 ],
]);
# true: lon, lat
$encoder->encode([
[ -120.2, 38.5 ],
[ -120.95, 40.7 ],
]);
Default: 0 = lat,lon
(Yes, the default feels wrong to the mathematician in me, but that's how Google
Maps do it, so for sake of consistency...)
=back
=head1 METHODS
=over 4
=item encode( \@points );
Encode the points into a string for use with Google Maps C
using a variant of the Douglas-Peucker algorithm to set levels, and the Polyline
encoding algorithm defined by Google.
Expects a reference to a C<@points> array:
[
{ lat => 38.5, lon => -120.2 },
{ lat => 40.7, lon => -120.95 },
{ lat => 43.252, lon => -126.453 },
];
The individual points can also be given as arrayrefs:
[
[ 38.5, -120.2 ],
[ 40.7, -120.95 ],
[ 43.252, -126.453 ],
];
I I tried to avoid this initially, because there's no standard for which
should come first: Is or Is. But I agree, it's more convenient in
some cases so I've given you enough rope to hang yourself... Of course you can
easily unhang yourself: the order for arrayrefs defaults to C, but
you can change that by setting L.
Returns a hashref containing:
{
points => 'encoded points string',
levels => 'encoded levels string',
num_levels => int($num_levels),
zoom_factor => int($zoom_factor),
};
You can then use the L modules (or XML, or whatever) to pass the encoded
values to your Javascript application for use there.
=item decode_points( $encoded_polyline );
Given an encoded polyline, returns the points:
[
{ lat => 38.5, lon => -120.2 },
{ lat => 40.7, lon => -120.95 },
{ lat => 43.252, lon => -126.453 },
];
Note that these will likely be slightly different from the original points due
to rounding errors during both L & decoding.
=item decode_levels( $encoded_levels );
Given encoded levels, returns the levels:
[ 17, 16, 17 ]
=back
=head1 WHY DO MY LINES LOOK FUNNY?
Do your lines all go through the north pole? Maybe you have your Is &
Is mixed up... If so and you're using point arrays, you can set
L.
Do your points not show up at particular zoom levels? That's not a bug, it's a
feature! Try playing with L.
Do your encoded lines cause your browser to crash? Sounds like a bug - file
it!
=head1 BUGS
L
=head1 TODO
More optimization: encoding big files is *slow*. Maybe XS implementation if
there's enough demand for it?
=head1 AUTHORS
Robert Rothenberg
Steve Purkis
Ported from Mark McClure's C which can be found here:
L
Some encoding ideas borrowed from L.
Bringing distance calcs in-line was Joel Rosenberg's idea:
L
=head1 COPYRIGHT
Copyright (c) 2008-2010 Steve Purkis.
Released under the same terms as Perl itself.
=head1 SEE ALSO
L,
L
(JavaScript implementation),
L (similar implementation in perl),
L,
L
=cut