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 *  $Id: 3dsc.hpp 4961 2012-03-07 23:44:07Z rusu $
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#ifndef PCL_FEATURES_IMPL_3DSC_HPP_
#define PCL_FEATURES_IMPL_3DSC_HPP_

#include <cmath>
#include <pcl/features/3dsc.h>
#include <pcl/common/utils.h>
#include <pcl/common/geometry.h>
#include <pcl/common/angles.h>

//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointNT, typename PointOutT> bool
pcl::ShapeContext3DEstimation<PointInT, PointNT, PointOutT>::initCompute ()
{
  if (!FeatureFromNormals<PointInT, PointNT, PointOutT>::initCompute ())
  {
    PCL_ERROR ("[pcl::%s::initCompute] Init failed.\n", getClassName ().c_str ());
    return (false);
  }

  if (search_radius_< min_radius_)
  {
    PCL_ERROR ("[pcl::%s::initCompute] search_radius_ must be GREATER than min_radius_.\n", getClassName ().c_str ());
    return (false);
  }

  // Update descriptor length
  descriptor_length_ = elevation_bins_ * azimuth_bins_ * radius_bins_;

  // Compute radial, elevation and azimuth divisions
  float azimuth_interval = 360.0f / static_cast<float> (azimuth_bins_);
  float elevation_interval = 180.0f / static_cast<float> (elevation_bins_);

  // Reallocate divisions and volume lut
  radii_interval_.clear ();
  phi_divisions_.clear ();
  theta_divisions_.clear ();
  volume_lut_.clear ();

  // Fills radii interval based on formula (1) in section 2.1 of Frome's paper
  radii_interval_.resize (radius_bins_ + 1);
  for (size_t j = 0; j < radius_bins_ + 1; j++)
    radii_interval_[j] = static_cast<float> (exp (log (min_radius_) + ((static_cast<float> (j) / static_cast<float> (radius_bins_)) * log (search_radius_ / min_radius_))));

  // Fill theta divisions of elevation
  theta_divisions_.resize (elevation_bins_ + 1);
  for (size_t k = 0; k < elevation_bins_ + 1; k++)
    theta_divisions_[k] = static_cast<float> (k) * elevation_interval;

  // Fill phi didvisions of elevation
  phi_divisions_.resize (azimuth_bins_ + 1);
  for (size_t l = 0; l < azimuth_bins_ + 1; l++)
    phi_divisions_[l] = static_cast<float> (l) * azimuth_interval;

  // LookUp Table that contains the volume of all the bins
  // "phi" term of the volume integral
  // "integr_phi" has always the same value so we compute it only one time
  float integr_phi  = pcl::deg2rad (phi_divisions_[1]) - pcl::deg2rad (phi_divisions_[0]);
  // exponential to compute the cube root using pow
  float e = 1.0f / 3.0f;
  // Resize volume look up table
  volume_lut_.resize (radius_bins_ * elevation_bins_ * azimuth_bins_);
  // Fill volumes look up table
  for (size_t j = 0; j < radius_bins_; j++)
  {
    // "r" term of the volume integral
    float integr_r = (radii_interval_[j+1] * radii_interval_[j+1] * radii_interval_[j+1] / 3.0f) - (radii_interval_[j] * radii_interval_[j] * radii_interval_[j] / 3.0f);
    
    for (size_t k = 0; k < elevation_bins_; k++)
    {
      // "theta" term of the volume integral
      float integr_theta = cosf (pcl::deg2rad (theta_divisions_[k])) - cosf (pcl::deg2rad (theta_divisions_[k+1]));
      // Volume
      float V = integr_phi * integr_theta * integr_r;
      // Compute cube root of the computed volume commented for performance but left 
      // here for clarity
      // float cbrt = pow(V, e);
      // cbrt = 1 / cbrt;
      
      for (size_t l = 0; l < azimuth_bins_; l++)
      {
        // Store in lut 1/cbrt
        //volume_lut_[ (l*elevation_bins_*radius_bins_) + k*radius_bins_ + j ] = cbrt;
        volume_lut_[(l*elevation_bins_*radius_bins_) + k*radius_bins_ + j] = 1.0f / powf (V, e);
      }
    }
  }
  return (true);
}

//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointNT, typename PointOutT> bool
pcl::ShapeContext3DEstimation<PointInT, PointNT, PointOutT>::computePoint (
    size_t index, const pcl::PointCloud<PointNT> &normals, float rf[9], std::vector<float> &desc)
{
  // The RF is formed as this x_axis | y_axis | normal
  Eigen::Map<Eigen::Vector3f> x_axis (rf);
  Eigen::Map<Eigen::Vector3f> y_axis (rf + 3);
  Eigen::Map<Eigen::Vector3f> normal (rf + 6);

  // Find every point within specified search_radius_
  std::vector<int> nn_indices;
  std::vector<float> nn_dists;
  const size_t neighb_cnt = searchForNeighbors ((*indices_)[index], search_radius_, nn_indices, nn_dists);
  if (neighb_cnt == 0)
  {
    for (size_t i = 0; i < desc.size (); ++i)
      desc[i] = std::numeric_limits<float>::quiet_NaN ();

    memset (rf, 0, sizeof (rf[0]) * 9);
    return (false);
  }

  float minDist = std::numeric_limits<float>::max ();
  int minIndex = -1;
  for (size_t i = 0; i < nn_indices.size (); i++)
  {
	  if (nn_dists[i] < minDist)
	  {
      minDist = nn_dists[i];
      minIndex = nn_indices[i];
	  }
  }
  
  // Get origin point
  Vector3fMapConst origin = input_->points[(*indices_)[index]].getVector3fMap ();
  // Get origin normal
  // Use pre-computed normals
  normal = normals[minIndex].getNormalVector3fMap ();

  // Compute and store the RF direction
  x_axis[0] = static_cast<float> (rnd ());
  x_axis[1] = static_cast<float> (rnd ());
  x_axis[2] = static_cast<float> (rnd ());
  if (!pcl::utils::equal (normal[2], 0.0f))
    x_axis[2] = - (normal[0]*x_axis[0] + normal[1]*x_axis[1]) / normal[2];
  else if (!pcl::utils::equal (normal[1], 0.0f))
    x_axis[1] = - (normal[0]*x_axis[0] + normal[2]*x_axis[2]) / normal[1];
  else if (!pcl::utils::equal (normal[0], 0.0f))
    x_axis[0] = - (normal[1]*x_axis[1] + normal[2]*x_axis[2]) / normal[0];

  x_axis.normalize ();

  // Check if the computed x axis is orthogonal to the normal
  assert (pcl::utils::equal (x_axis[0]*normal[0] + x_axis[1]*normal[1] + x_axis[2]*normal[2], 0.0f, 1E-6f));

  // Store the 3rd frame vector
  y_axis = normal.cross (x_axis);

  // For each point within radius
  for (size_t ne = 0; ne < neighb_cnt; ne++)
  {
    if (pcl::utils::equal (nn_dists[ne], 0.0f))
		  continue;
    // Get neighbours coordinates
    Eigen::Vector3f neighbour = surface_->points[nn_indices[ne]].getVector3fMap ();

    /// ----- Compute current neighbour polar coordinates -----
    /// Get distance between the neighbour and the origin
    float r = sqrt (nn_dists[ne]); 
    
    /// Project point into the tangent plane
    Eigen::Vector3f proj;
    pcl::geometry::project (neighbour, origin, normal, proj);
    proj -= origin;

    /// Normalize to compute the dot product
    proj.normalize ();
    
    /// Compute the angle between the projection and the x axis in the interval [0,360] 
    Eigen::Vector3f cross = x_axis.cross (proj);
    float phi = pcl::rad2deg (std::atan2 (cross.norm (), x_axis.dot (proj)));
    phi = cross.dot (normal) < 0.f ? (360.0f - phi) : phi;
    /// Compute the angle between the neighbour and the z axis (normal) in the interval [0, 180]
    Eigen::Vector3f no = neighbour - origin;
    no.normalize ();
    float theta = normal.dot (no);
    theta = pcl::rad2deg (acosf (std::min (1.0f, std::max (-1.0f, theta))));

    // Bin (j, k, l)
    size_t j = 0;
    size_t k = 0;
    size_t l = 0;

    // Compute the Bin(j, k, l) coordinates of current neighbour
    for (size_t rad = 1; rad < radius_bins_+1; rad++) 
    {
      if (r <= radii_interval_[rad]) 
      {
        j = rad-1;
        break;
      }
    }

    for (size_t ang = 1; ang < elevation_bins_+1; ang++) 
    {
      if (theta <= theta_divisions_[ang]) 
      {
        k = ang-1;
        break;
      }
    }

    for (size_t ang = 1; ang < azimuth_bins_+1; ang++) 
    {
      if (phi <= phi_divisions_[ang]) 
      {
        l = ang-1;
        break;
      }
    }

    // Local point density = number of points in a sphere of radius "point_density_radius_" around the current neighbour
    std::vector<int> neighbour_indices;
    std::vector<float> neighbour_distances;
    int point_density = searchForNeighbors (*surface_, nn_indices[ne], point_density_radius_, neighbour_indices, neighbour_distances);
    // point_density is NOT always bigger than 0 (on error, searchForNeighbors returns 0), so we must check for that
    if (point_density == 0)
      continue;

    float w = (1.0f / static_cast<float> (point_density)) * 
              volume_lut_[(l*elevation_bins_*radius_bins_) +  (k*radius_bins_) + j];
      
    assert (w >= 0.0);
    if (w == std::numeric_limits<float>::infinity ())
      PCL_ERROR ("Shape Context Error INF!\n");
    if (w != w)
      PCL_ERROR ("Shape Context Error IND!\n");
    /// Accumulate w into correspondant Bin(j,k,l)
    desc[(l*elevation_bins_*radius_bins_) + (k*radius_bins_) + j] += w;

    assert (desc[(l*elevation_bins_*radius_bins_) + (k*radius_bins_) + j] >= 0);
  } // end for each neighbour

  // 3DSC does not define a repeatable local RF, we set it to zero to signal it to the user 
  memset (rf, 0, sizeof (rf[0]) * 9);
  return (true);
}

//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointNT, typename PointOutT> void
pcl::ShapeContext3DEstimation<PointInT, PointNT, PointOutT>::shiftAlongAzimuth (
    size_t block_size, std::vector<float>& desc)
{
  assert (desc.size () == descriptor_length_);
  // L rotations for each descriptor
  desc.resize (descriptor_length_ * azimuth_bins_); 
  // Create L azimuth rotated descriptors from reference descriptor
  // The descriptor_length_ first ones are the same so start at 1
  for (size_t l = 1; l < azimuth_bins_; l++)
    for (size_t bin = 0; bin < descriptor_length_; bin++)
      desc[(l * descriptor_length_) + bin] = desc[(l*block_size + bin) % descriptor_length_];
}

//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointNT, typename PointOutT> void
pcl::ShapeContext3DEstimation<PointInT, PointNT, PointOutT>::computeFeature (PointCloudOut &output)
{
  output.is_dense = true;
  // Iterate over all points and compute the descriptors
	for (size_t point_index = 0; point_index < indices_->size (); point_index++)
  {
    output[point_index].descriptor.resize (descriptor_length_);

    // If the point is not finite, set the descriptor to NaN and continue
    if (!isFinite ((*input_)[(*indices_)[point_index]]))
    {
      for (size_t i = 0; i < descriptor_length_; ++i)
        output[point_index].descriptor[i] = std::numeric_limits<float>::quiet_NaN ();

      memset (output[point_index].rf, 0, sizeof (output[point_index].rf[0]) * 9);
      output.is_dense = false;
      continue;
    }
 
    if (!computePoint (point_index, *normals_, output[point_index].rf, output[point_index].descriptor))
      output.is_dense = false;
  }
}

//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointNT> void
pcl::ShapeContext3DEstimation<PointInT, PointNT, Eigen::MatrixXf>::computeFeatureEigen (
    pcl::PointCloud<Eigen::MatrixXf> &output)
{

  // Set up the output channels
  output.channels["3dsc"].name     = "3dsc";
  output.channels["3dsc"].offset   = 0;
  output.channels["3dsc"].size     = 4;
  output.channels["3dsc"].count    = static_cast<uint32_t> (descriptor_length_) + 9;
  output.channels["3dsc"].datatype = sensor_msgs::PointField::FLOAT32;

  // Resize the output dataset
  output.points.resize (indices_->size (), descriptor_length_ + 9);

  float rf[9];

  output.is_dense = true;
  // Iterate over all points and compute the descriptors
	for (size_t point_index = 0; point_index < indices_->size (); point_index++)
  {
    // If the point is not finite, set the descriptor to NaN and continue
    if (!isFinite ((*input_)[(*indices_)[point_index]]))
    {
      output.points.row (point_index).setConstant (std::numeric_limits<float>::quiet_NaN ());
      output.is_dense = false;
      continue;
    }

    std::vector<float> descriptor (descriptor_length_);
    if (!this->computePoint (point_index, *normals_, rf, descriptor))
      output.is_dense = false;
    for (int j = 0; j < 9; ++j)
      output.points (point_index, j) = rf[j];
    for (size_t j = 0; j < descriptor_length_; ++j)
      output.points (point_index, 9 + j) = descriptor[j];
  }
}

#define PCL_INSTANTIATE_ShapeContext3DEstimation(T,NT,OutT) template class PCL_EXPORTS pcl::ShapeContext3DEstimation<T,NT,OutT>;

#endif
