mapnik/src/placement_finder.cpp

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/*****************************************************************************
*
* This file is part of Mapnik (c++ mapping toolkit)
*
* Copyright (C) 2006 Artem Pavlenko
* Copyright (C) 2006 10East Corp.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
*****************************************************************************/
//$Id$
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//mapnik
#include <mapnik/placement_finder.hpp>
#include <mapnik/geometry.hpp>
#include <mapnik/text_path.hpp>
// agg
#include "agg_path_length.h"
#include "agg_conv_clip_polyline.h"
// boost
#include <boost/shared_ptr.hpp>
#include <boost/utility.hpp>
#include <boost/ptr_container/ptr_vector.hpp>
#include <boost/thread/mutex.hpp>
#include <boost/tuple/tuple.hpp>
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//stl
#include <string>
#include <vector>
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#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
namespace mapnik
{
placement::placement(string_info & info_,
shield_symbolizer const& sym, bool has_dimensions_)
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: info(info_),
displacement_(sym.get_displacement()),
label_placement(sym.get_label_placement()),
wrap_width(sym.get_wrap_width()),
text_ratio(sym.get_text_ratio()),
label_spacing(sym.get_label_spacing()),
label_position_tolerance(sym.get_label_position_tolerance()),
force_odd_labels(sym.get_force_odd_labels()),
max_char_angle_delta(sym.get_max_char_angle_delta()),
minimum_distance(sym.get_minimum_distance()),
avoid_edges(sym.get_avoid_edges()),
has_dimensions(has_dimensions_),
allow_overlap(false),
dimensions(std::make_pair(sym.get_image()->width(),
sym.get_image()->height()))
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{
}
placement::placement(string_info & info_,
text_symbolizer const& sym)
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: info(info_),
displacement_(sym.get_displacement()),
label_placement(sym.get_label_placement()),
wrap_width(sym.get_wrap_width()),
text_ratio(sym.get_text_ratio()),
label_spacing(sym.get_label_spacing()),
label_position_tolerance(sym.get_label_position_tolerance()),
force_odd_labels(sym.get_force_odd_labels()),
max_char_angle_delta(sym.get_max_char_angle_delta()),
minimum_distance(sym.get_minimum_distance()),
avoid_edges(sym.get_avoid_edges()),
has_dimensions(false),
allow_overlap(sym.get_allow_overlap()),
dimensions()
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{
}
placement::~placement()
{
}
template<typename T>
std::pair<double, double> get_position_at_distance(double target_distance, T & shape_path)
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{
double x1 = 0.0;
double y1 = 0.0;
double x2 = 0.0;
double y2 = 0.0;
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double distance = 0.0;
bool first = true;
unsigned cmd;
double x = 0.0;
double y = 0.0;
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shape_path.rewind(0);
while (!agg::is_stop(cmd = shape_path.vertex(&x2,&y2)))
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{
if (first || agg::is_move_to(cmd))
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{
first = false;
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}
else
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{
double dx = x2-x1;
double dy = y2-y1;
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double segment_length = std::sqrt(dx*dx + dy*dy);
distance +=segment_length;
if (distance > target_distance)
{
x = x2 - dx * (distance - target_distance)/segment_length;
y = y2 - dy * (distance - target_distance)/segment_length;
break;
}
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}
x1 = x2;
y1 = y2;
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}
return std::pair<double, double>(x, y);
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}
template<typename T>
double get_total_distance(T & shape_path)
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{
return agg::path_length(shape_path);
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}
template <typename DetectorT>
placement_finder<DetectorT>::placement_finder(DetectorT & detector)
: detector_(detector),
dimensions_(detector_.extent())
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{
}
template <typename DetectorT>
template <typename T>
void placement_finder<DetectorT>::find_point_placements(placement & p, T & shape_path)
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{
unsigned cmd;
double new_x = 0.0;
double new_y = 0.0;
double old_x = 0.0;
double old_y = 0.0;
bool first = true;
double total_distance = get_total_distance<T>(shape_path);
shape_path.rewind(0);
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if (distance == 0) //Point data, not a line
{
double x, y;
shape_path.vertex(&x,&y);
find_point_placement(p, x, y);
return;
}
int num_labels = 1;
if (p.label_spacing > 0)
num_labels = static_cast<int> (floor(total_distance / p.label_spacing));
if (p.force_odd_labels && num_labels%2 == 0)
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num_labels--;
if (num_labels <= 0)
num_labels = 1;
double distance = 0.0; // distance from last label
double spacing = total_distance / num_labels;
double target_distance = spacing / 2; // first label should be placed at half the spacing
while (!agg::is_stop(cmd = shape_path.vertex(&new_x,&new_y))) //For each node in the shape
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{
if (first || agg::is_move_to(cmd)) //Don't do any processing if it is the first node
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{
first = false;
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}
else
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{
//Add the length of this segment to the total we have saved up
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double segment_length = std::sqrt(std::pow(old_x-new_x,2) + std::pow(old_y-new_y,2)); //Pythagoras
distance += segment_length;
//While we have enough distance to place text in
while (distance > target_distance)
{
//Try place at the specified place
double new_weight = (segment_length - (distance - target_distance))/segment_length;
find_point_placement(p, old_x + (new_x-old_x)*new_weight, old_y + (new_y-old_y)*new_weight);
distance -= target_distance; //Consume the spacing gap we have used up
target_distance = spacing; //Need to reset the target_distance as it is spacing/2 for the first label.
}
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}
old_x = new_x;
old_y = new_y;
}
}
template <typename DetectorT>
void placement_finder<DetectorT>::find_point_placement(placement & p,
double label_x,
double label_y,
vertical_alignment_e valign)
{
double x, y;
std::auto_ptr<placement_element> current_placement(new placement_element);
std::pair<double, double> string_dimensions = p.info.get_dimensions();
double string_width = string_dimensions.first;
double string_height = string_dimensions.second;
// check if we need to wrap the string
double wrap_at = string_width + 1;
if (p.wrap_width && string_width > p.wrap_width)
{
if (p.text_ratio)
for (int i = 1; ((wrap_at = string_width/i)/(string_height*i)) > p.text_ratio && (string_width/i) > p.wrap_width; ++i);
else
wrap_at = p.wrap_width;
}
// work out where our line breaks need to be
std::vector<int> line_breaks;
std::vector<double> line_widths;
std::vector<double> line_heights;
if (wrap_at < string_width && p.info.num_characters() > 0)
{
int last_space = 0;
string_width = 0;
string_height = 0;
double line_width = 0;
double line_height = 0;
double word_width = 0;
double word_height = 0;
for (unsigned int ii = 0; ii < p.info.num_characters(); ii++)
{
character_info ci;
ci = p.info.at(ii);
unsigned c = ci.character;
word_width += ci.width;
word_height = word_height > ci.height ? word_height : ci.height;
if (c == ' ')
{
last_space = ii;
line_width += word_width;
line_height = line_height > word_height ? line_height : word_height;
word_width = 0;
word_height = 0;
}
if (line_width > 0 && line_width > wrap_at)
{
// Remove width of breaking space character since it is not rendered
line_width -= ci.width;
string_width = string_width > line_width ? string_width : line_width;
string_height += line_height;
line_breaks.push_back(last_space);
line_widths.push_back(line_width);
line_heights.push_back(line_height);
ii = last_space;
line_width = 0;
line_height = 0;
word_width = 0;
word_height = 0;
}
}
line_width += word_width;
line_height = line_height > word_height ? line_height : word_height;
string_width = string_width > line_width ? string_width : line_width;
string_height += line_height;
line_breaks.push_back(p.info.num_characters() + 1);
line_widths.push_back(line_width);
line_heights.push_back(line_height);
}
if (line_breaks.size() == 0)
{
line_breaks.push_back(p.info.num_characters() + 1);
line_widths.push_back(string_width);
line_heights.push_back(string_height);
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}
p.info.set_dimensions(string_width, string_height);
unsigned int line_number = 0;
unsigned int index_to_wrap_at = line_breaks[line_number];
double line_width = line_widths[line_number];
double line_height = line_heights[line_number];
current_placement->starting_x = label_x;
if (valign == BOTTOM)
{
current_placement->starting_y = label_y;
}
else if (valign == MIDDLE)
{
current_placement->starting_y = label_y - 0.5 * (line_heights.size() - 1) * line_height ;
}
else // TOP
{
current_placement->starting_y = label_y - line_heights.size() * line_height;
}
current_placement->starting_x += boost::tuples::get<0>(p.displacement_);
current_placement->starting_y += boost::tuples::get<1>(p.displacement_);
x = -line_width/2.0;
y = -line_height/2.0;
for (unsigned i = 0; i < p.info.num_characters(); i++)
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{
character_info ci;
ci = p.info.at(i);
unsigned c = ci.character;
if (i == index_to_wrap_at)
{
index_to_wrap_at = line_breaks[++line_number];
line_width = line_widths[line_number];
line_height = line_heights[line_number];
y -= line_height;
x = -line_width/2.0;
continue;
}
else
{
current_placement->add_node(c, x, y, 0.0);
Envelope<double> e;
if (p.has_dimensions)
{
e.init(current_placement->starting_x - (p.dimensions.first/2.0),
current_placement->starting_y - (p.dimensions.second/2.0),
current_placement->starting_x + (p.dimensions.first/2.0),
current_placement->starting_y + (p.dimensions.second/2.0));
}
else
{
e.init(current_placement->starting_x + x,
current_placement->starting_y - y,
current_placement->starting_x + x + ci.width,
current_placement->starting_y - y - ci.height);
}
if (!dimensions_.intersects(e) ||
(!p.allow_overlap && !detector_.has_point_placement(e,
p.minimum_distance)))
{
return;
}
if (p.avoid_edges && !dimensions_.contains(e)) return;
p.envelopes.push(e);
}
x += ci.width;
}
p.placements.push_back(current_placement.release());
//update_detector(p);
}
template <typename DetectorT>
template <typename PathT>
void placement_finder<DetectorT>::find_line_placements(placement & p, PathT & shape_path)
{
unsigned cmd;
double new_x = 0.0;
double new_y = 0.0;
double old_x = 0.0;
double old_y = 0.0;
bool first = true;
//Pre-Cache all the path_positions and path_distances
//This stops the PathT from having to do multiple re-projections if we need to reposition ourself
// and lets us know how many points are in the shape.
std::vector<vertex2d> path_positions;
std::vector<double> path_distances; // distance from node x-1 to node x
double total_distance = 0;
shape_path.rewind(0);
while (!agg::is_stop(cmd = shape_path.vertex(&new_x,&new_y))) //For each node in the shape
{
if (!first && agg::is_line_to(cmd))
{
double dx = old_x - new_x;
double dy = old_y - new_y;
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double distance = std::sqrt(dx*dx + dy*dy);
total_distance += distance;
path_distances.push_back(distance);
}
else
{
path_distances.push_back(0);
}
first = false;
path_positions.push_back(vertex2d(new_x, new_y, cmd));
old_x = new_x;
old_y = new_y;
}
//Now path_positions is full and total_distance is correct
//shape_path shouldn't be used from here
double distance = 0.0;
std::pair<double, double> string_dimensions = p.info.get_dimensions();
double string_width = string_dimensions.first;
double displacement = boost::tuples::get<1>(p.displacement_); // displace by dy
//Calculate a target_distance that will place the labels centered evenly rather than offset from the start of the linestring
if (total_distance < string_width) //Can't place any strings
return;
//If there is no spacing then just do one label, otherwise calculate how many there should be
int num_labels = 1;
if (p.label_spacing > 0)
num_labels = static_cast<int> (floor(total_distance / (p.label_spacing + string_width)));
if (p.force_odd_labels && num_labels%2 == 0)
num_labels--;
if (num_labels <= 0)
num_labels = 1;
//Now we know how many labels we are going to place, calculate the spacing so that they will get placed evenly
double spacing = total_distance / num_labels;
double target_distance = (spacing - string_width) / 2; // first label should be placed at half the spacing
//Calculate or read out the tolerance
double tolerance_delta, tolerance;
if (p.label_position_tolerance > 0)
{
tolerance = p.label_position_tolerance;
tolerance_delta = std::max ( 1.0, p.label_position_tolerance/100.0 );
}
else
{
tolerance = spacing/2.0;
tolerance_delta = std::max ( 1.0, spacing/100.0 );
}
first = true;
for (unsigned index = 0; index < path_positions.size(); index++) //For each node in the shape
{
cmd = path_positions[index].cmd;
new_x = path_positions[index].x;
new_y = path_positions[index].y;
if (first || agg::is_move_to(cmd)) //Don't do any processing if it is the first node
{
first = false;
}
else
{
//Add the length of this segment to the total we have saved up
double segment_length = path_distances[index];
distance += segment_length;
//While we have enough distance to place text in
while (distance > target_distance)
{
for (double diff = 0; diff < tolerance; diff += tolerance_delta)
{
for(int dir = -1; dir < 2; dir+=2) //-1, +1
{
//Record details for the start of the string placement
int orientation = 0;
std::auto_ptr<placement_element> current_placement = get_placement_offset(p, path_positions, path_distances, orientation, index, segment_length - (distance - target_distance) + (diff*dir));
//We were unable to place here
if (current_placement.get() == NULL)
continue;
//Apply displacement
//NOTE: The text is centered on the line in get_placement_offset, so we are offsetting from there
if (displacement != 0)
{
//Average the angle of all characters and then offset them all by that angle
//NOTE: This probably calculates a bad angle due to going around the circle, test this!
double anglesum = 0;
for (unsigned i = 0; i < current_placement->nodes_.size(); i++)
{
anglesum += current_placement->nodes_[i].angle;
}
anglesum /= current_placement->nodes_.size(); //Now it is angle average
//Offset all the characters by this angle
for (unsigned i = 0; i < current_placement->nodes_.size(); i++)
{
current_placement->nodes_[i].x += displacement*cos(anglesum+M_PI/2);
current_placement->nodes_[i].y += displacement*sin(anglesum+M_PI/2);
}
}
bool status = test_placement(p, current_placement, orientation);
if (status) //We have successfully placed one
{
p.placements.push_back(current_placement.release());
update_detector(p);
//Totally break out of the loops
diff = tolerance;
break;
}
else
{
//If we've failed to place, remove all the envelopes we've added up
while (!p.envelopes.empty())
p.envelopes.pop();
}
//Don't need to loop twice when diff = 0
if (diff == 0)
break;
}
}
distance -= target_distance; //Consume the spacing gap we have used up
target_distance = spacing; //Need to reset the target_distance as it is spacing/2 for the first label.
}
}
old_x = new_x;
old_y = new_y;
}
}
template <typename DetectorT>
std::auto_ptr<placement_element> placement_finder<DetectorT>::get_placement_offset(placement & p, const std::vector<vertex2d> &path_positions, const std::vector<double> &path_distances, int &orientation, unsigned index, double distance)
{
//Check that the given distance is on the given index and find the correct index and distance if not
while (distance < 0 && index > 1)
{
index--;
distance += path_distances[index];
}
if (index <= 1 && distance < 0) //We've gone off the start, fail out
return std::auto_ptr<placement_element>(NULL);
//Same thing, checking if we go off the end
while (index < path_distances.size() && distance > path_distances[index])
{
distance -= path_distances[index];
index++;
}
if (index >= path_distances.size())
return std::auto_ptr<placement_element>(NULL);
//Keep track of the initial index,distance incase we need to re-call get_placement_offset
const unsigned initial_index = index;
const double initial_distance = distance;
std::auto_ptr<placement_element> current_placement(new placement_element);
double string_height = p.info.get_dimensions().second;
double old_x = path_positions[index-1].x;
double old_y = path_positions[index-1].y;
double new_x = path_positions[index].x;
double new_y = path_positions[index].y;
double dx = new_x - old_x;
double dy = new_y - old_y;
double segment_length = path_distances[index];
if (segment_length == 0) {
// Not allowed to place across on 0 length segments or discontinuities
return std::auto_ptr<placement_element>(NULL);
}
current_placement->starting_x = old_x + dx*distance/segment_length;
current_placement->starting_y = old_y + dy*distance/segment_length;
double angle = atan2(-dy, dx);
bool orientation_forced = (orientation != 0); //Wether the orientation was set by the caller
if (!orientation_forced)
orientation = (angle > 0.55*M_PI || angle < -0.45*M_PI) ? -1 : 1;
unsigned upside_down_char_count = 0; //Count of characters that are placed upside down.
for (unsigned i = 0; i < p.info.num_characters(); ++i)
{
character_info ci;
unsigned c;
double last_character_angle = angle;
// grab the next character according to the orientation
ci = orientation > 0 ? p.info.at(i) : p.info.at(p.info.num_characters() - i - 1);
c = ci.character;
//Coordinates this character will start at
if (segment_length == 0) {
// Not allowed to place across on 0 length segments or discontinuities
return std::auto_ptr<placement_element>(NULL);
}
double start_x = old_x + dx*distance/segment_length;
double start_y = old_y + dy*distance/segment_length;
//Coordinates this character ends at, calculated below
double end_x = 0;
double end_y = 0;
if (segment_length - distance >= ci.width)
{
//if the distance remaining in this segment is enough, we just go further along the segment
distance += ci.width;
end_x = old_x + dx*distance/segment_length;
end_y = old_y + dy*distance/segment_length;
}
else
{
//If there isn't enough distance left on this segment
// then we need to search untill we find the line segment that ends further than ci.width away
do
{
old_x = new_x;
old_y = new_y;
index++;
if (index >= path_positions.size()) //Bail out if we run off the end of the shape
{
//std::clog << "FAIL: Out of space" << std::endl;
return std::auto_ptr<placement_element>(NULL);
}
new_x = path_positions[index].x;
new_y = path_positions[index].y;
dx = new_x - old_x;
dy = new_y - old_y;
segment_length = path_distances[index];
}
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while (std::sqrt(std::pow(start_x - new_x, 2) + std::pow(start_y - new_y, 2)) < ci.width); //Distance from start_ to new_
//Calculate the position to place the end of the character on
find_line_circle_intersection(
start_x, start_y, ci.width,
old_x, old_y, new_x, new_y,
end_x, end_y); //results are stored in end_x, end_y
//Need to calculate distance on the new segment
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distance = std::sqrt(std::pow(old_x - end_x, 2) + std::pow(old_y - end_y, 2));
}
//Calculate angle from the start of the character to the end based on start_/end_ position
angle = atan2(start_y-end_y, end_x-start_x);
//Test last_character_angle vs angle
// since our rendering angle has changed then check against our
// max allowable angle change.
double angle_delta = last_character_angle - angle;
// normalise between -180 and 180
while (angle_delta > M_PI)
angle_delta -= 2*M_PI;
while (angle_delta < -M_PI)
angle_delta += 2*M_PI;
if (p.max_char_angle_delta > 0 &&
fabs(angle_delta) > p.max_char_angle_delta*(M_PI/180))
{
//std::clog << "FAIL: Too Bendy!" << std::endl;
return std::auto_ptr<placement_element>(NULL);
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}
double render_angle = angle;
double render_x = start_x;
double render_y = start_y;
//Center the text on the line
render_x -= (((double)string_height/2.0) - 1.0)*cos(render_angle+M_PI/2);
render_y += (((double)string_height/2.0) - 1.0)*sin(render_angle+M_PI/2);
if (orientation < 0)
{
// rotate in place
render_x += ci.width*cos(render_angle) - (string_height-2)*sin(render_angle);
render_y -= ci.width*sin(render_angle) + (string_height-2)*cos(render_angle);
render_angle += M_PI;
}
current_placement->add_node(c,render_x - current_placement->starting_x,
-render_y + current_placement->starting_y,
render_angle);
//Normalise to 0 <= angle < 2PI
while (render_angle >= 2*M_PI)
render_angle -= 2*M_PI;
while (render_angle < 0)
render_angle += 2*M_PI;
if (render_angle > M_PI/2 && render_angle < 1.5*M_PI)
upside_down_char_count++;
}
//If we placed too many characters upside down
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if (upside_down_char_count >= p.info.num_characters()/2.0)
{
//if we auto-detected the orientation then retry with the opposite orientation
if (!orientation_forced)
{
orientation = -orientation;
current_placement = get_placement_offset(p, path_positions, path_distances, orientation, initial_index, initial_distance);
}
else
{
//Otherwise we have failed to find a placement
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//std::clog << "FAIL: Double upside-down!" << std::endl;
return std::auto_ptr<placement_element>(NULL);
}
}
return current_placement;
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}
template <typename DetectorT>
bool placement_finder<DetectorT>::test_placement(placement & p, const std::auto_ptr<placement_element> & current_placement, const int & orientation)
{
std::pair<double, double> string_dimensions = p.info.get_dimensions();
double string_height = string_dimensions.second;
//Create and test envelopes
bool status = true;
for (unsigned i = 0; i < p.info.num_characters(); ++i)
{
// grab the next character according to the orientation
character_info ci = orientation > 0 ? p.info.at(i) : p.info.at(p.info.num_characters() - i - 1);
int c;
double x, y, angle;
current_placement->vertex(&c, &x, &y, &angle);
x = current_placement->starting_x + x;
y = current_placement->starting_y - y;
if (orientation < 0)
{
// rotate in place
x += ci.width*cos(angle) - (string_height-2)*sin(angle);
y -= ci.width*sin(angle) + (string_height-2)*cos(angle);
angle += M_PI;
}
Envelope<double> e;
if (p.has_dimensions)
{
e.init(x, y, x + p.dimensions.first, y + p.dimensions.second);
}
else
{
// put four corners of the letter into envelope
e.init(x, y, x + ci.width*cos(angle),
y - ci.width*sin(angle));
e.expand_to_include(x - ci.height*sin(angle),
y - ci.height*cos(angle));
e.expand_to_include(x + (ci.width*cos(angle) - ci.height*sin(angle)),
y - (ci.width*sin(angle) + ci.height*cos(angle)));
}
if (!dimensions_.intersects(e) ||
!detector_.has_placement(e, p.info.get_string(), p.minimum_distance))
{
//std::clog << "No Intersects:" << !dimensions_.intersects(e) << ": " << e << " @ " << dimensions_ << std::endl;
//std::clog << "No Placements:" << !detector_.has_placement(e, p.info.get_string(), p.minimum_distance) << std::endl;
status = false;
break;
}
if (p.avoid_edges && !dimensions_.contains(e))
{
//std::clog << "Fail avoid edges" << std::endl;
status = false;
break;
}
p.envelopes.push(e);
}
current_placement->rewind();
return status;
}
template <typename DetectorT>
void placement_finder<DetectorT>::find_line_circle_intersection(
const double &cx, const double &cy, const double &radius,
const double &x1, const double &y1, const double &x2, const double &y2,
double &ix, double &iy)
{
double dx = x2 - x1;
double dy = y2 - y1;
double A = dx * dx + dy * dy;
double B = 2 * (dx * (x1 - cx) + dy * (y1 - cy));
double C = (x1 - cx) * (x1 - cx) + (y1 - cy) * (y1 - cy) - radius * radius;
double det = B * B - 4 * A * C;
if (A <= 0.0000001 || det < 0)
{
//Should never happen
//' No real solutions.
return;
}
else if (det == 0)
{
//Could potentially happen....
//One solution.
double t = -B / (2 * A);
ix = x1 + t * dx;
iy = y1 + t * dy;
return;
}
else
{
//Two solutions.
//Always use the 1st one
//We only really have one solution here, as we know the line segment will start in the circle and end outside
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double t = (-B + std::sqrt(det)) / (2 * A);
ix = x1 + t * dx;
iy = y1 + t * dy;
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//t = (-B - std::sqrt(det)) / (2 * A);
//ix = x1 + t * dx;
//iy = y1 + t * dy;
return;
}
}
template <typename DetectorT>
void placement_finder<DetectorT>::update_detector(placement & p)
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{
while (!p.envelopes.empty())
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{
Envelope<double> e = p.envelopes.front();
detector_.insert(e, p.info.get_string());
p.envelopes.pop();
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}
}
template <typename DetectorT>
void placement_finder<DetectorT>::clear()
{
detector_.clear();
}
typedef coord_transform2<CoordTransform,geometry2d> PathType;
typedef label_collision_detector4 DetectorType;
template class placement_finder<DetectorType>;
template void placement_finder<DetectorType>::find_point_placements<PathType> (placement&, PathType & );
template void placement_finder<DetectorType>::find_line_placements<PathType> (placement&, PathType & );
} // namespace