distance_calculations.h

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#ifndef DISTANCE_CALCULATIONS_H
#define DISTANCE_CALCULATIONS_H
 
#include <Eigen/Core>
#include <teb_local_planner/misc.h>
 
 
namespace teb_local_planner
{
  
typedef std::vector< Eigen::Vector2d, Eigen::aligned_allocator<Eigen::Vector2d> > Point2dContainer;
 
  
inline Eigen::Vector2d closest_point_on_line_segment_2d(const Eigen::Ref<const Eigen::Vector2d>& point, const Eigen::Ref<const Eigen::Vector2d>& line_start, const Eigen::Ref<const Eigen::Vector2d>& line_end)
{
  Eigen::Vector2d diff = line_end - line_start;
  double sq_norm = diff.squaredNorm();
  
  if (sq_norm == 0)
    return line_start;
 
  double u = ((point.x() - line_start.x()) * diff.x() + (point.y() - line_start.y())*diff.y()) / sq_norm;
  
  if (u <= 0) return line_start;
  else if (u >= 1) return line_end;
  
  return line_start + u*diff;
}
  
inline double distance_point_to_segment_2d(const Eigen::Ref<const Eigen::Vector2d>& point, const Eigen::Ref<const Eigen::Vector2d>& line_start, const Eigen::Ref<const Eigen::Vector2d>& line_end)
{
  return  (point - closest_point_on_line_segment_2d(point, line_start, line_end)).norm(); 
}
  
inline bool check_line_segments_intersection_2d(const Eigen::Ref<const Eigen::Vector2d>& line1_start, const Eigen::Ref<const Eigen::Vector2d>& line1_end, 
                                                const Eigen::Ref<const Eigen::Vector2d>& line2_start, const Eigen::Ref<const Eigen::Vector2d>& line2_end, Eigen::Vector2d* intersection = NULL)
{
  // http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
  double s_numer, t_numer, denom, t;
  Eigen::Vector2d line1 = line1_end - line1_start;
  Eigen::Vector2d line2 = line2_end - line2_start;
  
  denom = line1.x() * line2.y() - line2.x() * line1.y();
  if (denom == 0) return false; // Collinear
  bool denomPositive = denom > 0;
 
  Eigen::Vector2d aux = line1_start - line2_start;
  
  s_numer = line1.x() * aux.y() - line1.y() * aux.x();
  if ((s_numer < 0) == denomPositive)  return false; // No collision
 
  t_numer = line2.x() * aux.y() - line2.y() * aux.x();
  if ((t_numer < 0) == denomPositive)  return false; // No collision
 
  if (((s_numer > denom) == denomPositive) || ((t_numer > denom) == denomPositive)) return false; // No collision
  
  // Otherwise collision detected
  t = t_numer / denom;
  if (intersection)
  {
    *intersection = line1_start + t * line1;
  }
 
  return true;
}
  
  
inline double distance_segment_to_segment_2d(const Eigen::Ref<const Eigen::Vector2d>& line1_start, const Eigen::Ref<const Eigen::Vector2d>& line1_end, 
                                             const Eigen::Ref<const Eigen::Vector2d>& line2_start, const Eigen::Ref<const Eigen::Vector2d>& line2_end)
{
  // TODO more efficient implementation
  
  // check if segments intersect
  if (check_line_segments_intersection_2d(line1_start, line1_end, line2_start, line2_end))
    return 0;
  
  // check all 4 combinations
  std::array<double,4> distances;
  
  distances[0] = distance_point_to_segment_2d(line1_start, line2_start, line2_end);
  distances[1] = distance_point_to_segment_2d(line1_end, line2_start, line2_end);
  distances[2] = distance_point_to_segment_2d(line2_start, line1_start, line1_end);
  distances[3] = distance_point_to_segment_2d(line2_end, line1_start, line1_end);
  
  return *std::min_element(distances.begin(), distances.end());
}
  
  
inline double distance_point_to_polygon_2d(const Eigen::Vector2d& point, const Point2dContainer& vertices)
{
  double dist = HUGE_VAL;
    
  // the polygon is a point
  if (vertices.size() == 1)
  {
    return (point - vertices.front()).norm();
  }
    
  // check each polygon edge
  for (int i=0; i<(int)vertices.size()-1; ++i)
  {
      double new_dist = distance_point_to_segment_2d(point, vertices.at(i), vertices.at(i+1));
//       double new_dist = calc_distance_point_to_segment( position,  vertices.at(i), vertices.at(i+1));
      if (new_dist < dist)
        dist = new_dist;
  }
 
  if (vertices.size()>2) // if not a line close polygon
  {
    double new_dist = distance_point_to_segment_2d(point, vertices.back(), vertices.front()); // check last edge
    if (new_dist < dist)
      return new_dist;
  }
  
  return dist;
}  
 
inline double distance_segment_to_polygon_2d(const Eigen::Vector2d& line_start, const Eigen::Vector2d& line_end, const Point2dContainer& vertices)
{
  double dist = HUGE_VAL;
    
  // the polygon is a point
  if (vertices.size() == 1)
  {
    return distance_point_to_segment_2d(vertices.front(), line_start, line_end);
  }
    
  // check each polygon edge
  for (int i=0; i<(int)vertices.size()-1; ++i)
  {
      double new_dist = distance_segment_to_segment_2d(line_start, line_end, vertices.at(i), vertices.at(i+1));
//       double new_dist = calc_distance_point_to_segment( position,  vertices.at(i), vertices.at(i+1));
      if (new_dist < dist)
        dist = new_dist;
  }
 
  if (vertices.size()>2) // if not a line close polygon
  {
    double new_dist = distance_segment_to_segment_2d(line_start, line_end, vertices.back(), vertices.front()); // check last edge
    if (new_dist < dist)
      return new_dist;
  }
  
  return dist;
}
 
inline double distance_polygon_to_polygon_2d(const Point2dContainer& vertices1, const Point2dContainer& vertices2)
{
  double dist = HUGE_VAL;
    
  // the polygon1 is a point
  if (vertices1.size() == 1)
  {
    return distance_point_to_polygon_2d(vertices1.front(), vertices2);
  }
    
  // check each edge of polygon1
  for (int i=0; i<(int)vertices1.size()-1; ++i)
  {
      double new_dist = distance_segment_to_polygon_2d(vertices1[i], vertices1[i+1], vertices2);
      if (new_dist < dist)
        dist = new_dist;
  }
 
  if (vertices1.size()>2) // if not a line close polygon1
  {
    double new_dist = distance_segment_to_polygon_2d(vertices1.back(), vertices1.front(), vertices2); // check last edge
    if (new_dist < dist)
      return new_dist;
  }
 
  return dist;
}
  
  
  
  
// Further distance calculations:
 
 
// The Distance Calculations are mainly copied from http://geomalgorithms.com/a07-_distance.html
// Copyright 2001 softSurfer, 2012 Dan Sunday
// This code may be freely used and modified for any purpose
// providing that this copyright notice is included with it.
// SoftSurfer makes no warranty for this code, and cannot be held
// liable for any real or imagined damage resulting from its use.
// Users of this code must verify correctness for their application.
 
inline double calc_distance_line_to_line_3d(const Eigen::Ref<const Eigen::Vector3d>& x1, Eigen::Ref<const Eigen::Vector3d>& u,
              const Eigen::Ref<const Eigen::Vector3d>& x2, Eigen::Ref<const Eigen::Vector3d>& v)
{
  Eigen::Vector3d   w = x2 - x1;
  double a = u.squaredNorm();         // dot(u,u) always >= 0
  double b = u.dot(v);
  double c = v.squaredNorm();         // dot(v,v) always >= 0
  double d = u.dot(w);
  double e = v.dot(w);
  double D = a*c - b*b;        // always >= 0
  double sc, tc;
 
  // compute the line parameters of the two closest points
  if (D < SMALL_NUM) {          // 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) / D;
    tc = (a*e - b*d) / D;
  }
 
  // get the difference of the two closest points
  Eigen::Vector3d dP = w + (sc * u) - (tc * v);  // =  L1(sc) - L2(tc)
 
  return dP.norm();   // return the closest distance
}
 
 
 
 
 
inline double calc_distance_segment_to_segment3D(const Eigen::Ref<const Eigen::Vector3d>& line1_start, Eigen::Ref<const Eigen::Vector3d>& line1_end,
             const Eigen::Ref<const Eigen::Vector3d>& line2_start, Eigen::Ref<const Eigen::Vector3d>& line2_end)
{
  Eigen::Vector3d u = line1_end - line1_start;
  Eigen::Vector3d v = line2_end - line2_start;
  Eigen::Vector3d w = line2_start - line1_start;
  double a = u.squaredNorm();         // dot(u,u) always >= 0
  double b = u.dot(v);
  double c = v.squaredNorm();         // dot(v,v) always >= 0
  double d = u.dot(w);
  double e = v.dot(w);
  double D = a*c - b*b;        // always >= 0
  double sc, sN, sD = D;       // sc = sN / sD, default sD = D >= 0
  double tc, tN, tD = D;       // tc = tN / tD, default tD = D >= 0
 
  // compute the line parameters of the two closest points
  if (D < SMALL_NUM) 
  { // the lines are almost parallel
    sN = 0.0;         // force using point P0 on segment S1
    sD = 1.0;         // to prevent possible division by 0.0 later
    tN = e;
    tD = c;
  }
  else 
  {       // get the closest points on the infinite lines
    sN = (b*e - c*d);
    tN = (a*e - b*d);
    if (sN < 0.0)
    {        // sc < 0 => the s=0 edge is visible
      sN = 0.0;
      tN = e;
      tD = c;
    }
    else if (sN > sD)
    {  // sc > 1  => the s=1 edge is visible
      sN = sD;
      tN = e + b;
      tD = c;
    }
  }
 
  if (tN < 0.0) 
  {   // tc < 0 => the t=0 edge is visible
    tN = 0.0;
    // recompute sc for this edge
    if (-d < 0.0)
      sN = 0.0;
    else if (-d > a)
      sN = sD;
    else 
    {
      sN = -d;
      sD = a;
    }
  }
  else if (tN > tD)
  {      // tc > 1  => the t=1 edge is visible
    tN = tD;
    // recompute sc for this edge
    if ((-d + b) < 0.0)
      sN = 0;
    else if ((-d + b) > a)
      sN = sD;
    else
    {
      sN = (-d +  b);
      sD = a;
    }
  }
  // finally do the division to get sc and tc
  sc = (abs(sN) < SMALL_NUM ? 0.0 : sN / sD);
  tc = (abs(tN) < SMALL_NUM ? 0.0 : tN / tD);
 
  // get the difference of the two closest points
  Eigen::Vector3d dP = w + (sc * u) - (tc * v);  // =  S1(sc) - S2(tc)
 
  return dP.norm();   // return the closest distance
}
 
 
 
 
template <typename VectorType>
double calc_closest_point_to_approach_time(const VectorType& x1, const VectorType& vel1, const VectorType& x2, const VectorType& vel2)
{
  VectorType dv = vel1 - vel2;
 
  double dv2 = dv.squaredNorm(); // dot(v,v)
  if (dv2 < SMALL_NUM)      // the  tracks are almost parallel
    return 0.0;             // any time is ok.  Use time 0.
 
  VectorType w0 = x1 - x2;
  double cpatime = -w0.dot(dv) / dv2;
 
  return cpatime;             // time of CPA
}
 
template <typename VectorType>
double calc_closest_point_to_approach_distance(const VectorType& x1, const VectorType& vel1, const VectorType& x2, const VectorType& vel2, double bound_cpa_time = 0)
{
  double ctime = calc_closest_point_to_approach_time<VectorType>(x1, vel1, x2, vel2);
  if (bound_cpa_time!=0 && ctime > bound_cpa_time) ctime = bound_cpa_time;
  VectorType P1 = x1 + (ctime * vel1);
  VectorType P2 = x2 + (ctime * vel2);
 
  return (P2-P1).norm(); // distance at CPA
}
 
 
 
// dist_Point_to_Line(): get the distance of a point to a line
//     Input:  a Point P and a Line L (in any dimension)
//     Return: the shortest distance from P to L
template <typename VectorType>
double calc_distance_point_to_line( const VectorType& point, const VectorType& line_base, const VectorType& line_dir)
{
  VectorType w = point - line_base;
 
  double c1 = w.dot(line_dir);
  double c2 = line_dir.dot(line_dir);
  double b = c1 / c2;
 
  VectorType Pb = line_base + b * line_dir;
  return (point-Pb).norm();
}
//===================================================================
 
 
// dist_Point_to_Segment(): get the distance of a point to a segment
//     Input:  a Point P and a Segment S (in any dimension)
//     Return: the shortest distance from P to S
template <typename VectorType>
double calc_distance_point_to_segment( const VectorType& point, const VectorType& line_start, const VectorType& line_end)
{
  VectorType v = line_end - line_start;
  VectorType w = point - line_start;
 
  double c1 = w.dot(v);
  if ( c1 <= 0 )
    return w.norm();
 
  double c2 = v.dot(v);
  if ( c2 <= c1 )
    return (point-line_end).norm();
 
  double b = c1 / c2;
  VectorType Pb = line_start + b * v;
  return (point-Pb).norm();
}
 
  
  
} // namespace teb_local_planner
 
#endif /* DISTANCE_CALCULATIONS_H */