G4TessellatedGeometryAlgorithms.cc

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//
// G4TessellatedGeometryAlgorithms implementation
//
// 07 August 2007, P R Truscott, QinetiQ Ltd, UK - Created, with member
//                 functions based on the work of Rickard Holmberg.
// 12 October 2012, M Gayer, CERN, - Reviewed optimized implementation.
// --------------------------------------------------------------------
 
#include "G4TessellatedGeometryAlgorithms.hh"
 
#include <cfloat> 
 
///////////////////////////////////////////////////////////////////////////////
//
// IntersectLineAndTriangle2D
//
// Determines whether there is an intersection between a line defined
// by r = p + s.v and a triangle defined by verticies p0, p0+e0 and p0+e1.
//
// Here:
//        p = 2D vector
//        s = scaler on [0,infinity)
//        v = 2D vector
//        p0, e0 and e1 are 2D vectors
// Information about where the intersection occurs is returned in the
// variable location.
//
// This is based on the work of Rickard Holmberg.
//
G4bool G4TessellatedGeometryAlgorithms::IntersectLineAndTriangle2D (
  const G4TwoVector& p,  const G4TwoVector& v,
  const G4TwoVector& p0, const G4TwoVector& e0, const G4TwoVector& e1,
  G4TwoVector location[2])
{
  G4TwoVector loc0[2];
  G4int e0i = IntersectLineAndLineSegment2D (p,v,p0,e0,loc0);
  if (e0i == 2)
  {
    location[0] = loc0[0];
    location[1] = loc0[1];
    return true;
  }
 
  G4TwoVector loc1[2];
  G4int e1i = IntersectLineAndLineSegment2D (p,v,p0,e1,loc1);
  if (e1i == 2)
  {
    location[0] = loc1[0];
    location[1] = loc1[1];
    return true;
  }
 
  if ((e0i == 1) && (e1i == 1))
  {
    if ((loc0[0]-p).mag2() < (loc1[0]-p).mag2())
    {
      location[0] = loc0[0];
      location[1] = loc1[0];
    }
    else
    {
      location[0] = loc1[0];
      location[1] = loc0[0];
    }
    return true;
  }
 
  G4TwoVector p1 = p0 + e0;
  G4TwoVector DE = e1 - e0;
  G4TwoVector loc2[2];
  G4int e2i = IntersectLineAndLineSegment2D (p,v,p1,DE,loc2);
  if (e2i == 2)
  {
    location[0] = loc2[0];
    location[1] = loc2[1];
    return true;
  }
 
  if ((e0i == 0) && (e1i == 0) && (e2i == 0)) { return false; }
 
  if ((e0i == 1) && (e2i == 1))
  {
    if ((loc0[0]-p).mag2() < (loc2[0]-p).mag2())
    {
      location[0] = loc0[0];
      location[1] = loc2[0];
    }
    else
    {
      location[0] = loc2[0];
      location[1] = loc0[0];
    }
    return true;
  }
 
  if ((e1i == 1) && (e2i == 1))
  {
    if ((loc1[0]-p).mag2() < (loc2[0]-p).mag2())
    {
      location[0] = loc1[0];
      location[1] = loc2[0];
    }
    else
    {
      location[0] = loc2[0];
      location[1] = loc1[0];
    }
    return true;
  }
 
  return false;
}
 
///////////////////////////////////////////////////////////////////////////////
//
// IntersectLineAndLineSegment2D
//
// Determines whether there is an intersection between a line defined
// by r = p0 + s.d0 and a line-segment with endpoints p1 and p1+d1.
// Here:
//        p0 = 2D vector
//        s  = scaler on [0,infinity)
//        d0 = 2D vector
//        p1 and d1 are 2D vectors
//
// This function returns:
// 0 - if there is no intersection;
// 1 - if there is a unique intersection;
// 2 - if the line and line-segments overlap, and the intersection is a
//     segment itself.
// Information about where the intersection occurs is returned in the
// as ??.
//
// This is based on the work of Rickard Holmberg as well as material published
// by Philip J Schneider and David H Eberly, "Geometric Tools for Computer
// Graphics," ISBN 1-55860-694-0, pp 244-245, 2003.
//
G4int G4TessellatedGeometryAlgorithms::IntersectLineAndLineSegment2D (
  const G4TwoVector& p0, const G4TwoVector& d0,
  const G4TwoVector& p1, const G4TwoVector& d1, G4TwoVector location[2])
{
  G4TwoVector e     = p1 - p0;
  G4double kross    = cross(d0,d1);
  G4double sqrKross = kross * kross;
  G4double sqrLen0  = d0.mag2();
  G4double sqrLen1  = d1.mag2();
  location[0]       = G4TwoVector(0.0,0.0);
  location[1]       = G4TwoVector(0.0,0.0);
 
  if (sqrKross > DBL_EPSILON * DBL_EPSILON * sqrLen0 * sqrLen1)
  {
    //
    // The line and line segment are not parallel. Determine if the intersection
    // is in positive s where r=p0 + s*d0, and for 0<=t<=1 where r=p1 + t*d1.
    //
    G4double ss = cross(e,d1)/kross;
    if (ss < 0)
    {
      return 0; // Intersection does not occur for positive ss
    }
    G4double t = cross(e,d0)/kross;
    if (t < 0 || t > 1)
    {
      return 0; // Intersection does not occur on line-segment
    }
    //
    // Intersection of lines is a single point on the forward-propagating line
    // defined by r=p0 + ss*d0, and the line segment defined by  r=p1 + t*d1.
    //
    location[0] = p0 + ss*d0;
    return 1;
  }
  //
  // Line and line segment are parallel. Determine whether they overlap or not.
  //
  G4double sqrLenE = e.mag2();
  kross            = cross(e,d0);
  sqrKross         = kross * kross;
  if (sqrKross > DBL_EPSILON * DBL_EPSILON * sqrLen0 * sqrLenE)
  {
    return 0; //Lines are different.
  }
  //
  // Lines are the same.  Test for overlap.
  //
  G4double s0   = d0.dot(e)/sqrLen0;
  G4double s1   = s0 + d0.dot(d1)/sqrLen0;
  G4double smin = 0.0;
  G4double smax = 0.0;
 
  if (s0 < s1) { smin = s0; smax = s1; }
  else         { smin = s1; smax = s0; }
 
  if (smax < 0.0)
  {
    return 0;
  }
  if (smin < 0.0)
  {
    location[0] = p0;
    location[1] = p0 + smax*d0;
    return 2;
  }
  
  location[0] = p0 + smin*d0;
  location[1] = p0 + smax*d0;
  return 2;
}
 
///////////////////////////////////////////////////////////////////////////////
//
// CrossProduct
//
// This is just a ficticious "cross-product" function for two 2D vectors...
// "ficticious" because such an operation is not relevant to 2D space compared
// with 3D space.
//
G4double G4TessellatedGeometryAlgorithms::cross(const G4TwoVector& v1,
                                                const G4TwoVector& v2)
{
  return v1.x()*v2.y() - v1.y()*v2.x();
}