polygon_operations.hpp

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#ifndef PCL_GEOMETRY_POLYGON_OPERATIONS_HPP_
#define PCL_GEOMETRY_POLYGON_OPERATIONS_HPP_

#include <pcl/geometry/polygon_operations.h>

template<typename PointT> void
pcl::approximatePolygon (const PlanarPolygon<PointT>& polygon, PlanarPolygon<PointT>& approx_polygon, float threshold, bool refine, bool closed)
{
  const Eigen::Vector4f& coefficients = polygon.getCoefficients ();
  const typename pcl::PointCloud<PointT>::VectorType &contour = polygon.getContour ();
  
  Eigen::Vector3f rotation_axis (coefficients[1], -coefficients[0], 0.0f);
  rotation_axis.normalize ();

  float rotation_angle = acosf (coefficients [2]);
  Eigen::Affine3f transformation = Eigen::Translation3f (0, 0, coefficients [3]) * Eigen::AngleAxisf (rotation_angle, rotation_axis);

  typename pcl::PointCloud<PointT>::VectorType polygon2D (contour.size ());
  for (unsigned pIdx = 0; pIdx < polygon2D.size (); ++pIdx)
    polygon2D [pIdx].getVector3fMap () = transformation * contour [pIdx].getVector3fMap ();

  typename pcl::PointCloud<PointT>::VectorType approx_polygon2D;
  approximatePolygon2D<PointT> (polygon2D, approx_polygon2D, threshold, refine, closed);
  
  typename pcl::PointCloud<PointT>::VectorType &approx_contour = approx_polygon.getContour ();
  approx_contour.resize (approx_polygon2D.size ());
  
  Eigen::Affine3f inv_transformation = transformation.inverse ();
  for (unsigned pIdx = 0; pIdx < approx_polygon2D.size (); ++pIdx)
    approx_contour [pIdx].getVector3fMap () = inv_transformation * approx_polygon2D [pIdx].getVector3fMap ();
}

template <typename PointT> void
pcl::approximatePolygon2D (const typename pcl::PointCloud<PointT>::VectorType &polygon, 
                           typename pcl::PointCloud<PointT>::VectorType &approx_polygon, 
                           float threshold, bool refine, bool closed)
{
  approx_polygon.clear ();
  if (polygon.size () < 3)
    return;
  
  std::vector<std::pair<unsigned, unsigned> > intervals;
  std::pair<unsigned,unsigned> interval (0, 0);
  
  if (closed)
  {
    float max_distance = .0f;
    for (unsigned idx = 1; idx < polygon.size (); ++idx)
    {
      float distance = (polygon [0].x - polygon [idx].x) * (polygon [0].x - polygon [idx].x) + 
                       (polygon [0].y - polygon [idx].y) * (polygon [0].y - polygon [idx].y);

      if (distance > max_distance)
      {
        max_distance = distance;
        interval.second = idx;
      }
    }

    for (unsigned idx = 1; idx < polygon.size (); ++idx)
    {
      float distance = (polygon [interval.second].x - polygon [idx].x) * (polygon [interval.second].x - polygon [idx].x) + 
                       (polygon [interval.second].y - polygon [idx].y) * (polygon [interval.second].y - polygon [idx].y);

      if (distance > max_distance)
      {
        max_distance = distance;
        interval.first = idx;
      }
    }

    if (max_distance < threshold * threshold)
      return;

    intervals.push_back (interval);
    std::swap (interval.first, interval.second);
    intervals.push_back (interval);
  }
  else
  {
    interval.first = 0;
    interval.second = static_cast<unsigned int> (polygon.size ()) - 1;
    intervals.push_back (interval);
  }
  
  std::vector<unsigned> result;
  // recursively refine
  while (!intervals.empty ())
  {
    std::pair<unsigned, unsigned>& currentInterval = intervals.back ();
    float line_x = polygon [currentInterval.first].y - polygon [currentInterval.second].y;
    float line_y = polygon [currentInterval.second].x - polygon [currentInterval.first].x;
    float line_d = polygon [currentInterval.first].x * polygon [currentInterval.second].y - polygon [currentInterval.first].y * polygon [currentInterval.second].x;
    
    float linelen = 1.0f / sqrtf (line_x * line_x + line_y * line_y);
    
    line_x *= linelen;
    line_y *= linelen;
    line_d *= linelen;
    
    float max_distance = 0.0;
    unsigned first_index = currentInterval.first + 1;
    unsigned max_index = 0;

    // => 0-crossing
    if (currentInterval.first > currentInterval.second)
    {
      for (unsigned idx = first_index; idx < polygon.size(); idx++)
      {
        float distance = fabsf (line_x * polygon[idx].x + line_y * polygon[idx].y + line_d);
        if (distance > max_distance)
        {
          max_distance = distance;
          max_index  = idx;
        }
      }
      first_index = 0;
    }

    for (unsigned int idx = first_index; idx < currentInterval.second; idx++)
    {
      float distance = fabsf (line_x * polygon[idx].x + line_y * polygon[idx].y + line_d);
      if (distance > max_distance)
      {
        max_distance = distance;
        max_index  = idx;
      }
    }

    if (max_distance > threshold)
    {
      std::pair<unsigned, unsigned> interval (max_index, currentInterval.second);
      currentInterval.second = max_index;
      intervals.push_back (interval);
    }
    else
    {
      result.push_back (currentInterval.second);
      intervals.pop_back ();
    }
  }
  
  approx_polygon.reserve (result.size ());
  if (refine)
  {
    std::vector<Eigen::Vector3f> lines (result.size ());
    std::reverse (result.begin (), result.end ());
    for (unsigned rIdx = 0; rIdx < result.size (); ++rIdx)
    {
      unsigned nIdx = rIdx + 1;
      if (nIdx == result.size ())
        nIdx = 0;
      
      Eigen::Vector2f centroid = Eigen::Vector2f::Zero ();
      Eigen::Matrix2f covariance = Eigen::Matrix2f::Zero ();
      unsigned pIdx = result[rIdx];
      unsigned num_points = 0;
      if (pIdx > result[nIdx])
      {
        num_points = static_cast<unsigned> (polygon.size ()) - pIdx;
        for (; pIdx < polygon.size (); ++pIdx)
        {
          covariance.coeffRef (0) += polygon [pIdx].x * polygon [pIdx].x;
          covariance.coeffRef (1) += polygon [pIdx].x * polygon [pIdx].y;
          covariance.coeffRef (3) += polygon [pIdx].y * polygon [pIdx].y;
          centroid [0] += polygon [pIdx].x;
          centroid [1] += polygon [pIdx].y;
        }
        pIdx = 0;
      }
      
      num_points += result[nIdx] - pIdx;
      for (; pIdx < result[nIdx]; ++pIdx)
      {
        covariance.coeffRef (0) += polygon [pIdx].x * polygon [pIdx].x;
        covariance.coeffRef (1) += polygon [pIdx].x * polygon [pIdx].y;
        covariance.coeffRef (3) += polygon [pIdx].y * polygon [pIdx].y;
        centroid [0] += polygon [pIdx].x;
        centroid [1] += polygon [pIdx].y;
      }
      
      covariance.coeffRef (2) = covariance.coeff (1);
      
      float norm = 1.0f / float (num_points);
      centroid *= norm;
      covariance *= norm;
      covariance.coeffRef (0) -= centroid [0] * centroid [0];
      covariance.coeffRef (1) -= centroid [0] * centroid [1];
      covariance.coeffRef (3) -= centroid [1] * centroid [1];
      
      float eval;
      Eigen::Vector2f normal;
      eigen22 (covariance, eval, normal);

      // select the one which is more "parallel" to the original line
      Eigen::Vector2f direction;
      direction [0] = polygon[result[nIdx]].x - polygon[result[rIdx]].x;
      direction [1] = polygon[result[nIdx]].y - polygon[result[rIdx]].y;
      direction.normalize ();
      
      if (fabs (direction.dot (normal)) > float(M_SQRT1_2))
      {
        std::swap (normal [0], normal [1]);
        normal [0] = -normal [0];
      }
      
      // needs to be on the left side of the edge
      if (direction [0] * normal [1] < direction [1] * normal [0])
        normal *= -1.0;
      
      lines [rIdx].head<2> ().matrix () = normal;
      lines [rIdx] [2] = -normal.dot (centroid);
    }
    
    float threshold2 = threshold * threshold;
    for (unsigned rIdx = 0; rIdx < lines.size (); ++rIdx)
    {
      unsigned nIdx = rIdx + 1;
      if (nIdx == result.size ())
        nIdx = 0;      
      
      Eigen::Vector3f vertex = lines [rIdx].cross (lines [nIdx]);
      vertex /= vertex [2];
      vertex [2] = 0.0;

      PointT point;      
      // test whether we need another edge since the intersection point is too far away from the original vertex
      Eigen::Vector3f pq = polygon [result[nIdx]].getVector3fMap () - vertex;
      pq [2] = 0.0;
      
      float distance = pq.squaredNorm ();
      if (distance > threshold2)
      {
        // test whether the old point is inside the new polygon or outside
        if ((pq [0] * lines [rIdx] [0] + pq [1] * lines [rIdx] [1] < 0.0) &&
            (pq [0] * lines [nIdx] [0] + pq [1] * lines [nIdx] [1] < 0.0) )
        {
          float distance1 = lines [rIdx] [0] * polygon[result[nIdx]].x + lines [rIdx] [1] * polygon[result[nIdx]].y + lines [rIdx] [2];
          float distance2 = lines [nIdx] [0] * polygon[result[nIdx]].x + lines [nIdx] [1] * polygon[result[nIdx]].y + lines [nIdx] [2];

          point.x = polygon[result[nIdx]].x - distance1 * lines [rIdx] [0];
          point.y = polygon[result[nIdx]].y - distance1 * lines [rIdx] [1];

          approx_polygon.push_back (point);

          vertex [0] = polygon[result[nIdx]].x - distance2 * lines [nIdx] [0];
          vertex [1] = polygon[result[nIdx]].y - distance2 * lines [nIdx] [1];
        }
      }
      point.getVector3fMap () = vertex;
      approx_polygon.push_back (point);
    }
  }
  else
  {
    // we have a new polygon in results, but inverted (clockwise <-> counter-clockwise)    
    for (std::vector<unsigned>::reverse_iterator it = result.rbegin (); it != result.rend (); ++it)
      approx_polygon.push_back (polygon [*it]);
  }
}

#endif // PCL_GEOMETRY_POLYGON_OPERATIONS_HPP_