/*****************************************************************************
 * 
 * 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
 *
 *****************************************************************************/

//$Id$

//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>

//stl
#include <string>
#include <vector>

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

namespace mapnik
{
   placement::placement(string_info & info_, 
                        shield_symbolizer const& sym)
      : 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(true), 
        dimensions(std::make_pair(sym.get_image()->width(),
                                  sym.get_image()->height()))
   {
   }
   
   placement::placement(string_info & info_,
                        text_symbolizer const& sym)
      : 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),
        dimensions()
   {
   }
   placement::~placement()
   {
   }
   
   template<typename T>
   std::pair<double, double> get_position_at_distance(double target_distance, T & shape_path)
   {
      double x1 = 0.0;
      double y1 = 0.0;
      double x2 = 0.0;
      double y2 = 0.0;
      double distance = 0.0;
      bool first = true;
      unsigned cmd;
      double x = 0.0;
      double y = 0.0;
      shape_path.rewind(0);
      while (!agg::is_stop(cmd = shape_path.vertex(&x2,&y2)))
      {
         if (first || agg::is_move_to(cmd))
         {
            first = false;
         }
         else
         {
            double dx = x2-x1;
            double dy = y2-y1;
            
            double segment_length = ::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;
            }
         }
         x1 = x2;
         y1 = y2;
      }
      return std::pair<double, double>(x, y);
   }
   
   template<typename T>
   double get_total_distance(T & shape_path)
   {
      return agg::path_length(shape_path);
   }
   
   template <typename DetectorT>
   placement_finder<DetectorT>::placement_finder(DetectorT & detector)
      : detector_(detector),
        dimensions_(detector_.extent())
   {
   }

   template <typename DetectorT>
   void placement_finder<DetectorT>::get_ideal_placements(placement & p, double distance, std::vector<double> & ideal_label_distances)
   {
      std::pair<double, double> string_dimensions = p.info.get_dimensions();
      double string_width = string_dimensions.first;
    
      if (p.label_placement == LINE_PLACEMENT && string_width > distance)
      {
         //Empty!
         return ;
      }
      
      int num_labels = 0;
      if (p.label_spacing && p.label_placement == LINE_PLACEMENT)
      {
         num_labels = static_cast<int> (floor(distance / (p.label_spacing + string_width)));
      }
      else if (p.label_spacing && p.label_placement == POINT_PLACEMENT)
      {
         num_labels = static_cast<int> (floor(distance / p.label_spacing));
      }
      
      if (p.force_odd_labels && num_labels%2 == 0)
         num_labels--;
      if (num_labels <= 0)
         num_labels = 1;


      double ideal_spacing = distance/num_labels;
      
      double middle; //try draw text centered
      if (p.label_placement == LINE_PLACEMENT)
        middle = (distance / 2.0) - (string_width/2.0);
      else //  (p.label_placement == point_placement)
        middle = distance / 2.0;
		
      if (num_labels % 2) //odd amount of labels
      {
         for (int a = 0; a < (num_labels+1)/2; a++)
         {
            ideal_label_distances.push_back(middle - (a*ideal_spacing));
	
            if (a != 0)
               ideal_label_distances.push_back(middle + (a*ideal_spacing));
         }
      }
      else //even amount of labels
      {
         for (int a = 0; a < num_labels/2; a++)
         {
            ideal_label_distances.push_back(middle - (ideal_spacing/2.0) - (a*ideal_spacing));
            ideal_label_distances.push_back(middle + (ideal_spacing/2.0) + (a*ideal_spacing));
         }
      }
      
      if (p.label_position_tolerance == 0)
      {
         p.label_position_tolerance = unsigned(ideal_spacing/2.0);
      }
   }
   
   template <typename DetectorT>
   template <typename T>
   void placement_finder<DetectorT>::find_placements(placement & p, T & shape_path)
   {
      double distance = get_total_distance<T>(shape_path);
      std::vector<double> ideal_label_distances;
      get_ideal_placements(p,distance,ideal_label_distances);
      std::vector<double>::const_iterator itr = ideal_label_distances.begin();
      std::vector<double>::const_iterator end = ideal_label_distances.end();
      for (; itr != end; ++itr)
      {
               
         if ((p.label_placement == LINE_PLACEMENT &&
              build_path_follow(p, *itr , shape_path ) ) ||
             (p.label_placement == POINT_PLACEMENT &&
              build_path_horizontal(p, *itr, shape_path)) )
         {
            update_detector(p);
            break;
         }
      }    
   }
   
   template <typename DetectorT>
   void placement_finder<DetectorT>::find_point_placement(placement & p, 
                                                          double label_x, double label_y)
   {
      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;
      if (wrap_at < string_width && p.info.num_characters() > 0)
      {
         int line_count=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;
            ++line_count;
        
            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)
            {
               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);
               ii = last_space;
               line_count = 0;
               line_width = 0;
               line_height = 0;
               word_width = 0;
               word_height = 0;
            }
         }
         line_width += word_width;
         string_width = string_width > line_width ? string_width : line_width;
         line_breaks.push_back(p.info.num_characters() + 1);
         line_widths.push_back(line_width);
      }
      if (line_breaks.size() == 0)
      {
         line_breaks.push_back(p.info.num_characters() + 1);
         line_widths.push_back(string_width);
      }
        
      p.info.set_dimensions(string_width, string_height);
      
       
      current_placement->starting_x = label_x;
      current_placement->starting_y = label_y;
      
      current_placement->starting_x += boost::tuples::get<0>(p.displacement_);
      current_placement->starting_y += boost::tuples::get<1>(p.displacement_); 
      
      double line_height = 0;
      unsigned int line_number = 0;
      unsigned int index_to_wrap_at = line_breaks[line_number];
      double line_width = line_widths[line_number];
    
      x = -line_width/2.0 - 1.0;
      y = -string_height/2.0 + 1.0;
    
      for (unsigned i = 0; i < p.info.num_characters(); i++)
      {
         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];
            y -= line_height;
            x = -line_width/2.0;
            line_height = 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) || 
                !detector_.has_placement(e, p.info.get_string(), p.minimum_distance))
            {
               return;
            }
            
            if (p.avoid_edges && !dimensions_.contains(e)) return;
            
            p.envelopes.push(e);
         }
         x += ci.width;
         line_height = line_height > ci.height ? line_height : ci.height;
      }
      p.placements.push_back(current_placement.release());
      update_detector(p);
   }
   
   
   
   template <typename DetectorT>
   template <typename PathT>
   void placement_finder<DetectorT>::find_line_placement(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;
            double distance = 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/3.0;
         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);
      
      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];
      
      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);
      orientation = (angle > 0.55*M_PI || angle < -0.45*M_PI) ? -1 : 1;
      
      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
         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];
            }
            while (sqrt(pow(start_x - new_x, 2) + 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
            distance = sqrt(pow(old_x - end_x, 2) + 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);
         }
         
         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);
      }
      
      return current_placement;
   }
   
   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
         double t = (-B + sqrt(det)) / (2 * A);
         ix = x1 + t * dx;
         iy = y1 + t * dy;
         
         //t = (-B - sqrt(det)) / (2 * A);
         //ix = x1 + t * dx;
         //iy = y1 + t * dy;
         
         return;
      }
   }

   template <typename DetectorT>
   void placement_finder<DetectorT>::update_detector(placement & p)
   {
      while (!p.envelopes.empty())
      {
         Envelope<double> e = p.envelopes.front();
         detector_.insert(e, p.info.get_string());
         p.envelopes.pop();
      }
   }

   template <typename DetectorT>
   template <typename PathT>
   bool placement_finder<DetectorT>::build_path_follow(placement & p, 
                                                       double target_distance, 
                                                       PathT & shape_path)
   {
      double new_x = 0.0;
      double new_y = 0.0;
      double old_x = 0.0;
      double old_y = 0.0;
      double next_char_x = 0.0;
      double next_char_y = 0.0;
      
      double angle = 0.0;
      int orientation = 0;
      double displacement = boost::tuples::get<1>(p.displacement_); // displace by dy
  
      std::auto_ptr<placement_element> current_placement(new placement_element);
      
      double x = 0.0;
      double y = 0.0;
      
      double distance = 0.0;
      
      std::pair<double, double> string_dimensions = p.info.get_dimensions();
      double string_height = string_dimensions.second;
      
      // find the segment that our text should start on
      shape_path.rewind(0);
      
      unsigned cmd;
      bool first = true;
      while (!agg::is_stop(cmd = shape_path.vertex(&new_x,&new_y)))
      {
         if (first || agg::is_move_to(cmd))
         {
            first = false;
         }
         else
         {
            double dx = new_x - old_x;
            double dy = new_y - old_y;
            double segment_length = sqrt(dx*dx + dy*dy);
            distance += segment_length;
            if (distance > target_distance)
            {
               current_placement->starting_x = new_x - dx*(distance - target_distance)/segment_length;
               current_placement->starting_y = new_y - dy*(distance - target_distance)/segment_length;
               
               // angle text starts at and orientation
               angle = atan2(-dy, dx);
               orientation = (angle > 0.55*M_PI || angle < -0.45*M_PI) ? -1 : 1;
               
               distance -= target_distance;
               
               break;
            }
         }
         old_x = new_x;
         old_y = new_y;
      }
      
      // now find the placement of each character starting from our initial segment
      // determined above
      double last_angle = angle; 
      for (unsigned i = 0; i < p.info.num_characters(); ++i)
      {
         character_info ci;
         unsigned c;

         // 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;
    
         double angle_delta = 0;

         // if the distance remaining in this segment is less than the character width
         // move to the next segment
         if (distance <= ci.width) 
         {
            last_angle = angle;
            while (distance <= ci.width) 
            {
               double dx, dy;
               old_x = new_x;
               old_y = new_y;
                    
               if (agg::is_stop(shape_path.vertex(&new_x,&new_y)))
                  return false;
               dx = new_x - old_x;
               dy = new_y - old_y;
               
               angle = atan2(-dy, dx );
               distance += sqrt(dx*dx+dy*dy);
            }
            // since our rendering angle has changed then check against our
            // max allowable angle change.
            angle_delta = last_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))
            {
               return false;
            }
         }
            
         Envelope<double> e;
         if (p.has_dimensions)
         {
            e.init(x, y, x + p.dimensions.first, y + p.dimensions.second);
         }

         double render_angle = angle;

         x = new_x - (distance)*cos(angle);
         y = new_y + (distance)*sin(angle);
         //Center the text on the line, unless displacement != 0
         if (displacement == 0.0) {
           x -= (((double)string_height/2.0) - 1.0)*cos(render_angle+M_PI/2);
           y += (((double)string_height/2.0) - 1.0)*sin(render_angle+M_PI/2);
         } else if (displacement*orientation > 0.0) {
           x -= ((fabs(displacement) - (double)string_height) + 1.0)*cos(render_angle+M_PI/2);
           y += ((fabs(displacement) - (double)string_height) + 1.0)*sin(render_angle+M_PI/2);
         } else { // displacement < 0
           x -= ((fabs(displacement) + (double)string_height) - 1.0)*cos(render_angle+M_PI/2);
           y += ((fabs(displacement) + (double)string_height) - 1.0)*sin(render_angle+M_PI/2);
         }
         distance -= ci.width;
         next_char_x = ci.width*cos(render_angle);
         next_char_y = ci.width*sin(render_angle);

         double render_x = x;
         double render_y = y;

         if (!p.has_dimensions)
         {
            // put four corners of the letter into envelope
            e.init(render_x, render_y, render_x + ci.width*cos(render_angle), render_y - ci.width*sin(render_angle));
            e.expand_to_include(render_x - ci.height*sin(render_angle), render_y - ci.height*cos(render_angle));
            e.expand_to_include(render_x + (ci.width*cos(render_angle) - ci.height*sin(render_angle)), 
                                render_y - (ci.width*sin(render_angle) + ci.height*cos(render_angle)));
         }
         
         if (!dimensions_.intersects(e) || 
             !detector_.has_placement(e, p.info.get_string(), p.minimum_distance))
         {
            return false;
         }
         
         if (p.avoid_edges && !dimensions_.contains(e))
         {
            return false;
         }
         
         p.envelopes.push(e);

         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);
         x += next_char_x;
         y -= next_char_y;
      }
      
      p.placements.push_back(current_placement.release());
      
      return true;
   }

   template <typename DetectorT>
   template <typename PathT>
   bool placement_finder<DetectorT>::build_path_horizontal(placement & p, double target_distance, PathT & shape_path)
   {
      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;
      if (wrap_at < string_width && p.info.num_characters() > 0)
      {
         int line_count=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;
            ++line_count;
        
            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)
            {
               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);
               ii = last_space;
               line_count = 0;
               line_width = 0;
               line_height = 0;
               word_width = 0;
               word_height = 0;
            }
         }
         line_width += word_width;
         string_width = string_width > line_width ? string_width : line_width;
         line_breaks.push_back(p.info.num_characters() + 1);
         line_widths.push_back(line_width);
      }
      if (line_breaks.size() == 0)
      {
         line_breaks.push_back(p.info.num_characters() + 1);
         line_widths.push_back(string_width);
      }
        
      p.info.set_dimensions(string_width, string_height);
      
      std::pair<double, double> starting_pos = 
         get_position_at_distance<PathT>(target_distance,shape_path);
      current_placement->starting_x = starting_pos.first;
      current_placement->starting_y = starting_pos.second;
      
      double line_height = 0;
      unsigned int line_number = 0;
      unsigned int index_to_wrap_at = line_breaks[line_number];
      double line_width = line_widths[line_number];
    
      x = -line_width/2.0 - 1.0;
      y = -string_height/2.0 + 1.0;
    
      for (unsigned i = 0; i < p.info.num_characters(); i++)
      {
         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];
            y -= line_height;
            x = -line_width/2.0;
            line_height = 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) || 
                !detector_.has_placement(e, p.info.get_string(), p.minimum_distance))
            {
               return false;
            }
            
            if (p.avoid_edges && !dimensions_.contains(e))
            {
               return false;
            }
            
            p.envelopes.push(e);
         }
         x += ci.width;
         line_height = line_height > ci.height ? line_height : ci.height;
      }
      p.placements.push_back(current_placement.release());
      
      return true;
   }
   
   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_placements<PathType> (placement&, PathType & );
   template void placement_finder<DetectorType>::find_line_placement<PathType> (placement&, PathType & );
   
}  // namespace