text: // David Eberly, Geometric Tools, Redmond WA 98052
  // Copyright (c) 1998-2020
  // Distributed under the Boost Software License, Version 1.0.
  // https://www.boost.org/LICENSE_1_0.txt
  // https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
  // Version: 4.0.2019.08.13
  
  #pragma once
  
  #include <Mathematics/DCPQuery.h>
  #include <Mathematics/Segment.h>
  
  namespace gte
  {
      template <int N, typename Real>
      class DCPQuery<Real, Vector<N, Real>, Segment<N, Real>>
      {
      public:
          struct Result
          {
              Real distance, sqrDistance;
              Real segmentParameter;  // t in [0,1]
              Vector<N, Real> segmentClosest;  // (1-t)*p[0] + t*p[1]
          };
  
          Result operator()(Vector<N, Real> const& point, Segment<N, Real> const& segment)
          {
              Result result;
  
              // The direction vector is not unit length.  The normalization is
              // deferred until it is needed.
              Vector<N, Real> direction = segment.p[1] - segment.p[0];
              Vector<N, Real> diff = point - segment.p[1];
              Real t = Dot(direction, diff);
              if (t >= (Real)0)
              {
                  result.segmentParameter = (Real)1;
                  result.segmentClosest = segment.p[1];
              }
              else
              {
                  diff = point - segment.p[0];
                  t = Dot(direction, diff);
                  if (t <= (Real)0)
                  {
                      result.segmentParameter = (Real)0;
                      result.segmentClosest = segment.p[0];
                  }
                  else
                  {
                      Real sqrLength = Dot(direction, direction);
                      if (sqrLength > (Real)0)
                      {
                          t /= sqrLength;
                          result.segmentParameter = t;
                          result.segmentClosest = segment.p[0] + t * direction;
                      }
                      else
                      {
                          result.segmentParameter = (Real)0;
                          result.segmentClosest = segment.p[0];
                      }
                  }
              }
  
              diff = point - result.segmentClosest;
              result.sqrDistance = Dot(diff, diff);
              result.distance = std::sqrt(result.sqrDistance);
  
              return result;
          }
      };
  
      // Template aliases for convenience.
      template <int N, typename Real>
      using DCPPointSegment = DCPQuery<Real, Vector<N, Real>, Segment<N, Real>>;
  
      template <typename Real>
      using DCPPoint2Segment2 = DCPPointSegment<2, Real>;
  
      template <typename Real>
      using DCPPoint3Segment3 = DCPPointSegment<3, Real>;
  }
  