MortarSegmentHelper Class Reference

This class supports defining mortar segment mesh elements in 3D by projecting secondary and primary elements onto a linearized plane, computing the overlapping polygon formed by their projections, and triangulating the resulting nodes. More...

#include <MortarSegmentHelper.h>

Classes
struct	ReferenceMappingData
	Output containers and filtering data used while generating reference-coordinate mappings. More...

Public Member Functions
	MortarSegmentHelper (std::vector< Point > secondary_nodes, const Point &center, const Point &normal, const MortarSegmentTriangulationMode triangulation_mode, const bool triangulate_triangles)
	Construct a helper that generates mortar segment geometry only. More...
	MortarSegmentHelper (std::vector< Point > secondary_nodes, std::vector< Point > secondary_reference_points, const Point &center, const Point &normal, const MortarSegmentTriangulationMode triangulation_mode, const bool triangulate_triangles)
	Construct a helper that also tracks secondary parent-reference coordinates. More...
Point	getIntersection (const Point &p1, const Point &p2, const Point &q1, const Point &q2, Real &s) const
	Computes the intersection between line segments defined by point pairs (p1,p2) and (q1,q2) Also computes s, the ratio of distance between (p1,p2) that the intersection falls, quantity s is useful in avoiding adding nearly degenerate nodes. More...
bool	isInsideSecondary (const Point &pt) const
	Check that a point is inside the secondary polygon (for verification only) More...
bool	isDisjoint (const std::vector< Point > &poly) const
	Checks whether polygons are disjoint for an easy out. More...
std::vector< Point >	projectPrimaryPoly (const std::vector< Point > &primary_nodes) const
	Project a primary polygon into the helper plane while preserving the clipping orientation. More...
std::vector< Point >	clipPoly (const std::vector< Point > &primary_nodes) const
	Clip secondary element (defined in instantiation) against given primary polygon result is a set of 2D nodes defining clipped polygon. More...
void	triangulatePoly (std::vector< Point > &poly_nodes, std::vector< std::vector< unsigned int >> &tri_map) const
	Triangulate a polygon according to the configured mortar-segment triangulation mode. More...
void	getMortarSegments (const std::vector< Point > &primary_nodes, std::vector< Point > &nodes, std::vector< std::vector< unsigned int >> &elem_to_nodes)
	Get mortar segments generated by a secondary and primary element pair. More...
void	getMortarSegments (const std::vector< Point > &primary_nodes, const std::vector< Point > &primary_reference_points, std::vector< Point > &nodes, std::vector< std::vector< unsigned int >> &elem_to_nodes, std::vector< std::array< Point, 3 >> &elem_to_secondary_reference_points, std::vector< std::array< Point, 3 >> &elem_to_primary_reference_points, Real minimum_segment_area=0.)
	Get mortar segments and aligned parent-reference coordinates by appending to the output containers. More...
Real	area (const std::vector< Point > &nodes) const
	Compute area of polygon. More...
const Point &	center () const
	Get center point of secondary element. More...
const Point &	normal () const
	Get the unit normal of the projection plane. More...
Real	remainder () const
	Get area fraction remaining after clipping against primary elements. More...
Point	point (unsigned int i) const
	Get 3D position of node of linearized secondary element. More...

Private Member Functions
void	getMortarSegmentsImpl (const std::vector< Point > &primary_nodes, std::vector< Point > &nodes, std::vector< std::vector< unsigned int >> &elem_to_nodes, ReferenceMappingData *reference_mapping)
std::vector< Point >	clipProjectedPoly (const std::vector< Point > &primary_poly) const
	Clip an already projected primary polygon against the secondary polygon. More...
std::optional< Point >	referencePoint (const Point &point, const std::vector< Point > &poly, const std::vector< Point > &reference_points, std::string *failure_reason=nullptr) const
	Recover a parent-reference point from a projected sub-element map. More...

Private Attributes
Point	_center
	Geometric center of secondary element. More...
Point	_normal
	Unit normal of the plane used to project and clip the linearized secondary subpatch. More...
Point	_u
	Vectors orthogonal to normal that span the plane projection will be performed on. More...
Point	_v
Real	_secondary_area
	Area of projected secondary element. More...
Real	_remaining_area_fraction
	Fraction of area remaining after overlapping primary polygons clipped. More...
bool	_debug
Real	_tolerance = 1e-8
	Tolerance for intersection and clipping. More...
const MortarSegmentTriangulationMode	_triangulation_mode
	Triangulation mode used for clipped polygons. More...
const bool	_triangulate_triangles
	Whether already-triangular polygons should still be centroid-subdivided. More...
Real	_area_tol
	Tolerance times secondary area for dimensional consistency. More...
Real	_length_tol
	Tolerance times secondary area for dimensional consistency. More...
std::vector< Point >	_secondary_poly
	List of projected points on the linearized secondary element. More...
std::vector< Point >	_secondary_reference_points
	Parent reference points corresponding to _secondary_poly. More...

Friends
class	MortarSegmentHelperTest

Detailed Description

This class supports defining mortar segment mesh elements in 3D by projecting secondary and primary elements onto a linearized plane, computing the overlapping polygon formed by their projections, and triangulating the resulting nodes.

Definition at line 35 of file MortarSegmentHelper.h.

Constructor & Destructor Documentation

MortarSegmentHelper() [1/2]

MortarSegmentHelper::MortarSegmentHelper	(	std::vector< Point >	secondary_nodes,
		const Point &	center,
		const Point &	normal,
		const MortarSegmentTriangulationMode	triangulation_mode,
		const bool	triangulate_triangles
	)

Construct a helper that generates mortar segment geometry only.

Definition at line 291 of file MortarSegmentHelper.C.

  : MortarSegmentHelper(
        std::move(secondary_nodes), {}, center, normal, triangulation_mode, triangulate_triangles)
{
}

MortarSegmentHelper() [2/2]

MortarSegmentHelper::MortarSegmentHelper	(	std::vector< Point >	secondary_nodes,
		std::vector< Point >	secondary_reference_points,
		const Point &	center,
		const Point &	normal,
		const MortarSegmentTriangulationMode	triangulation_mode,
		const bool	triangulate_triangles
	)

Construct a helper that also tracks secondary parent-reference coordinates.

Definition at line 301 of file MortarSegmentHelper.C.

  : _center(center),
    _normal(normal),
    _debug(false),
    _triangulation_mode(triangulation_mode),
    _triangulate_triangles(triangulate_triangles),
    _secondary_reference_points(std::move(secondary_reference_points))
{
  mooseAssert(_secondary_reference_points.empty() ||
                  secondary_nodes.size() == _secondary_reference_points.size(),
              "Each projected secondary node needs one parent reference point.");

  _secondary_poly.clear();
  _secondary_poly.reserve(secondary_nodes.size());

  // Get orientation of secondary poly
  const Point e1 = secondary_nodes[0] - secondary_nodes[1];
  const Point e2 = secondary_nodes[2] - secondary_nodes[1];
  const Real orient = e2.cross(e1) * _normal;

  // u and v define the tangent plane of the element (at center)
  // Note we embed orientation into our transformation to make 2D poly always
  // positively oriented
  _u = _normal.cross(secondary_nodes[0] - center).unit();
  _v = (orient > 0) ? _normal.cross(_u).unit() : _u.cross(_normal).unit();

  // Transform problem to 2D plane spanned by u and v
  for (const auto & node : secondary_nodes)
  {
    Point pt = node - _center;
    _secondary_poly.emplace_back(pt * _u, pt * _v, 0);
  }

  // Initialize area of secondary polygon
  _remaining_area_fraction = 1.0;
  _secondary_area = area(_secondary_poly);

  // Tolerance for quantities with area dimensions
  _area_tol = _tolerance * _secondary_area;

  // Tolerance for quantites with length dimensions
  _length_tol = _tolerance * std::sqrt(_secondary_area);
}

Member Function Documentation

area()

Real MortarSegmentHelper::area

(

const std::vector< Point > &

nodes

)

const

Compute area of polygon.

Definition at line 1283 of file MortarSegmentHelper.C.

Referenced by getMortarSegmentsImpl(), MortarSegmentHelper(), and triangulatePoly().

{
  Real poly_area = 0;
  for (auto i : index_range(nodes))
    poly_area += nodes[i](0) * nodes[(i + 1) % nodes.size()](1) -
                 nodes[i](1) * nodes[(i + 1) % nodes.size()](0);
  poly_area *= 0.5;
  return poly_area;
}

center()

const Point& MortarSegmentHelper::center ( ) const

inline

Get center point of secondary element.

Definition at line 130 of file MortarSegmentHelper.h.

Referenced by MortarSegmentHelper().

{ return _center; }

clipPoly()

std::vector< Point > MortarSegmentHelper::clipPoly

(

const std::vector< Point > &

primary_nodes

)

const

Clip secondary element (defined in instantiation) against given primary polygon result is a set of 2D nodes defining clipped polygon.

Definition at line 443 of file MortarSegmentHelper.C.

Referenced by getMortarSegmentsImpl().

{
  return clipProjectedPoly(projectPrimaryPoly(primary_nodes));
}

clipProjectedPoly()

std::vector< Point > MortarSegmentHelper::clipProjectedPoly ( const std::vector< Point > &  primary_poly ) const

private

Clip an already projected primary polygon against the secondary polygon.

Keeping projection separate preserves the ordering shared with primary reference points.

Definition at line 449 of file MortarSegmentHelper.C.

Referenced by clipPoly(), and getMortarSegmentsImpl().

{
  if (isDisjoint(primary_poly))
    return {};

  // Initialize clipped poly with secondary poly (secondary is target poly)
  std::vector<Point> clipped_poly = _secondary_poly;

  // Loop through clipping edges
  for (auto i : index_range(primary_poly))
  {
    // If clipped poly trivial, return
    if (clipped_poly.size() < 3)
    {
      clipped_poly.clear();
      return clipped_poly;
    }

    // Set input poly to current clipped poly
    std::vector<Point> input_poly(clipped_poly);
    clipped_poly.clear();

    // Get clipping edge
    const Point & clip_pt1 = primary_poly[i];
    const Point & clip_pt2 = primary_poly[(i + 1) % primary_poly.size()];
    const Point edg = clip_pt2 - clip_pt1;
    const Real cp = clip_pt2(0) * clip_pt1(1) - clip_pt2(1) * clip_pt1(0);

    // Check if point is to the left of (or on) clip_edge
    /*
     * Note that use of tolerance here is to avoid degenerate case when lines are
     * essentially on top of each other (common when meshes match across interface)
     * since finding intersection is ill-conditioned in this case.
     */
    auto is_inside = [&edg, cp](const Point & pt, Real tol)
    { return pt(0) * edg(1) - pt(1) * edg(0) + cp < tol; };

    // Loop through edges of target polygon (with previous clippings already included)
    for (auto j : index_range(input_poly))
    {
      // Get target edge
      const Point curr_pt = input_poly[(j + 1) % input_poly.size()];
      const Point prev_pt = input_poly[j];

      // TODO: Don't need to calculate both each loop
      const bool is_current_inside = is_inside(curr_pt, _area_tol);
      const bool is_previous_inside = is_inside(prev_pt, _area_tol);

      if (is_current_inside)
      {
        if (!is_previous_inside)
        {
          Real s;
          Point intersect = getIntersection(prev_pt, curr_pt, clip_pt1, clip_pt2, s);

          /*
           * s is the fraction of distance along clip poly edge that intersection lies
           * It is used here to avoid degenerate polygon cases. For example, consider a
           * case like:
           *          o
           *          |    (inside)
           *    ------|------
           *          |    (outside)
           * when the distance is small (< 1e-7) we don't want to to add both the point
           * and intersection. Also note that when distance on the scale of 1e-7,
           * area on scale of 1e-14 so is insignificant if this results in dropping
           * a tri (for example if next edge crosses again)
           */
          if (s < (1 - _tolerance))
            clipped_poly.push_back(intersect);
        }
        clipped_poly.push_back(curr_pt);
      }
      else if (is_previous_inside)
      {
        Real s;
        Point intersect = getIntersection(prev_pt, curr_pt, clip_pt1, clip_pt2, s);
        if (s > _tolerance)
          clipped_poly.push_back(intersect);
      }
    }
  }

  // Make sure final clipped poly is not trivial
  if (clipped_poly.size() < 3)
  {
    clipped_poly.clear();
    return clipped_poly;
  }

  // Clean up result by removing any duplicate nodes
  std::vector<Point> cleaned_poly;
  cleaned_poly.push_back(clipped_poly.back());
  for (auto i : make_range(clipped_poly.size() - 1))
  {
    const Point prev_pt = cleaned_poly.back();
    const Point curr_pt = clipped_poly[i];

    // If points are sufficiently distanced, add to output
    if ((curr_pt - prev_pt).norm() > _length_tol)
      cleaned_poly.push_back(curr_pt);
  }

  mooseAssert(
      cleaned_poly.size() <= 8,
      "Our distributed mesh numbering scheme assumes that we have at most 8 nodes resulting from "
      "clipping the projection of the primary sub-element onto the secondary sub-element");
  return cleaned_poly;
}

getIntersection()

Point MortarSegmentHelper::getIntersection	(	const Point &	p1,
		const Point &	p2,
		const Point &	q1,
		const Point &	q2,
		Real &	s
	)		const

Computes the intersection between line segments defined by point pairs (p1,p2) and (q1,q2) Also computes s, the ratio of distance between (p1,p2) that the intersection falls, quantity s is useful in avoiding adding nearly degenerate nodes.

Definition at line 351 of file MortarSegmentHelper.C.

Referenced by clipProjectedPoly().

{
  const Point dp = p2 - p1;
  const Point dq = q2 - q1;
  const Real cp1q1 = p1(0) * q1(1) - p1(1) * q1(0);
  const Real cp1q2 = p1(0) * q2(1) - p1(1) * q2(0);
  const Real cq1q2 = q1(0) * q2(1) - q1(1) * q2(0);
  const Real alpha = 1. / (dp(0) * dq(1) - dp(1) * dq(0));
  s = -alpha * (cp1q2 - cp1q1 - cq1q2);

  // Intersection should be between p1 and p2, if it's not (due to poor conditioning), simply
  // move it to one of the end points
  s = s > 1 ? 1. : s;
  s = s < 0 ? 0. : s;
  return p1 + s * dp;
}

getMortarSegments() [1/2]

void MortarSegmentHelper::getMortarSegments	(	const std::vector< Point > &	primary_nodes,
		std::vector< Point > &	nodes,
		std::vector< std::vector< unsigned int >> &	elem_to_nodes
	)

Get mortar segments generated by a secondary and primary element pair.

Parameters

primary_nodes

List of primary element 3D nodes

Returns

nodes List of 3D mortar segment nodes

tri_map List of integer arrays defining which nodes belong to each mortar segment

Definition at line 930 of file MortarSegmentHelper.C.

{
  getMortarSegmentsImpl(primary_nodes, nodes, elem_to_nodes, nullptr);
}

getMortarSegments() [2/2]

void MortarSegmentHelper::getMortarSegments	(	const std::vector< Point > &	primary_nodes,
		const std::vector< Point > &	primary_reference_points,
		std::vector< Point > &	nodes,
		std::vector< std::vector< unsigned int >> &	elem_to_nodes,
		std::vector< std::array< Point, 3 >> &	elem_to_secondary_reference_points,
		std::vector< std::array< Point, 3 >> &	elem_to_primary_reference_points,
		Real	minimum_segment_area = 0.
	)

Get mortar segments and aligned parent-reference coordinates by appending to the output containers.

Segments below minimum_segment_area are removed before mapping; retained vertices must map uniquely.

Definition at line 938 of file MortarSegmentHelper.C.

{
  ReferenceMappingData reference_mapping{primary_reference_points,
                                         elem_to_secondary_reference_points,
                                         elem_to_primary_reference_points,
                                         minimum_segment_area};
  getMortarSegmentsImpl(primary_nodes, nodes, elem_to_nodes, &reference_mapping);
}

getMortarSegmentsImpl()

void MortarSegmentHelper::getMortarSegmentsImpl ( const std::vector< Point > &  primary_nodes, std::vector< Point > &  nodes, std::vector< std::vector< unsigned int >> &  elem_to_nodes, ReferenceMappingData *  reference_mapping  )

private

Definition at line 955 of file MortarSegmentHelper.C.

Referenced by getMortarSegments().

{
  std::vector<Point> primary_poly;
  std::vector<Point> primary_poly_reference_points;

  if (reference_mapping)
  {
    if (primary_nodes.size() != reference_mapping->primary_reference_points.size())
      mooseError("Reference-interpolation mortar segment generation requires one primary "
                 "reference point per primary sub-element node.");
    if (_secondary_poly.size() != _secondary_reference_points.size())
      mooseError("Reference-interpolation mortar segment generation requires one secondary "
                 "reference point per secondary sub-element node.");
    if (reference_mapping->elem_to_secondary_reference_points.size() != elem_to_nodes.size() ||
        reference_mapping->elem_to_primary_reference_points.size() != elem_to_nodes.size())
      mooseError("Reference-interpolation mortar segment outputs must be aligned before appending "
                 "new segments.");

    // Keep reference points in the projected polygon's orientation.
    const Point e1 = primary_nodes[0] - primary_nodes[1];
    const Point e2 = primary_nodes[2] - primary_nodes[1];
    const Real orient = e2.cross(e1) * _u.cross(_v);
    const auto n_verts = primary_nodes.size();

    primary_poly = projectPrimaryPoly(primary_nodes);
    primary_poly_reference_points.reserve(reference_mapping->primary_reference_points.size());
    for (const auto n : index_range(primary_nodes))
    {
      const auto primary_node_index = (orient > 0) ? n : n_verts - 1 - n;
      primary_poly_reference_points.push_back(
          reference_mapping->primary_reference_points[primary_node_index]);
    }
  }

  // Clip primary elem against secondary elem. Reference mode preserves the projected primary
  // ordering so its reference points remain aligned.
  std::vector<Point> clipped_poly =
      reference_mapping ? clipProjectedPoly(primary_poly) : clipPoly(primary_nodes);
  if (clipped_poly.size() < 3)
    return;

  if (_debug)
    for (const auto & point : clipped_poly)
      if (!isInsideSecondary(point))
        mooseError("Clipped polygon not inside linearized secondary element");

  // Compute area of clipped polygon, update remaining area fraction
  _remaining_area_fraction -= area(clipped_poly) / _secondary_area;

  // Triangulate clip polygon. tri_map indices are local to clipped_poly (starting at 0); we
  // shift them into the global node numbering after appending the polygon nodes below.
  std::vector<std::vector<unsigned int>> tri_map;
  triangulatePoly(clipped_poly, tri_map);
  if (reference_mapping && reference_mapping->minimum_segment_area > 0.)
    tri_map.erase(
        std::remove_if(tri_map.begin(),
                       tri_map.end(),
                       [&clipped_poly, reference_mapping](const std::vector<unsigned int> & tri)
                       {
                         mooseAssert(tri.size() == 3,
                                     "Mortar segment triangulation should only produce TRI3 maps.");
                         return triangleAreaHelper(clipped_poly[tri[0]],
                                                   clipped_poly[tri[1]],
                                                   clipped_poly[tri[2]]) <
                                reference_mapping->minimum_segment_area;
                       }),
        tri_map.end());
  if (tri_map.empty())
    return;

  std::vector<Point> secondary_node_reference_points;
  std::vector<Point> primary_node_reference_points;
  if (reference_mapping)
  {
    secondary_node_reference_points.reserve(clipped_poly.size());
    primary_node_reference_points.reserve(clipped_poly.size());

    const auto recover_reference_point = [this](const Point & projected_point,
                                                const std::vector<Point> & poly,
                                                const std::vector<Point> & reference_points,
                                                const char * const parent_name,
                                                const std::size_t node_index)
    {
      std::string failure_reason;
      const auto reference_point =
          referencePoint(projected_point, poly, reference_points, &failure_reason);
      if (!reference_point)
        mooseError("Unable to recover the ",
                   parent_name,
                   " parent reference point for retained 3D mortar overlap vertex ",
                   node_index,
                   " at projected point ",
                   projected_point,
                   ". Reason: ",
                   failure_reason,
                   ". Reference interpolation does not fall back to normal projection.");

      return *reference_point;
    };

    for (const auto node_index : index_range(clipped_poly))
    {
      const auto & point = clipped_poly[node_index];
      secondary_node_reference_points.push_back(recover_reference_point(
          point, _secondary_poly, _secondary_reference_points, "secondary", node_index));
      primary_node_reference_points.push_back(recover_reference_point(
          point, primary_poly, primary_poly_reference_points, "primary", node_index));
    }
  }

  // Transform clipped poly back to (linearized) 3d and append to list
  const auto offset = cast_int<unsigned int>(nodes.size());
  for (const auto & point : clipped_poly)
    nodes.emplace_back((point(0) * _u) + (point(1) * _v) + _center);

  for (const auto & tri : tri_map)
  {
    std::vector<unsigned int> shifted_tri;
    shifted_tri.reserve(tri.size());
    for (const auto local_index : tri)
      shifted_tri.push_back(offset + local_index);
    elem_to_nodes.push_back(std::move(shifted_tri));

    if (reference_mapping)
    {
      mooseAssert(tri.size() == 3, "Mortar segment triangulation should only produce TRI3 maps.");
      std::array<Point, 3> elem_secondary_reference_points;
      std::array<Point, 3> elem_primary_reference_points;
      for (const auto n : index_range(tri))
      {
        const auto local_node = tri[n];
        elem_secondary_reference_points[n] = secondary_node_reference_points[local_node];
        elem_primary_reference_points[n] = primary_node_reference_points[local_node];
      }

      reference_mapping->elem_to_secondary_reference_points.push_back(
          elem_secondary_reference_points);
      reference_mapping->elem_to_primary_reference_points.push_back(elem_primary_reference_points);
    }
  }
}

isDisjoint()

bool MortarSegmentHelper::isDisjoint

(

const std::vector< Point > &

poly

)

const

Checks whether polygons are disjoint for an easy out.

Definition at line 392 of file MortarSegmentHelper.C.

Referenced by clipProjectedPoly().

{
  for (auto i : index_range(_secondary_poly))
  {
    // Get edge to check
    const Point & q1 = _secondary_poly[i];
    const Point & q2 = _secondary_poly[(i + 1) % _secondary_poly.size()];
    const Point edg = q2 - q1;
    const Real cp = q2(0) * q1(1) - q2(1) * q1(0);

    // If more optimization needed, could store these values for later
    // Check if point is to the left of (or on) clip_edge
    auto is_inside = [&edg, cp](Point & pt, Real tol)
    { return pt(0) * edg(1) - pt(1) * edg(0) + cp < -tol; };

    bool all_outside = true;
    for (auto pt : poly)
      if (is_inside(pt, _area_tol))
        all_outside = false;

    if (all_outside)
      return true;
  }
  return false;
}

isInsideSecondary()

bool MortarSegmentHelper::isInsideSecondary

(

const Point &

pt

)

const

Check that a point is inside the secondary polygon (for verification only)

Definition at line 370 of file MortarSegmentHelper.C.

Referenced by getMortarSegmentsImpl().

{
  for (auto i : index_range(_secondary_poly))
  {
    const Point & q1 = _secondary_poly[i];
    const Point & q2 = _secondary_poly[(i + 1) % _secondary_poly.size()];

    const Point e1 = q2 - q1;
    const Point e2 = pt - q1;

    // If point corresponds to one of the secondary vertices, skip
    if (e2.norm() < _tolerance)
      return true;

    const bool inside = (e1(0) * e2(1) - e1(1) * e2(0)) < _area_tol;
    if (!inside)
      return false;
  }
  return true;
}

normal()

const Point& MortarSegmentHelper::normal ( ) const

inline

Get the unit normal of the projection plane.

Definition at line 135 of file MortarSegmentHelper.h.

{ return _normal; }

point()

Point MortarSegmentHelper::point ( unsigned int  i ) const

inline

Get 3D position of node of linearized secondary element.

Definition at line 145 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl(), and referencePoint().

  {
    return (_secondary_poly[i](0) * _u) + (_secondary_poly[i](1) * _v) + _center;
  }

projectPrimaryPoly()

std::vector< Point > MortarSegmentHelper::projectPrimaryPoly

(

const std::vector< Point > &

primary_nodes

)

const

Project a primary polygon into the helper plane while preserving the clipping orientation.

Definition at line 419 of file MortarSegmentHelper.C.

Referenced by clipPoly(), and getMortarSegmentsImpl().

{
  // Check orientation of primary_poly
  const Point e1 = primary_nodes[0] - primary_nodes[1];
  const Point e2 = primary_nodes[2] - primary_nodes[1];

  // Note we use u x v here instead of normal because it may be flipped if secondary elem was
  // negatively oriented
  const Real orient = e2.cross(e1) * _u.cross(_v);

  // Get primary_poly (primary is clipping poly). If negatively oriented, reverse
  std::vector<Point> primary_poly;
  const int n_verts = primary_nodes.size();
  primary_poly.reserve(primary_nodes.size());
  for (auto n : index_range(primary_nodes))
  {
    Point pt = (orient > 0) ? primary_nodes[n] - _center : primary_nodes[n_verts - 1 - n] - _center;
    primary_poly.emplace_back(pt * _u, pt * _v, 0.);
  }

  return primary_poly;
}

referencePoint()

std::optional< Point > MortarSegmentHelper::referencePoint ( const Point &  point, const std::vector< Point > &  poly, const std::vector< Point > &  reference_points, std::string *  failure_reason = nullptr  ) const

private

Recover a parent-reference point from a projected sub-element map.

Returns

No value for invalid or out-of-tolerance maps.

Definition at line 1101 of file MortarSegmentHelper.C.

Referenced by getMortarSegmentsImpl().

{
  mooseAssert(poly.size() == reference_points.size(),
              "Projected point and reference point containers should be the same size.");

  if (failure_reason)
    failure_reason->clear();

  const auto fail = [failure_reason](const std::string & reason) -> std::optional<Point>
  {
    if (failure_reason)
      *failure_reason = reason;
    return std::nullopt;
  };

  if (!isFinitePoint(point))
    return fail("the projected target point contains a non-finite coordinate");

  for (const auto i : index_range(poly))
  {
    if (!isFinitePoint(poly[i]))
      return fail("projected polygon vertex " + std::to_string(i) +
                  " contains a non-finite coordinate");
    if (!isFinitePoint(reference_points[i]))
      return fail("parent reference vertex " + std::to_string(i) +
                  " contains a non-finite coordinate");
  }

  if (poly.size() != 3 && poly.size() != 4)
    return fail("reference point recovery only supports triangular and quadrilateral mortar "
                "sub-elements, but received " +
                std::to_string(poly.size()) + " vertices");

  Real minimum_edge_length = std::numeric_limits<Real>::max();
  Point local_origin;
  for (const auto & vertex : poly)
    local_origin += vertex;
  local_origin /= poly.size();

  Real local_scale = 0.;
  for (const auto i : index_range(poly))
  {
    minimum_edge_length =
        std::min(minimum_edge_length, (poly[(i + 1) % poly.size()] - poly[i]).norm());
    local_scale = std::max(local_scale, (poly[i] - local_origin).norm());
  }

  const Real singular_tolerance = 100. * std::numeric_limits<Real>::epsilon();
  if (!std::isfinite(local_scale) || local_scale <= singular_tolerance)
    return fail("the projected polygon has a zero local length scale");
  if (!std::isfinite(minimum_edge_length) ||
      minimum_edge_length / local_scale <= singular_tolerance)
    return fail("the projected polygon has a zero-length edge relative to its local scale");

  std::vector<Point> normalized_poly;
  normalized_poly.reserve(poly.size());
  for (const auto & vertex : poly)
    normalized_poly.push_back((vertex - local_origin) / local_scale);
  const Point normalized_point = (point - local_origin) / local_scale;
  const Real reference_tolerance =
      std::max(mortar_reference_mapping_tolerance, _area_tol / (minimum_edge_length * local_scale));
  std::array<Node, 4> element_nodes;
  const FEType fe_type(FIRST, LAGRANGE);
  const auto recover_with_libmesh = [&](auto & element) -> std::optional<Point>
  {
    for (const auto i : index_range(normalized_poly))
    {
      element_nodes[i] = normalized_poly[i];
      element_nodes[i].set_id(i);
      element.set_node(i, &element_nodes[i]);
    }

    if (!element.has_invertible_map(mortar_reference_mapping_tolerance))
      return fail("the projected sub-element map is degenerate or non-invertible");

    if (element.type() == QUAD4)
      for (const auto corner : make_range(element.n_vertices()))
      {
        Point tangent_xi;
        Point tangent_eta;
        for (const auto node : make_range(element.n_nodes()))
        {
          tangent_xi += FEInterface::shape_deriv(
                            fe_type, 0, &element, node, 0, element.master_point(corner)) *
                        element.point(node);
          tangent_eta += FEInterface::shape_deriv(
                             fe_type, 0, &element, node, 1, element.master_point(corner)) *
                         element.point(node);
        }

        const Real corner_jacobian = tangent_xi.cross(tangent_eta).norm();
        if (!std::isfinite(corner_jacobian) ||
            corner_jacobian <= mortar_reference_mapping_tolerance)
          return fail("the projected quadrilateral has a singular or ill-conditioned corner map");
      }

    Point local_reference = FEMap::inverse_map(
        2, &element, normalized_point, mortar_reference_mapping_tolerance, false, false);
    if (!isFinitePoint(local_reference))
      return fail("libMesh inverse_map produced a non-finite reference point");

    const Real inverse_map_error =
        (FEMap::map(2, &element, local_reference) - normalized_point).norm();
    if (!std::isfinite(inverse_map_error) || inverse_map_error > mortar_reference_mapping_tolerance)
    {
      std::ostringstream reason;
      reason << "the normalized inverse-map error " << inverse_map_error << " exceeds "
             << mortar_reference_mapping_tolerance;
      return fail(reason.str());
    }

    if (element.type() == TRI3)
    {
      std::array<Real, 3> weights;
      for (const auto i : index_range(weights))
        weights[i] = FEInterface::shape(fe_type, &element, i, local_reference, false);

      for (auto & weight : weights)
        weight = std::clamp(weight, 0., 1.);
      const Real weight_sum = std::accumulate(weights.begin(), weights.end(), 0.);
      if (!std::isfinite(weight_sum) || weight_sum <= singular_tolerance)
        return fail("clamped triangle barycentric coordinates have a zero or non-finite sum");
      for (auto & weight : weights)
        weight /= weight_sum;

      // Preserve partition of unity after clamping tolerance-sized violations.
      const auto corrected_weight =
          std::distance(weights.begin(), std::max_element(weights.begin(), weights.end()));
      weights[corrected_weight] = 1.;
      for (const auto i : index_range(weights))
        if (i != static_cast<unsigned int>(corrected_weight))
          weights[corrected_weight] -= weights[i];

      local_reference = Point();
      for (const auto i : index_range(weights))
        local_reference += weights[i] * element.master_point(i);
    }
    else
    {
      local_reference(0) = std::clamp(local_reference(0), -1., 1.);
      local_reference(1) = std::clamp(local_reference(1), -1., 1.);
      local_reference(2) = 0.;
    }

    if (!element.on_reference_element(local_reference, mortar_reference_mapping_tolerance))
      return fail("the clamped inverse-map result is outside the reference element");

    const Real round_trip_error =
        (FEMap::map(2, &element, local_reference) - normalized_point).norm();
    if (!std::isfinite(round_trip_error) || round_trip_error > reference_tolerance)
    {
      std::ostringstream reason;
      reason << "the normalized inverse-map round-trip error " << round_trip_error
             << " exceeds the clipping-consistent tolerance " << reference_tolerance;
      return fail(reason.str());
    }

    Point parent_reference;
    for (const auto i : index_range(normalized_poly))
      parent_reference +=
          FEInterface::shape(fe_type, &element, i, local_reference, false) * reference_points[i];

    if (!isFinitePoint(parent_reference))
      return fail("reference interpolation produced a non-finite parent reference point");

    return parent_reference;
  };

  if (poly.size() == 3)
  {
    Tri3 element;
    return recover_with_libmesh(element);
  }

  Quad4 element;
  return recover_with_libmesh(element);
}

remainder()

Real MortarSegmentHelper::remainder ( ) const

inline

Get area fraction remaining after clipping against primary elements.

Definition at line 140 of file MortarSegmentHelper.h.

{ return _remaining_area_fraction; }

triangulatePoly()

void MortarSegmentHelper::triangulatePoly	(	std::vector< Point > &	poly_nodes,
		std::vector< std::vector< unsigned int >> &	tri_map
	)		const

Triangulate a polygon according to the configured mortar-segment triangulation mode.

Parameters

poly_nodes	List of 2D nodes defining polygon. May be augmented with extra interior nodes (e.g. centroid) by triangulation modes that require them; callers should append the result to their nodes list before applying the offset to tri_map.
tri_map	Output triangle list expressed in indices local to poly_nodes (i.e. starting at 0). Callers are responsible for shifting these indices into the global node numbering.

Definition at line 560 of file MortarSegmentHelper.C.

Referenced by getMortarSegmentsImpl().

{
  // tri_map is populated with triangle indices that are local to poly_nodes (starting at 0).
  // Callers are responsible for shifting these indices into a global node numbering.
  const auto polygon_centroid = [](const std::vector<Point> & polygon_nodes)
  {
    Point centroid(0);
    Real double_area = 0;
    for (const auto i : index_range(polygon_nodes))
    {
      const auto & a = polygon_nodes[i];
      const auto & b = polygon_nodes[(i + 1) % polygon_nodes.size()];
      const Real cross = a(0) * b(1) - b(0) * a(1);
      double_area += cross;
      centroid(0) += (a(0) + b(0)) * cross;
      centroid(1) += (a(1) + b(1)) * cross;
    }

    if (std::abs(double_area) <= TOLERANCE)
    {
      for (const auto & node : polygon_nodes)
        centroid += node;
      centroid /= polygon_nodes.size();
      return centroid;
    }

    centroid /= (3. * double_area);
    centroid(2) = 0;
    return centroid;
  };

  const auto append_triangle = [this, &poly_nodes, &tri_map](
                                   const unsigned int a, const unsigned int b, const unsigned int c)
  {
    if (triangleAreaHelper(poly_nodes[a], poly_nodes[b], poly_nodes[c]) <= _area_tol)
      return false;

    if (orient2dHelper(poly_nodes[a], poly_nodes[b], poly_nodes[c]) >= 0)
      tri_map.push_back({a, b, c});
    else
      tri_map.push_back({a, c, b});

    return true;
  };

  const auto point_in_triangle =
      [this](const Point & p, const Point & a, const Point & b, const Point & c)
  {
    const Real ab = orient2dHelper(a, b, p);
    const Real bc = orient2dHelper(b, c, p);
    const Real ca = orient2dHelper(c, a, p);
    return ab >= -_area_tol && bc >= -_area_tol && ca >= -_area_tol;
  };

  const auto min_triangle_angle = [](const Point & a, const Point & b, const Point & c)
  {
    const auto clamp_cos = [](Real value) { return std::max(-1., std::min(1., value)); };
    const auto angle_at =
        [&clamp_cos](const Point & vertex, const Point & point_one, const Point & point_two)
    {
      const Point edge_one = point_one - vertex;
      const Point edge_two = point_two - vertex;
      const Real denom = edge_one.norm() * edge_two.norm();
      if (denom <= TOLERANCE)
        return 0.;
      return std::acos(clamp_cos((edge_one * edge_two) / denom));
    };

    return std::min({angle_at(a, b, c), angle_at(b, c, a), angle_at(c, a, b)});
  };

  const auto canonicalize_polygon = [this, &poly_nodes]()
  {
    if (poly_nodes.size() < 3)
      return;

    if (area(poly_nodes) < 0)
      std::reverse(poly_nodes.begin(), poly_nodes.end());

    bool changed = true;
    while (changed && poly_nodes.size() > 3)
    {
      changed = false;
      for (const auto i : index_range(poly_nodes))
      {
        const auto prev = (i + poly_nodes.size() - 1) % poly_nodes.size();
        const auto next = (i + 1) % poly_nodes.size();
        if ((poly_nodes[i] - poly_nodes[prev]).norm() <= _length_tol ||
            (poly_nodes[next] - poly_nodes[i]).norm() <= _length_tol ||
            triangleAreaHelper(poly_nodes[prev], poly_nodes[i], poly_nodes[next]) <= _area_tol)
        {
          poly_nodes.erase(poly_nodes.begin() + i);
          changed = true;
          break;
        }
      }
    }

    if (poly_nodes.size() >= 3 && area(poly_nodes) < 0)
      std::reverse(poly_nodes.begin(), poly_nodes.end());
  };

  const auto triangulate_with_ear_clipping =
      [this, &poly_nodes, &point_in_triangle, &min_triangle_angle](
          const bool perform_delaunay_flips)
  {
    std::vector<std::array<unsigned int, 3>> triangles;
    if (poly_nodes.size() < 3)
      return triangles;

    if (poly_nodes.size() == 3)
    {
      triangles.push_back(makeCCWTriangleHelper(poly_nodes, 0, 1, 2));
      return triangles;
    }

    std::vector<unsigned int> remaining_vertices(poly_nodes.size());
    std::iota(remaining_vertices.begin(), remaining_vertices.end(), 0);

    while (remaining_vertices.size() > 3)
    {
      std::optional<std::size_t> best_position;
      Real best_score = -std::numeric_limits<Real>::max();
      Real best_area = -std::numeric_limits<Real>::max();

      for (const auto position : index_range(remaining_vertices))
      {
        const auto prev_position =
            (position + remaining_vertices.size() - 1) % remaining_vertices.size();
        const auto next_position = (position + 1) % remaining_vertices.size();
        const auto prev = remaining_vertices[prev_position];
        const auto curr = remaining_vertices[position];
        const auto next = remaining_vertices[next_position];

        if (orient2dHelper(poly_nodes[prev], poly_nodes[curr], poly_nodes[next]) <= _area_tol)
          continue;

        bool contains_other_vertex = false;
        for (const auto other : remaining_vertices)
        {
          if (other == prev || other == curr || other == next)
            continue;

          if (point_in_triangle(
                  poly_nodes[other], poly_nodes[prev], poly_nodes[curr], poly_nodes[next]))
          {
            contains_other_vertex = true;
            break;
          }
        }

        if (contains_other_vertex)
          continue;

        const Real candidate_score =
            min_triangle_angle(poly_nodes[prev], poly_nodes[curr], poly_nodes[next]);
        const Real candidate_area =
            triangleAreaHelper(poly_nodes[prev], poly_nodes[curr], poly_nodes[next]);
        if (!best_position || candidate_score > best_score + TOLERANCE ||
            (std::abs(candidate_score - best_score) <= TOLERANCE &&
             candidate_area > best_area + _area_tol))
        {
          best_position = position;
          best_score = candidate_score;
          best_area = candidate_area;
        }
      }

      if (!best_position)
      {
        std::vector<std::array<unsigned int, 3>> best_fan;
        Real best_fan_score = -std::numeric_limits<Real>::max();
        Real best_fan_area = -std::numeric_limits<Real>::max();

        for (const auto root_position : index_range(remaining_vertices))
        {
          std::vector<std::array<unsigned int, 3>> candidate_fan;
          Real candidate_score = std::numeric_limits<Real>::max();
          Real candidate_area = std::numeric_limits<Real>::max();
          bool valid_fan = true;
          const auto root = remaining_vertices[root_position];

          for (unsigned int step = 1; step + 1 < remaining_vertices.size(); ++step)
          {
            const auto next_position = (root_position + step) % remaining_vertices.size();
            const auto following_position = (root_position + step + 1) % remaining_vertices.size();
            const auto vertex_one = remaining_vertices[next_position];
            const auto vertex_two = remaining_vertices[following_position];

            if (orient2dHelper(poly_nodes[root], poly_nodes[vertex_one], poly_nodes[vertex_two]) <=
                _area_tol)
            {
              valid_fan = false;
              break;
            }

            candidate_fan.push_back(
                makeCCWTriangleHelper(poly_nodes, root, vertex_one, vertex_two));
            candidate_score =
                std::min(candidate_score,
                         min_triangle_angle(
                             poly_nodes[root], poly_nodes[vertex_one], poly_nodes[vertex_two]));
            candidate_area =
                std::min(candidate_area,
                         triangleAreaHelper(
                             poly_nodes[root], poly_nodes[vertex_one], poly_nodes[vertex_two]));
          }

          if (!valid_fan || candidate_fan.empty())
            continue;

          if (candidate_score > best_fan_score + TOLERANCE ||
              (std::abs(candidate_score - best_fan_score) <= TOLERANCE &&
               candidate_area > best_fan_area + _area_tol))
          {
            best_fan = std::move(candidate_fan);
            best_fan_score = candidate_score;
            best_fan_area = candidate_area;
          }
        }

        if (best_fan.empty())
          for (unsigned int i = 1; i + 1 < remaining_vertices.size(); ++i)
            best_fan.push_back(makeCCWTriangleHelper(poly_nodes,
                                                     remaining_vertices[0],
                                                     remaining_vertices[i],
                                                     remaining_vertices[i + 1]));

        triangles.insert(triangles.end(), best_fan.begin(), best_fan.end());
        break;
      }

      const auto prev_position =
          (*best_position + remaining_vertices.size() - 1) % remaining_vertices.size();
      const auto next_position = (*best_position + 1) % remaining_vertices.size();
      triangles.push_back(makeCCWTriangleHelper(poly_nodes,
                                                remaining_vertices[prev_position],
                                                remaining_vertices[*best_position],
                                                remaining_vertices[next_position]));
      remaining_vertices.erase(remaining_vertices.begin() + *best_position);
    }

    if (remaining_vertices.size() == 3)
      triangles.push_back(makeCCWTriangleHelper(
          poly_nodes, remaining_vertices[0], remaining_vertices[1], remaining_vertices[2]));

    if (!perform_delaunay_flips)
      return triangles;

    std::set<std::array<unsigned int, 2>> boundary_edges;
    for (const auto i : index_range(poly_nodes))
      boundary_edges.insert(canonicalEdgeHelper(i, (i + 1) % poly_nodes.size()));

    performLocalDelaunayFlips(poly_nodes, boundary_edges, triangles);
    return triangles;
  };

  const auto is_convex_polygon = [this](const std::vector<Point> & polygon_nodes)
  {
    if (polygon_nodes.size() <= 3)
      return true;

    for (const auto i : index_range(polygon_nodes))
    {
      const auto prev = (i + polygon_nodes.size() - 1) % polygon_nodes.size();
      const auto next = (i + 1) % polygon_nodes.size();
      if (orient2dHelper(polygon_nodes[prev], polygon_nodes[i], polygon_nodes[next]) <= _area_tol)
        return false;
    }

    return true;
  };

  // Fewer than 3 nodes can't be triangulated
  if (poly_nodes.size() < 3)
    mooseError("Can't triangulate poly with fewer than 3 nodes");

  // Legacy centroid path: when the default triangulation (centroid) is selected
  // and triangle re-tessellation is not requested, reproduce the legacy
  // algorithm byte-for-byte so existing mortar baselines remain valid.
  // Uses the arithmetic mean of the vertices (not the area-weighted centroid),
  // emits one triangle per polygon edge without degeneracy filtering, and skips
  // the canonicalization pass which would drop near-degenerate vertices and
  // perturb integration weights in downstream test baselines.
  if (_triangulation_mode == MortarSegmentTriangulationMode::Centroid && !_triangulate_triangles)
  {
    if (poly_nodes.size() == 3)
    {
      tri_map.push_back({0, 1, 2});
      return;
    }

    const unsigned int n_verts = poly_nodes.size();
    Point poly_center;
    for (const auto & node : poly_nodes)
      poly_center += node;
    poly_center /= n_verts;

    for (const auto i : make_range(n_verts))
      tri_map.push_back({i, (i + 1) % n_verts, n_verts});

    poly_nodes.push_back(poly_center);
    return;
  }

  canonicalize_polygon();
  if (poly_nodes.size() < 3)
    return;

  if (poly_nodes.size() == 3 && !_triangulate_triangles)
  {
    append_triangle(0, 1, 2);
    return;
  }

  const bool force_triangle_centroid_split = _triangulate_triangles && poly_nodes.size() == 3;

  if (_triangulation_mode == MortarSegmentTriangulationMode::Vertex &&
      !force_triangle_centroid_split)
  {
    const unsigned int n_verts = poly_nodes.size();
    for (unsigned int i = 1; i + 1 < n_verts; ++i)
      append_triangle(0, i, i + 1);
    return;
  }

  if (_triangulation_mode == MortarSegmentTriangulationMode::Delaunay &&
      !force_triangle_centroid_split)
  {
#if defined(LIBMESH_HAVE_TRIANGLE) || defined(LIBMESH_HAVE_POLY2TRI)
    triangulateConstrainedDelaunayPolygon(poly_nodes, _area_tol, _length_tol, tri_map);
    return;
#else
    mooseError("The 'delaunay' mortar triangulation mode requires libMesh TriangleInterface or "
               "Poly2Tri support.");
#endif
  }

  if (_triangulation_mode == MortarSegmentTriangulationMode::EarClipping &&
      !force_triangle_centroid_split)
  {
    for (const auto & triangle : triangulate_with_ear_clipping(true))
      append_triangle(triangle[0], triangle[1], triangle[2]);
    return;
  }

  if (!force_triangle_centroid_split && !is_convex_polygon(poly_nodes))
  {
    for (const auto & triangle : triangulate_with_ear_clipping(true))
      append_triangle(triangle[0], triangle[1], triangle[2]);
    return;
  }

  const unsigned int n_verts = poly_nodes.size();
  const Point poly_center = polygon_centroid(poly_nodes);

  bool added_triangle = false;
  for (const auto i : make_range(n_verts))
    if (triangleAreaHelper(poly_nodes[i], poly_nodes[(i + 1) % n_verts], poly_center) > _area_tol)
    {
      tri_map.push_back({i, (i + 1) % n_verts, n_verts});
      added_triangle = true;
    }

  if (added_triangle)
    poly_nodes.push_back(poly_center);
}

Friends And Related Function Documentation

MortarSegmentHelperTest

friend class MortarSegmentHelperTest

friend

Definition at line 183 of file MortarSegmentHelper.h.

Member Data Documentation

_area_tol

Real MortarSegmentHelper::_area_tol

private

Tolerance times secondary area for dimensional consistency.

Definition at line 233 of file MortarSegmentHelper.h.

Referenced by clipProjectedPoly(), isDisjoint(), isInsideSecondary(), MortarSegmentHelper(), referencePoint(), and triangulatePoly().

_center

Point MortarSegmentHelper::_center

private

Geometric center of secondary element.

Definition at line 189 of file MortarSegmentHelper.h.

Referenced by center(), getMortarSegmentsImpl(), MortarSegmentHelper(), point(), and projectPrimaryPoly().

_debug

bool MortarSegmentHelper::_debug

private

Definition at line 213 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl().

_length_tol

Real MortarSegmentHelper::_length_tol

private

Tolerance times secondary area for dimensional consistency.

Definition at line 238 of file MortarSegmentHelper.h.

Referenced by clipProjectedPoly(), MortarSegmentHelper(), and triangulatePoly().

_normal

Point MortarSegmentHelper::_normal

private

Unit normal of the plane used to project and clip the linearized secondary subpatch.

Definition at line 194 of file MortarSegmentHelper.h.

Referenced by MortarSegmentHelper(), and normal().

_remaining_area_fraction

Real MortarSegmentHelper::_remaining_area_fraction

private

Fraction of area remaining after overlapping primary polygons clipped.

Definition at line 211 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl(), MortarSegmentHelper(), and remainder().

_secondary_area

Real MortarSegmentHelper::_secondary_area

private

Area of projected secondary element.

Definition at line 206 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl(), and MortarSegmentHelper().

_secondary_poly

std::vector<Point> MortarSegmentHelper::_secondary_poly

private

List of projected points on the linearized secondary element.

Definition at line 243 of file MortarSegmentHelper.h.

Referenced by clipProjectedPoly(), getMortarSegmentsImpl(), isDisjoint(), isInsideSecondary(), MortarSegmentHelper(), and point().

_secondary_reference_points

std::vector<Point> MortarSegmentHelper::_secondary_reference_points

private

Parent reference points corresponding to _secondary_poly.

Definition at line 246 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl(), and MortarSegmentHelper().

_tolerance

Real MortarSegmentHelper::_tolerance = 1e-8

private

Tolerance for intersection and clipping.

Definition at line 218 of file MortarSegmentHelper.h.

Referenced by clipProjectedPoly(), isInsideSecondary(), and MortarSegmentHelper().

_triangulate_triangles

const bool MortarSegmentHelper::_triangulate_triangles

private

Whether already-triangular polygons should still be centroid-subdivided.

Definition at line 228 of file MortarSegmentHelper.h.

Referenced by triangulatePoly().

_triangulation_mode

const MortarSegmentTriangulationMode MortarSegmentHelper::_triangulation_mode

private

Triangulation mode used for clipped polygons.

Definition at line 223 of file MortarSegmentHelper.h.

Referenced by triangulatePoly().

_u

Point MortarSegmentHelper::_u

private

Vectors orthogonal to normal that span the plane projection will be performed on.

These vectors are used to project the polygon clipping problem on a 2D plane, they are defined so the nodes of the projected polygon are listed with positive orientation

Definition at line 201 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl(), MortarSegmentHelper(), point(), and projectPrimaryPoly().

_v

Point MortarSegmentHelper::_v

private

Definition at line 201 of file MortarSegmentHelper.h.

Referenced by getMortarSegmentsImpl(), MortarSegmentHelper(), point(), and projectPrimaryPoly().

---

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

• include/constraints/MortarSegmentHelper.h
• src/constraints/MortarSegmentHelper.C