placement_finder.cpp

/*****************************************************************************
 *
 * This file is part of Mapnik (c++ mapping toolkit)
 *
 * Copyright (C) 2011 Artem Pavlenko
 *
 * 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>
#include <mapnik/label_collision_detector.hpp>
#include <mapnik/fastmath.hpp>
#include <mapnik/text_placements/base.hpp>
#include <mapnik/ctrans.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/tuple/tuple.hpp>
#include <boost/foreach.hpp>

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

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

namespace mapnik
{

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 = 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;
            }
        }
        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(Feature const& feature,
                                              text_placement_info const& placement_info,
                                              string_info const& info,
                                              DetectorT & detector,
                                              box2d<double> const& extent)
    : detector_(detector),
      dimensions_(extent),
      info_(info),
      p(placement_info.properties),
      pi(placement_info),
      string_width_(0),
      string_height_(0),
      first_line_space_(0),
      valign_(V_AUTO),
      halign_(H_AUTO),
      line_breaks_(),
      line_sizes_(),
      collect_extents_(false)
{
    init_string_size();
    init_alignment();
}

template <typename DetectorT>
template <typename T>
void placement_finder<DetectorT>::find_point_placements(T & 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;

    double total_distance = get_total_distance<T>(shape_path);
    shape_path.rewind(0);

    if (distance == 0) //Point data, not a line
    {
        double x, y;
        shape_path.vertex(&x,&y);
        find_point_placement(x, y);
        return;
    }

    int num_labels = 1;
    if (p.label_spacing > 0)
        num_labels = static_cast<int> (floor(total_distance / pi.get_actual_label_spacing()));

    if (p.force_odd_labels && num_labels % 2 == 0)
        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
    {

        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 = 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(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.
            }
        }

        old_x = new_x;
        old_y = new_y;
    }

}

template <typename DetectorT>
void placement_finder<DetectorT>::init_string_size()
{
    // Get total string size
    if (!info_.num_characters()) return; //At least one character is required
    for (unsigned i = 0; i < info_.num_characters(); i++)
    {
        char_info const& ci = info_.at(i);
        if (!ci.width || !ci.line_height) continue; //Skip empty chars (add no character_spacing for them)
        string_width_ += ci.width + ci.format->character_spacing;
        string_height_ = std::max(string_height_, ci.line_height+ci.format->line_spacing);
        first_line_space_ = std::max(first_line_space_, ci.line_height-ci.avg_height);
    }
    string_width_ -= info_.at(info_.num_characters()-1).format->character_spacing; //Remove last space
    string_height_ -= first_line_space_; //First line is a bit smaller
}




template <typename DetectorT>
void placement_finder<DetectorT>::find_line_breaks()
{
    if (!line_sizes_.empty()) return;
    bool first_line = true;
    // check if we need to wrap the string
    double wrap_at = string_width_ + 1.0;
    if (p.wrap_width && string_width_ > p.wrap_width)
    {
        if (p.text_ratio)
        {
            for (double i = 1.0; ((wrap_at = string_width_/i)/(string_height_*i)) > p.text_ratio && (string_width_/i) > p.wrap_width; i += 1.0) ;
        }
        else
        {
            wrap_at = p.wrap_width;
        }
    }

    // work out where our line breaks need to be and the resultant width to the 'wrapped' string
    if ((wrap_at < string_width_) || info_.has_line_breaks())
    {
        first_line_space_ = 0.0;
        int last_wrap_char_pos = 0; //Position of last char where wrapping is possible
        double last_char_spacing = 0.0;
        double last_wrap_char_width = 0.0; //Include char_spacing before and after
        string_width_ = 0.0;
        string_height_ = 0.0;
        double line_width = 0.0;
        double line_height = 0.0; //Height of tallest char in line
        double word_width = 0.0; //Current unfinished word width
        double word_height = 0.0;
        //line_width and word_width include char width + spacing, but not the spacing after the last char

        for (unsigned int ii = 0; ii < info_.num_characters(); ii++)
        {
            char_info const& ci = info_.at(ii);
            unsigned c = ci.c;

            if ((c == ci.format->wrap_char) || (c == '\n'))
            {
                last_wrap_char_pos = ii;
                //No wrap at previous position
                line_width += word_width + last_wrap_char_width;
                line_height = std::max(line_height, word_height);
                last_wrap_char_width = last_char_spacing + ci.width + ci.format->character_spacing;
                last_char_spacing = 0.0; //Current one is included in last_wrap_char_width
                word_width = 0.0;
                word_height = 0.0;
            } else {
                //No wrap char
                word_width += last_char_spacing + ci.width;
                last_char_spacing = ci.format->character_spacing;
                word_height = std::max(word_height, ci.line_height + ci.format->line_spacing);
                //TODO: I think this calculation could be wrong if height changes for the first word in the second line
                if (first_line) first_line_space_ = std::max(first_line_space_, ci.line_height-ci.avg_height);
            }

            // wrap text at first wrap_char after (default) the wrap width or immediately before the current word
            if ((c == '\n') ||
                (line_width > 0 &&
                 ((line_width > wrap_at && !ci.format->wrap_before) ||
                  ((line_width + last_wrap_char_width + word_width) > wrap_at && ci.format->wrap_before)) )
                )
            {
                add_line(line_width, line_height, first_line);
                line_breaks_.push_back(last_wrap_char_pos);
                line_width = 0.0;
                line_height = 0.0;
                last_wrap_char_width = 0; //Wrap char supressed
                first_line = false;
            }
        }
        line_width += last_wrap_char_width + word_width;
        line_height = std::max(line_height, word_height);
        add_line(line_width, line_height, first_line);
    } else {
        //No linebreaks
        line_sizes_.push_back(std::make_pair(string_width_, string_height_));
    }
    line_breaks_.push_back(info_.num_characters());
}

template <typename DetectorT>
void placement_finder<DetectorT>::add_line(double width, double height, bool first_line)
{
    if (first_line) height -= first_line_space_;
    string_width_ = std::max(string_width_, width); //Total width is the longest line
    string_height_ += height;
    line_sizes_.push_back(std::make_pair(width, height));
}


template <typename DetectorT>
void placement_finder<DetectorT>::init_alignment()
{
    valign_ = p.valign;
    if (valign_ == V_AUTO) {
        if (p.displacement.second > 0.0)
            valign_ = V_BOTTOM;
        else if (p.displacement.second < 0.0)
            valign_ = V_TOP;
        else
            valign_ = V_MIDDLE;
    }

    halign_ = p.halign;
    if (halign_ == H_AUTO) {
        if (p.displacement.first > 0.0)
            halign_ = H_RIGHT;
        else if (p.displacement.first < 0.0)
            halign_ = H_LEFT;
        else
            halign_ = H_MIDDLE;
    }
}


template <typename DetectorT>
void placement_finder<DetectorT>::adjust_position(text_path *current_placement)
{
    // if needed, adjust for desired vertical alignment
    if (valign_ == V_TOP)
    {
        current_placement->center.y -= 0.5 * string_height_;  // move center up by 1/2 the total height
    } else if (valign_ == V_BOTTOM)
    {
        current_placement->center.y += 0.5 * string_height_;  // move center down by the 1/2 the total height
    }

    // set horizontal position to middle of text
    if (halign_ == H_LEFT)
    {
        current_placement->center.x -= 0.5 * string_width_;  // move center left by 1/2 the string width
    } else if (halign_ == H_RIGHT)
    {
        current_placement->center.x += 0.5 * string_width_;  // move center right by 1/2 the string width
    }

    // adjust text envelope position by user's x-y displacement (dx, dy)
    current_placement->center.x += pi.get_scale_factor() * p.displacement.first;
    current_placement->center.y += pi.get_scale_factor() * p.displacement.second;

}

template <typename DetectorT>
void placement_finder<DetectorT>::find_point_placement(double label_x,
                                                       double label_y,
                                                       double angle)
{
    find_line_breaks();

    double rad = M_PI * angle/180.0;
    double cosa = std::cos(rad);
    double sina = std::sin(rad);

    double x, y;
    std::auto_ptr<text_path> current_placement(new text_path(label_x, label_y));

    adjust_position(current_placement.get());

    // presets for first line
    unsigned int line_number = 0;
    unsigned int index_to_wrap_at = line_breaks_[0];
    double line_width = line_sizes_[0].first;
    double line_height = line_sizes_[0].second;

    /* IMPORTANT NOTE:
       x and y are relative to the center of the text
       coordinate system:
       x: grows from left to right
       y: grows from bottom to top (opposite of normal computer graphics)
    */

    // set for upper left corner of text envelope for the first line, bottom left of first character
    y = string_height_ / 2.0 - line_height;
    // RTL text is converted to a mirrored representation in get_string_info()
    // so we have to fix line break order here
    if (info_.get_rtl()) y = -y;

    // adjust for desired justification
    if (p.jalign == J_LEFT)
        x = -(string_width_ / 2.0);
    else if (p.jalign == J_RIGHT)
        x = (string_width_ / 2.0) - line_width;
    else /* J_MIDDLE */
        x = -(line_width / 2.0);

    // save each character rendering position and build envelope as go thru loop
    std::queue< box2d<double> > c_envelopes;

    for (unsigned i = 0; i < info_.num_characters(); i++)
    {
        char_info const& ci = info_.at(i);

        double cwidth = ci.width + ci.format->character_spacing;

        if (i == index_to_wrap_at)
        {
            index_to_wrap_at = line_breaks_[++line_number];
            line_width = line_sizes_[line_number].first;
            line_height= line_sizes_[line_number].second;

            if (info_.get_rtl())
            {
                y += line_height;
            } else
            {
                y -= line_height;  // move position down to line start
            }

            // reset to begining of line position
            if (p.jalign == J_LEFT)
                x = -(string_width_ / 2.0);
            else if (p.jalign == J_RIGHT)
                x = (string_width_ / 2.0) - line_width;
            else
                x = -(line_width / 2.0);
            continue;
        }
        else
        {
            // place the character relative to the center of the string envelope
            double dx = x * cosa - y*sina;
            double dy = x * sina + y*cosa;

            current_placement->add_node(&ci, dx, dy, rad);

            // compute the Bounding Box for each character and test for:
            // overlap, minimum distance or edge avoidance - exit if condition occurs
            box2d<double> e;
            /*x axis: left to right, y axis: top to bottom (negative values higher)*/
            e.init(current_placement->center.x + dx,                    // Bottom Left
                   current_placement->center.y - dy - ci.ymin,          // ymin usually <0
                   current_placement->center.x + dx + ci.width,         // Top Right
                   current_placement->center.y - dy - ci.ymax);

            // if there is an overlap with existing envelopes, then exit - no placement

            if (!detector_.extent().intersects(e) ||
                (!p.allow_overlap &&
                 !detector_.has_point_placement(e, pi.get_actual_minimum_distance())))
            {
                return;
            }

            // if avoid_edges test dimensions contains e
            if (p.avoid_edges && !dimensions_.contains(e))
            {
                return;
            }

            if (p.minimum_padding > 0)
            {
                double min_pad = pi.get_actual_minimum_padding();
                box2d<double> epad(e.minx()-min_pad,
                                   e.miny()-min_pad,
                                   e.maxx()+min_pad,
                                   e.maxy()+min_pad);
                if (!dimensions_.contains(epad))
                {
                    return;
                }
            }


            c_envelopes.push(e);  // add character's envelope to temp storage
        }
        x += cwidth;  // move position to next character
    }

    // check the placement of any additional envelopes
    if (!p.allow_overlap && !additional_boxes.empty())
    {
        BOOST_FOREACH(box2d<double> box, additional_boxes)
        {
            box2d<double> pt(box.minx() + current_placement->center.x,
                             box.miny() + current_placement->center.y,
                             box.maxx() + current_placement->center.x,
                             box.maxy() + current_placement->center.y);

            // abort the whole placement if the additional envelopes can't be placed.
            if (!detector_.has_point_placement(pt, p.minimum_distance)) return;

            c_envelopes.push(pt);
        }
    }

    // since there was no early exit, add the character envelopes to the placements' envelopes
    while (!c_envelopes.empty())
    {
        envelopes_.push(c_envelopes.front());
        c_envelopes.pop();
    }

    placements_.push_back(current_placement.release());
}


template <typename DetectorT>
template <typename PathT>
void placement_finder<DetectorT>::find_line_placements(PathT & shape_path)
{
#ifdef MAPNIK_DEBUG
    if (!line_sizes_.empty())
    {
        std::cerr << "WARNING: Internal error. Text contains line breaks, but line placement is used. Please file a bug report!\n";
    }
#endif

    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 = 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

    // Ensure lines have a minimum length.
    if (total_distance < p.minimum_path_length)
        return;

    double distance = 0.0;

    double displacement = p.displacement.second; // 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 / (pi.get_actual_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<text_path> current_placement = get_placement_offset(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].pos.x += pi.get_scale_factor() * displacement*cos(anglesum+M_PI/2);
                                current_placement->nodes_[i].pos.y += pi.get_scale_factor() * displacement*sin(anglesum+M_PI/2);
                            }
                        }

                        bool status = test_placement(current_placement, orientation);

                        if (status) //We have successfully placed one
                        {
                            placements_.push_back(current_placement.release());
                            update_detector();

                            //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 (!envelopes_.empty())
                                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<text_path> placement_finder<DetectorT>::get_placement_offset(std::vector<vertex2d> const& path_positions,
                                                                           std::vector<double> const& 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<text_path>(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<text_path>(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;

    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<text_path>(NULL);
    }

    std::auto_ptr<text_path> current_placement(
        new text_path((old_x + dx*distance/segment_length),
                      (old_y + dy*distance/segment_length)
            )
        );

    double angle = atan2(-dy, dx);

    bool orientation_forced = (orientation != 0); // Whether 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 < info_.num_characters(); ++i)
    {
        // grab the next character according to the orientation
        char_info const &ci = orientation > 0 ? info_.at(i) : info_.at(info_.num_characters() - i - 1);
        double cwidth = ci.width + ci.format->character_spacing;

        double last_character_angle = angle;

        //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<text_path>(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  >= cwidth)
        {
            //if the distance remaining in this segment is enough, we just go further along the segment
            distance += cwidth;

            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 until 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<text_path>(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 (std::sqrt(std::pow(start_x - new_x, 2) + std::pow(start_y - new_y, 2)) < cwidth); //Distance from start_ to new_

            //Calculate the position to place the end of the character on
            find_line_circle_intersection(
                start_x, start_y, cwidth,
                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 = 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 = fast_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)
        {
            //std::clog << "FAIL: Too Bendy!" << std::endl;
            return std::auto_ptr<text_path>(NULL);
        }

        double render_angle = angle;
        double cosa = fast_cos(angle);
        double sina = fast_sin(angle);

        double render_x = start_x;
        double render_y = start_y;

        //Center the text on the line
        double char_height = ci.avg_height;
        render_x += char_height/2.0*sina;
        render_y += char_height/2.0*cosa;

        if (orientation < 0)
        {
            // rotate in place
            render_x += cwidth*cosa - char_height*sina;
            render_y -= cwidth*sina + char_height*cosa;
            render_angle += M_PI;
        }
        current_placement->add_node(&ci,
                                    render_x - current_placement->center.x,
                                    -render_y + current_placement->center.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
    if (upside_down_char_count >= 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(path_positions,
                                                     path_distances,
                                                     orientation,
                                                     initial_index,
                                                     initial_distance);
        }
        else
        {
            //Otherwise we have failed to find a placement
            //std::clog << "FAIL: Double upside-down!" << std::endl;
            return std::auto_ptr<text_path>(NULL);
        }
    }

    return current_placement;
}

template <typename DetectorT>
bool placement_finder<DetectorT>::test_placement(std::auto_ptr<text_path> const& current_placement,
                                                 int orientation)
{
    //Create and test envelopes
    bool status = true;
    for (unsigned i = 0; i < info_.num_characters(); ++i)
    {
        //TODO: I think this can be simplified by taking the char_info from vertex() but this needs to be carefully tested!
        // grab the next character according to the orientation
        char_info const& ci = orientation > 0 ? info_.at(i) : info_.at(info_.num_characters() - i - 1);
        double cwidth = ci.width + ci.format->character_spacing;
        char_info_ptr c;
        double x, y, angle;
        current_placement->vertex(&c, &x, &y, &angle);
        x = current_placement->center.x + x;
        y = current_placement->center.y - y;

        double sina = fast_sin(angle);
        double cosa = fast_cos(angle);
        if (orientation < 0)
        {
            // rotate in place
            x += cwidth * cosa - string_height_ * sina;
            y -= cwidth * sina + string_height_ * cosa;
            angle += M_PI;
            //sin(x+PI) = -sin(x)
            sina = -sina;
            cosa = -cosa;
        }

        box2d<double> e(x, y, x + cwidth*cosa, y - cwidth*sina);
        // put four corners of the letter into envelope
        e.expand_to_include(x - ci.height()*sina,
                            y - ci.height()*cosa);
        e.expand_to_include(x + (cwidth*cosa - ci.height()*sina),
                            y - (cwidth*sina + ci.height()*cosa));

        if (!detector_.extent().intersects(e) ||
            (!p.allow_overlap &&
             !detector_.has_placement(e, info_.get_string(), pi.get_actual_minimum_distance())
                )
            )
        {
            //std::clog << "No Intersects:" << !dimensions_.intersects(e) << ": " << e << " @ " << dimensions_ << std::endl;
            //std::clog << "No Placements:" << !detector_.has_placement(e, 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;
        }
        if (p.minimum_padding > 0)
        {
            double min_pad = pi.get_actual_minimum_padding();
            box2d<double> epad(e.minx()-min_pad,
                               e.miny()-min_pad,
                               e.maxx()+min_pad,
                               e.maxy()+min_pad);
            if (!dimensions_.contains(epad))
            {
                status = false;
                break;
            }
        }
        envelopes_.push(e);
    }

    current_placement->rewind();

    return status;
}

template <typename DetectorT>
void placement_finder<DetectorT>::find_line_circle_intersection(
    double cx, double cy, double radius,
    double x1, double y1, double x2, 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 + std::sqrt(det)) / (2 * A);
        ix = x1 + t * dx;
        iy = y1 + t * dy;

        //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()
{
    if (collect_extents_) extents_.init(0,0,0,0);
    // add the bboxes to the detector and remove from the placement
    while (!envelopes_.empty())
    {
        box2d<double> e = envelopes_.front();
        detector_.insert(e, info_.get_string());
        envelopes_.pop();

        if (collect_extents_)
        {
            extents_.expand_to_include(e);
        }
    }
}

template <typename DetectorT>
void placement_finder<DetectorT>::clear_placements()
{
    placements_.clear();
    while (!envelopes_.empty()) envelopes_.pop();
}

typedef agg::conv_clip_polyline<geometry_type> clipped_geometry_type;
typedef coord_transform2<CoordTransform,clipped_geometry_type> PathType;
typedef label_collision_detector4 DetectorType;

template class placement_finder<DetectorType>;
template void placement_finder<DetectorType>::find_point_placements<PathType>(PathType &);
template void placement_finder<DetectorType>::find_line_placements<PathType>(PathType &);
}  // namespace