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 * $Id: distances.cpp 2617 2011-09-30 21:37:23Z rusu $
 *
 */
#include "pcl/common/distances.h"

void
pcl::lineToLineSegment (const Eigen::VectorXf &line_a, const Eigen::VectorXf &line_b, 
                        Eigen::Vector4f &pt1_seg, Eigen::Vector4f &pt2_seg)
{
  // point + direction = 2nd point
  Eigen::Vector4f p1 = Eigen::Vector4f::Zero ();
  Eigen::Vector4f p2 = Eigen::Vector4f::Zero ();
  Eigen::Vector4f dir1 = Eigen::Vector4f::Zero ();
  p1.head<3> () = line_a.head<3> ();
  dir1.head<3> () = line_a.segment<3> (3);
  p2 = p1 + dir1;

  // point + direction = 2nd point
  Eigen::Vector4f q1 = Eigen::Vector4f::Zero ();
  Eigen::Vector4f q2 = Eigen::Vector4f::Zero ();
  Eigen::Vector4f dir2 = Eigen::Vector4f::Zero ();
  q1.head<3> () = line_b.head<3> ();
  dir2.head<3> () = line_b.segment<3> (3);
  q2 = q1 + dir2;

  // a = x2 - x1 = line_a[1] - line_a[0]
  Eigen::Vector4f u = dir1;
  // b = x4 - x3 = line_b[1] - line_b[0]
  Eigen::Vector4f v = dir2;
  // c = x2 - x3 = line_a[1] - line_b[0]
  Eigen::Vector4f w = p2 - q1;

  double a = u.dot (u);
  double b = u.dot (v);
  double c = v.dot (v);
  double d = u.dot (w);
  double e = v.dot (w);
  double denominator = a*c - b*b;
  double sc, tc;
  // Compute the line parameters of the two closest points
  if (denominator < 1e-5)          // The lines are almost parallel
  {
    sc = 0.0;
    tc = (b > c ? d / b : e / c);  // Use the largest denominator
  }
  else
  {
    sc = (b*e - c*d) / denominator;
    tc = (a*e - b*d) / denominator;
  }
  // Get the closest points
  pt1_seg = Eigen::Vector4f::Zero ();
  pt1_seg = p2 + sc * u;

  pt2_seg = Eigen::Vector4f::Zero ();
  pt2_seg = q1 + tc * v;
}

