LineSegment Class Reference

The LineSegment class is used by the LineMaterialSamplerBase class and for some ray tracing stuff. More...

#include <LineSegment.h>

Public Member Functions
	LineSegment ()=default
	LineSegment (const Point &p0, const Point &p1)
virtual	~LineSegment ()=default
Point	closest_point (const Point &p) const
	Returns the closest point on the LineSegment to the passed in point. More...
bool	closest_normal_point (const Point &p, Point &closest_p) const
	Finds the closest point on the Line determined by the Line Segments. More...
bool	contains_point (const Point &p) const
	Determines whether a point is in a line segment or not. More...
bool	intersect (const Plane &pl, Point &intersect_p) const
bool	intersect (const LineSegment &l1, Point &intersect_p) const
const Point &	start () const
	Beginning of the line segment. More...
const Point &	end () const
	Ending of the line segment. More...
void	setStart (const Point &p0)
	Sets the beginning of the line segment. More...
void	setEnd (const Point &p1)
	Sets the end of the line segment. More...
void	set (const Point &p0, const Point &p1)
	Sets the points on the line segment. More...
Real	length () const
	Length of segment. More...

Private Member Functions
bool	closest_point (const Point &p, bool clamp_to_segment, Point &closest_p) const

Private Attributes
Point	_p0
Point	_p1

Detailed Description

The LineSegment class is used by the LineMaterialSamplerBase class and for some ray tracing stuff.

Definition at line 29 of file LineSegment.h.

Constructor & Destructor Documentation

LineSegment() [1/2]

LineSegment::LineSegment ( )

default

LineSegment() [2/2]

LineSegment::LineSegment	(	const Point &	p0,
		const Point &	p1
	)

Definition at line 17 of file LineSegment.C.

: _p0(p0), _p1(p1) {}

~LineSegment()

virtual LineSegment::~LineSegment ( )

virtualdefault

Member Function Documentation

closest_normal_point()

bool LineSegment::closest_normal_point	(	const Point &	p,
		Point &	closest_p
	)		const

Finds the closest point on the Line determined by the Line Segments.

Returns a boolean indicating whether that normal point is within the LineSegment or not

Definition at line 53 of file LineSegment.C.

{
  return closest_point(p, false, closest_p);
}

closest_point() [1/2]

Point LineSegment::closest_point

(

const Point &

p

)

const

Returns the closest point on the LineSegment to the passed in point.

Note that the closest point may be one of the ends of the LineSegment.

Definition at line 45 of file LineSegment.C.

Referenced by closest_normal_point(), and contains_point().

{
  Point closest_p;
  closest_point(p, true, closest_p);
  return closest_p;
}

closest_point() [2/2]

bool LineSegment::closest_point ( const Point &  p, bool  clamp_to_segment, Point &  closest_p  ) const

private

Definition at line 20 of file LineSegment.C.

{
  Point p0_p = p - _p0;
  Point p0_p1 = _p1 - _p0;
  Real p0_p1_2 = p0_p1.norm_sq();
  Real perp = p0_p(0) * p0_p1(0) + p0_p(1) * p0_p1(1) + p0_p(2) * p0_p1(2);
  Real t = perp / p0_p1_2;
  bool on_segment = true;

  if (t < 0.0 || t > 1.0)
    on_segment = false;

  if (clamp_to_segment)
  {
    if (t < 0.0)
      t = 0.0;
    else if (t > 1.0)
      t = 1.0;
  }

  closest_p = _p0 + p0_p1 * t;
  return on_segment;
}

contains_point()

bool LineSegment::contains_point

(

const Point &

p

)

const

Determines whether a point is in a line segment or not.

Definition at line 59 of file LineSegment.C.

Referenced by Moose::sideIntersectedByLine().

{
  Point closest_p;
  return closest_point(p, false, closest_p) && closest_p.absolute_fuzzy_equals(p);
}

end()

const Point& LineSegment::end ( ) const

inline

Ending of the line segment.

Definition at line 68 of file LineSegment.h.

Referenced by dataStore(), IntersectionPointsAlongLine::execute(), Moose::recursivelyFindElementsIntersectedByLine(), and to_json().

{ return _p1; }

intersect() [1/2]

bool LineSegment::intersect	(	const Plane &	pl,
		Point &	intersect_p
	)		const

There are three cases in 3D for intersection of a line and a plane Case 1: The line is parallel to the plane - No intersection Numerator = non-zero Denominator = zero

Case 2: The line is within the plane - Inf intersection Numerator = zero Denominator = zero

Case 3: The line intersects the plane at a single point Denominator = non-zero

Definition at line 66 of file LineSegment.C.

Referenced by Moose::sideIntersectedByLine().

{
  Point pl0 = pl.get_planar_point();
  RealVectorValue N = pl.unit_normal(_p0);
  RealVectorValue I = (_p1 - _p0).unit();

  Real numerator = (pl0 - _p0) * N;
  Real denominator = I * N;

  // The Line is parallel to the plane
  if (std::abs(denominator) < 1.e-10)
  {
    // The Line is on the plane
    if (std::abs(numerator) < 1.e-10)
    {
      // The solution is not unique so we'll just pick an end point for now
      intersect_p = _p0;
      return true;
    }
    return false;
  }

  Real d = numerator / denominator;

  // Make sure we haven't moved off the line segment!
  if (d + libMesh::TOLERANCE < 0 || d - libMesh::TOLERANCE > (_p1 - _p0).norm())
    return false;

  intersect_p = d * I + _p0;

  return true;
}

intersect() [2/2]

bool LineSegment::intersect	(	const LineSegment &	l1,
		Point &	intersect_p
	)		const

First check for concurance:

| x1 y1 z1 1 | | x2 y2 z2 1 | = (x3 - x1) * [(x2-x1) x (x4-x3)] = 0 | x3 y3 z3 1 | | x4 y4 z4 1 |

Solve: x = _p0 + (_p1 - _p0)*s x = l.p0 + (l._p1 - l.p0)*t

where a = _p1 - _p0 b = l._p1 - l._p0 c = l._p0 - _p0

s = (c x b) * (a x b) / | a x b |^2

 Parameteric Equation of lines
 _p0 + t(v0) = l._p0 + u(v1)

 Case 1: Parallel Lines
         v0 x v1 == 0

 Case 1a: Collinear Lines
         v0 x v1 == 0
         (l._p0 - _p0) x (_p1 - _p0) == 0

 Case 2: Intersecting Lines
         0 <= t <= 1
         0 <= u <= 1


 Case 1: The lines do not intersect
         vleft cross vright = non-zero

 Case 2: The lines are co-linear
         vleft cross vright = zero
         vleft (Denominator) = zero

 Case 3: The line intersect at a single point
         vleft cross vright = zero
         vleft (Denominator) = non-zero

RealVectorValue v0 = _p1 - _p0; RealVectorValue v1 = l._p1 - l._p0; RealVectorValue v2 = l._p0 - _p0;

RealVectorValue vbot = v0.cross(v1); RealVectorValue vtop = v2.cross(v1);

RealVectorValue crossed = vleft.cross(vright);

Case 1: No intersection if (std::abs(vleft.cross(vright).size()) > 1.e-10) return false;

Case 2: Co-linear (just return one of the end points) if (std::abs(vleft.size()) < 1.e-10) { intersect_p = _p0; return true; }

Case 3:

TODO: We could detect whether the Line Segments actually overlap instead of whether the Lines are co-linear

Real a = vright.size()/vleft.size(); intersect_p = _p0 + a*v0; return true;

Definition at line 114 of file LineSegment.C.

{
  RealVectorValue a = _p1 - _p0;
  RealVectorValue b = l._p1 - l._p0;
  RealVectorValue c = l._p0 - _p0;

  RealVectorValue v = a.cross(b);

  // Check for parallel lines
  if (std::abs(v.norm()) < 1.e-10 && std::abs(c.cross(a).norm()) < 1.e-10)
  {
    // TODO: The lines are co-linear but more work is needed to determine and intersection point
    //       it could be the case that the line segments don't lie on the same line or overlap only
    //       a bit
    return true;
  }

  // Check that the lines are coplanar
  Real concur = c * (a.cross(b));
  if (std::abs(concur) > 1.e-10)
    return false;

  Real s = (c.cross(b) * v) / (v * v);
  Real t = (c.cross(a) * v) / (v * v);

  // if s and t are between 0 and 1 then the Line Segments intersect
  // TODO: We could handle other case of clamping to the end of Line
  //       Segements if we want to here

  if (s >= 0 && s <= 1 && t >= 0 && t <= 1)
  {
    intersect_p = _p0 + s * a;
    return true;
  }
  return false;

}

length()

Real LineSegment::length ( ) const

inline

Length of segment.

Definition at line 90 of file LineSegment.h.

{ return (_p0 - _p1).norm(); }

set()

void LineSegment::set	(	const Point &	p0,
		const Point &	p1
	)

Sets the points on the line segment.

Parameters

p0	The start point of the line segment
p1	The end point of the line segment

Definition at line 229 of file LineSegment.C.

Referenced by dataLoad().

{
  setStart(p0);
  setEnd(p1);
}

setEnd()

void LineSegment::setEnd ( const Point &  p1 )

inline

Sets the end of the line segment.

Definition at line 78 of file LineSegment.h.

Referenced by set().

{ _p1 = p1; }

setStart()

void LineSegment::setStart ( const Point &  p0 )

inline

Sets the beginning of the line segment.

Definition at line 73 of file LineSegment.h.

Referenced by set().

{ _p0 = p0; }

start()

const Point& LineSegment::start ( ) const

inline

Beginning of the line segment.

Definition at line 63 of file LineSegment.h.

Referenced by dataStore(), and to_json().

{ return _p0; }

Member Data Documentation

_p0

Point LineSegment::_p0

private

Definition at line 95 of file LineSegment.h.

Referenced by closest_point(), intersect(), length(), setStart(), and start().

_p1

Point LineSegment::_p1

private

Definition at line 95 of file LineSegment.h.

Referenced by closest_point(), end(), intersect(), length(), and setEnd().

---

The documentation for this class was generated from the following files:

• include/utils/LineSegment.h
• src/utils/LineSegment.C