Example #1
0
int ON_Intersect( // returns 0 = no intersections, 
                  // 1 = one intersection, 
                  // 2 = 2 intersections
                  // If 0 is returned, first point is point 
                  // on line closest to sphere and 2nd point is the point
                  // on the sphere closest to the line.
                  // If 1 is returned, first point is obtained by evaluating
                  // the line and the second point is obtained by evaluating
                  // the sphere.
                 const ON_Line& line, const ON_Sphere& sphere,
                  ON_3dPoint& A, ON_3dPoint& B // intersection point(s) returned here
                  )
{
  int rc = 0;
  const ON_3dPoint sphere_center = sphere.plane.origin;
  const double sphere_radius = fabs(sphere.radius);
  double tol = sphere_radius*ON_SQRT_EPSILON;
  if ( tol < ON_ZERO_TOLERANCE )
    tol = ON_ZERO_TOLERANCE;
  ON_3dPoint line_center = line.ClosestPointTo(sphere_center);
  double d = line_center.DistanceTo(sphere_center);
  if ( d >= sphere_radius-tol ) {
    rc = ( d <= sphere_radius-tol ) ? 1 : 0;
    A = line_center;
    B = sphere.ClosestPointTo(line_center);
  }
  else {
    d /= sphere_radius;
    double h = sphere_radius*sqrt(1.0 - d*d);
    ON_3dVector V = line.Direction();
    V.Unitize();
    A = sphere.ClosestPointTo(line_center - h*V);
    B = sphere.ClosestPointTo(line_center + h*V);
    d = A.DistanceTo(B);
    if ( d <= ON_ZERO_TOLERANCE ) {
      A = line_center;
      B = sphere.ClosestPointTo(line_center);
      rc = 1;
    }
    else
      rc = 2;
  }
  return rc;
}
Example #2
0
int ON_Intersect( // returns 0 = no intersections, 
                  // 1 = intersection = single point, 
                  // 2 = intersection = circle
                  // If 0 is returned, returned circle has radius=0
                  // and center = point on sphere closest to plane.
                  // If 1 is returned, intersection is a single
                  // point and returned circle has radius=0
                  // and center = intersection point on sphere.
                 const ON_Plane& plane, const ON_Sphere& sphere, ON_Circle& circle
                  )
{
  int rc = 0;
  const ON_3dPoint sphere_center = sphere.plane.origin;
  const double sphere_radius = fabs(sphere.radius);
  double tol = sphere_radius*ON_SQRT_EPSILON;
  if ( tol < ON_ZERO_TOLERANCE )
    tol = ON_ZERO_TOLERANCE;

  circle.plane = plane;

  ON_3dPoint plane_center = plane.ClosestPointTo(sphere_center);
  double d = plane_center.DistanceTo(sphere_center);

  if ( d >= sphere_radius-tol ) {
    rc = ( d <= sphere_radius-tol ) ? 1 : 0;
    circle.plane.origin = sphere.ClosestPointTo(plane_center);
    circle.plane.UpdateEquation();
    circle.radius = 0.0;
  }
  else {
    d /= sphere_radius;
    circle.radius = sphere_radius*sqrt(1.0 - d*d);
    if ( circle.radius <= ON_ZERO_TOLERANCE ) {
      circle.radius = 0.0;
      rc = 1;
    }
    else
      rc = 2;
  }
  //circle.UpdatePoints();    
  return rc;
}
Example #3
0
int ON_Intersect( const ON_Sphere& sphere0, 
                  const ON_Sphere& sphere1, 
                  ON_Circle& circle
                 )

{
  double r0 = sphere0.Radius();
  double r1 = sphere1.Radius();
  ON_3dPoint C0 = sphere0.Center();
  ON_3dPoint C1 = sphere1.Center();
  ON_3dVector D = C1-C0;
  double d = D.Length();
  if (!D.Unitize()){
    if (fabs(r1-r0) > ON_ZERO_TOLERANCE)
      return 0;//Same center, different radii
    return 3;//Same sphere.
  }

  //Spheres are appart.
  if (d > r0 + r1)
    return 0;

  //Spheres tangent and appart
  if (d == r0+r1){
    ON_3dPoint P = C0 + r0*D;
    circle.Create(P, 0.0);
    return 1;
  }

  //Spheres tangent, one inside the other
  if (d == fabs(r0-r1)){
    ON_3dPoint P = (r0 > r1) ? C0 + r0*D : C0 - r0*D;
    circle.Create(P, 0.0);
    return 1;
  }

  //Spheres don't intersect, one inside the other.
  if (d < fabs(r0-r1))
    return 0;

  //Intersection is a circle
  double x = 0.5*(d*d + r0*r0 - r1*r1)/d;
  if (x >= r0){//Shouldn't happen
    ON_3dPoint P = C0 + r0*D;
    circle.Create(P, 0.0);
    return 1;
  }
  if (x <= -r0){//Shouldn't happen
    ON_3dPoint P = C0 - r0*D;
    circle.Create(P, 0.0);
    return 1;
  }
  double y = r0*r0 - x*x;
  if (y < 0.0)//Shouldn't happen
    return 0;
  y = sqrt(y);

  ON_3dPoint P = C0 + x*D;
  ON_Plane plane(P, D);
  circle.Create(plane, y);
  return 2;
}
Example #4
0
// Copied from opennurbs_intersect.cpp but with a bug fix.
// We can remove it once the bug is fixed in OpenNurbs and once 
// Grasshopper has dropped Rhino4 support.
int PS_Intersect(
        const ON_Plane& plane,
        const ON_Sphere& sphere, 
        ON_Circle& circle
        )
{
  // 16 April 2011 Dale Lear
  //   Prior to this date, this function did not return the correct answer.

  int rc = 0;
  const double sphere_radius = fabs(sphere.radius);
  double tol = sphere_radius*ON_SQRT_EPSILON;
  if ( !(tol >= ON_ZERO_TOLERANCE) )
    tol = ON_ZERO_TOLERANCE;
  const ON_3dPoint sphere_center = sphere.Center();
  ON_3dPoint circle_center = plane.ClosestPointTo(sphere_center);
  double d = circle_center.DistanceTo(sphere_center);

  circle.radius = 0.0;

  if ( ON_IsValid(sphere_radius) && ON_IsValid(d) && d <= sphere_radius + tol )
  {
    if ( sphere_radius > 0.0 )
    {
      d /= sphere_radius;
      d = 1.0 - d*d;
      // The d > 4.0*ON_EPSILON was picked by testing spheres with
      // radius = 1 and center = (0,0,0).  Do not make 4.0*ON_EPSILON 
      // any smaller and please discuss changes with Dale Lear.
      circle.radius = (d > 4.0*ON_EPSILON) ? sphere_radius*sqrt(d) : 0.0;
    }
    else
      circle.radius = 0.0;

    if ( circle.radius <= ON_ZERO_TOLERANCE )
    {
      // return a single point
      rc = 1;
      
      circle.radius = 0.0;

      //  When tolerance is in play, put the point on the sphere.
      //  If the caller prefers the plane, then they can adjust the
      //  returned answer to get the plane.
      ON_3dVector R = circle_center - sphere_center;
      double r0 = R.Length();
      if ( r0 > 0.0 )
      {
        R.Unitize();
        ON_3dPoint C1 = sphere_center + sphere_radius*R;
        double r1 = C1.DistanceTo(sphere_center);
        if ( fabs(sphere.radius-r1) < fabs(sphere.radius-r0) )
          circle_center = C1;
      }
    }
    else 
    {
      // return a circle
      rc = 2;
    }
  }

  // Update circle's plane here in case the input plane 
  // is the circle's plane member.
  circle.plane = plane;
  circle.plane.origin = circle_center;
  circle.plane.UpdateEquation();

  return rc;
}