Triangle Class Reference

Triangle geometry helper. More...

#include <Triangle.h>

Inheritance diagram for Triangle:

Public Member Functions
	Triangle ()=default
	Triangle (const libMesh::Point &p0, const libMesh::Point &p1, const libMesh::Point &p2)
	~Triangle () override=default
libMesh::Point	normal () const
	Normal vector of the triangle. More...
bool	intersect (const LineSegment &l, libMesh::Point &intersect_p) const
	Check if a line segment intersects this triangle. More...
bool	intersect (const LineSegment &line_segment) const override
	Check if a line segment intersects this triangle, without returning the intersection point. More...
Ball	computeBoundingBall () const override
	Compute a bounding ball for this triangle. More...

Private Attributes
libMesh::Point	_p0
libMesh::Point	_p1
libMesh::Point	_p2

Detailed Description

Triangle geometry helper.

Definition at line 21 of file Triangle.h.

Constructor & Destructor Documentation

Triangle() [1/2]

Triangle::Triangle ( )

default

Triangle() [2/2]

Triangle::Triangle	(	const libMesh::Point &	p0,
		const libMesh::Point &	p1,
		const libMesh::Point &	p2
	)

Definition at line 18 of file Triangle.C.

                                                                       : _p0(p0), _p1(p1), _p2(p2)
{
}

~Triangle()

Triangle::~Triangle ( )

overridedefault

Member Function Documentation

computeBoundingBall()

Ball Triangle::computeBoundingBall ( ) const

overridevirtual

Compute a bounding ball for this triangle.

Implements GeometryBase.

Definition at line 88 of file Triangle.C.

{
  const Point centroid = (_p0 + _p1 + _p2) / 3.0;

  Real max_sq_dist = 0.0;
  for (const auto * p : {&_p0, &_p1, &_p2})
  {
    const Real dist_sq = (*p - centroid).norm_sq();
    if (dist_sq > max_sq_dist)
      max_sq_dist = dist_sq;
  }

  const Real radius = std::sqrt(max_sq_dist);
  return Ball(centroid, radius);
}

intersect() [1/2]

bool Triangle::intersect	(	const LineSegment &	l,
		libMesh::Point &	intersect_p
	)		const

Check if a line segment intersects this triangle.

Definition at line 35 of file Triangle.C.

Referenced by intersect().

{
  const auto & a = line_segment.start();
  const auto & b = line_segment.end();

  // (a) Build basic vectors and choose a robust tolerance
  const Point dir = b - a;

  const Point edge1 = _p1 - _p0;
  const Point edge2 = _p2 - _p0;
  constexpr Real eps = libMesh::TOLERANCE;

  // (b) Test for parallel or degenerate configuration
  const Point pvec = dir.cross(edge2);
  const Real det = edge1 * pvec;
  if (std::abs(det) < eps)
    return false; // ray nearly parallel to triangle

  const Real inv_det = 1.0 / det;

  // (c) Compute barycentric coordinate u and check 0 <= u <= 1
  const Point tvec = a - _p0;
  const Real u = (tvec * pvec) * inv_det;
  if (!MooseUtils::absoluteFuzzyGreaterEqual(u, 0.0, eps) ||
      !MooseUtils::absoluteFuzzyLessEqual(u, 1.0, eps))
    return false;

  // (d) Compute barycentric coordinate v and check 0 <= v and u + v <= 1
  const Point qvec = tvec.cross(edge1);
  const Real v = (dir * qvec) * inv_det;
  if (!MooseUtils::absoluteFuzzyGreaterEqual(v, 0.0, eps) ||
      !MooseUtils::absoluteFuzzyLessEqual(u + v, 1.0, eps))
    return false;

  // (e) Locate intersection along line segment (0 <= t <= 1 constrains to a--b)
  const Real t = (edge2 * qvec) * inv_det;
  if (!MooseUtils::absoluteFuzzyGreaterEqual(t, 0.0, eps) ||
      !MooseUtils::absoluteFuzzyLessEqual(t, 1.0, eps))
    return false;

  // (f) Intersection lies inside both the triangle and the segment
  intersect_p = a + dir * t;
  return true;
}

intersect() [2/2]

bool Triangle::intersect ( const LineSegment &  line_segment ) const

overridevirtual

Check if a line segment intersects this triangle, without returning the intersection point.

Implements GeometryBase.

Definition at line 81 of file Triangle.C.

{
  libMesh::Point p;
  return intersect(line_segment, p);
}

normal()

Point Triangle::normal

(

)

const

Normal vector of the triangle.

Definition at line 23 of file Triangle.C.

{
  const auto v1 = _p1 - _p0;
  const auto v2 = _p2 - _p0;

  auto n = v1.cross(v2);
  n /= n.norm();

  return n;
}

Member Data Documentation

_p0

libMesh::Point Triangle::_p0

private

Definition at line 50 of file Triangle.h.

Referenced by computeBoundingBall(), intersect(), and normal().

_p1

libMesh::Point Triangle::_p1

private

Definition at line 50 of file Triangle.h.

Referenced by computeBoundingBall(), intersect(), and normal().

_p2

libMesh::Point Triangle::_p2

private

Definition at line 50 of file Triangle.h.

Referenced by computeBoundingBall(), intersect(), and normal().

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

• include/geometries/Triangle.h
• src/geometries/Triangle.C