186 lines
7.6 KiB
C++
186 lines
7.6 KiB
C++
//============================================================================
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// Copyright (c) Kitware, Inc.
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// All rights reserved.
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// See LICENSE.txt for details.
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// This software is distributed WITHOUT ANY WARRANTY; without even
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// the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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// PURPOSE. See the above copyright notice for more information.
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//
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// Copyright 2018 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
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// Copyright 2018 UT-Battelle, LLC.
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// Copyright 2018 Los Alamos National Security.
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//
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// Under the terms of Contract DE-NA0003525 with NTESS,
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// the U.S. Government retains certain rights in this software.
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//
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// Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
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// Laboratory (LANL), the U.S. Government retains certain rights in
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// this software.
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//============================================================================
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#ifndef vtk_m_worklet_cellmetrics_CellMaxAngleMetric_h
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#define vtk_m_worklet_cellmetrics_CellMaxAngleMetric_h
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/*
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* Mesh quality metric functions that compute the maximum angle of cell in a mesh.
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** These metric computations are adapted from the VTK implementation of the Verdict library,
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* which provides a set of mesh/cell metrics for evaluating the geometric qualities of regions
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* of mesh spaces.
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** See: The Verdict Library Reference Manual (for per-cell-type metric formulae)
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* See: vtk/ThirdParty/verdict/vtkverdict (for VTK code implementation of this metric)
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*/
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#include "TypeOfCellHexahedral.h"
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#include "TypeOfCellQuadrilateral.h"
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#include "TypeOfCellTetrahedral.h"
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#include "TypeOfCellTriangle.h"
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#include "vtkm/CellShape.h"
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#include "vtkm/CellTraits.h"
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#include "vtkm/VecTraits.h"
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#include "vtkm/VectorAnalysis.h"
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#include "vtkm/exec/FunctorBase.h"
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#define UNUSED(expr) (void)(expr);
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namespace vtkm
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{
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namespace worklet
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{
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namespace cellmetrics
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{
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// ========================= Unsupported cells ==================================
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// By default, cells have zero shape unless the shape type template is specialized below.
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template <typename OutType, typename PointCoordVecType, typename CellShapeType>
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VTKM_EXEC OutType CellMaxAngleMetric(const vtkm::IdComponent& numPts,
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const PointCoordVecType& pts,
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CellShapeType shape,
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const vtkm::exec::FunctorBase&)
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{
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UNUSED(numPts);
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UNUSED(pts);
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UNUSED(shape);
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return OutType(-1.0);
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}
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// ========================= 2D cells ==================================
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// Compute the maximum angle of a triangle.
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// Formula: q = max( arccos((Ln dot Ln+1)/(||Ln|| * ||Ln+1||))(180º/π) for n 0,1, and 2 )
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// - L3 = L0
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// - if any edge has length 0, return q = 360º
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// - All angle measurements are in degrees
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// q equals 60 for a unit triangle
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// Acceptable range: [30º, 60º]
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// Normal Range: [0º, 360º]
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// Full range: [0º, 360º]
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template <typename OutType, typename PointCoordVecType>
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VTKM_EXEC OutType CellMaxAngleMetric(const vtkm::IdComponent& numPts,
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const PointCoordVecType& pts,
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vtkm::CellShapeTagTriangle,
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const vtkm::exec::FunctorBase& worklet)
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{
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if (numPts != 3)
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{
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worklet.RaiseError("Minimum angle metric (triangle) requires 3 points.");
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return OutType(0.0);
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}
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using Scalar = OutType;
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using CollectionOfPoints = PointCoordVecType;
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using Vector = typename PointCoordVecType::ComponentType;
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const Scalar l0 = GetTriangleL0Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar l1 = GetTriangleL1Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar l2 = GetTriangleL2Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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if (l0 <= Scalar(0.0) || l1 <= Scalar(0.0) || l2 <= Scalar(0.0))
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{
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return Scalar(0.0);
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}
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const Scalar oneEightyOverPi = (Scalar)57.2957795131;
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const Scalar two(2.0);
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const Scalar q0 = vtkm::ACos(((l1 * l1) + (l2 * l2) - (l0 * l0)) / (two * l1 * l2));
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const Scalar q1 = vtkm::ACos(((l2 * l2) + (l0 * l0) - (l1 * l1)) / (two * l2 * l0));
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const Scalar q2 = vtkm::ACos(((l0 * l0) + (l1 * l1) - (l2 * l2)) / (two * l0 * l1));
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const Scalar q = vtkm::Max(q0, vtkm::Max(q1, q2));
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const Scalar qInDegrees = q * oneEightyOverPi;
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return qInDegrees;
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}
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// Compute the max angle of a quadrilateral.
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// Formula: q = max( Ai for i 0,1,2, and 3 )
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// - L4 = L0
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// - Ai = -1^Si arccos(-1(Li dot Li+1)/(||Li||||Li+1||) )(180/π) + 360º*Si
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// - if ||Li|| <= FLOAT_MIN or ||Li+1|| <= FLOAT_MIN, return q = 360º
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// q = 90º for a unit square
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// Acceptable range: [45º, 90º]
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// Normal Range: [0º, 90º]
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// Full range: [0º, 360º]
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template <typename OutType, typename PointCoordVecType>
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VTKM_EXEC OutType CellMaxAngleMetric(const vtkm::IdComponent& numPts,
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const PointCoordVecType& pts,
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vtkm::CellShapeTagQuad,
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const vtkm::exec::FunctorBase& worklet)
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{
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if (numPts != 4)
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{
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worklet.RaiseError("Minimum angle metric(quad) requires 4 points.");
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return OutType(0.0);
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}
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using Scalar = OutType;
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using CollectionOfPoints = PointCoordVecType;
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using Vector = typename PointCoordVecType::ComponentType;
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const Scalar l0 = GetQuadL0Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar l1 = GetQuadL1Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar l2 = GetQuadL2Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar l3 = GetQuadL3Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
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if (l0 <= Scalar(0.0) || l1 <= Scalar(0.0) || l2 <= Scalar(0.0) || l3 <= Scalar(0.0))
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{
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return Scalar(0.0);
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}
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const Scalar alpha0 = GetQuadAlpha0<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar alpha1 = GetQuadAlpha1<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar alpha2 = GetQuadAlpha2<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar alpha3 = GetQuadAlpha3<Scalar, Vector, CollectionOfPoints>(pts);
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const Scalar s0 = alpha0 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
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const Scalar s1 = alpha1 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
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const Scalar s2 = alpha2 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
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const Scalar s3 = alpha3 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
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const Vector L0 = GetQuadL0<Scalar, Vector, CollectionOfPoints>(pts);
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const Vector L1 = GetQuadL1<Scalar, Vector, CollectionOfPoints>(pts);
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const Vector L2 = GetQuadL2<Scalar, Vector, CollectionOfPoints>(pts);
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const Vector L3 = GetQuadL3<Scalar, Vector, CollectionOfPoints>(pts);
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// This angle is given in degrees, not radians. The verdict definition (1) converts to degrees, (2) gives co(terminal) angles, and (3) takes the min/max.
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// Further, it combines steps 1 & 2 into a single expression using clever (-1)^power flags.
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const Scalar neg1(-1.0);
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const Scalar oneEightyOverPi = (Scalar)57.2957795131; // ~ 180/pi
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const Scalar threeSixty(360.0);
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const Scalar q0 =
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(vtkm::Pow(neg1, s0) * vtkm::ACos(neg1 * ((vtkm::Dot(L0, L1)) / (l0 * l1))) * oneEightyOverPi) +
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(threeSixty * s0);
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const Scalar q1 =
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(vtkm::Pow(neg1, s1) * vtkm::ACos(neg1 * ((vtkm::Dot(L1, L2)) / (l1 * l2))) * oneEightyOverPi) +
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(threeSixty * s1);
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const Scalar q2 =
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(vtkm::Pow(neg1, s2) * vtkm::ACos(neg1 * ((vtkm::Dot(L2, L3)) / (l2 * l3))) * oneEightyOverPi) +
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(threeSixty * s2);
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const Scalar q3 =
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(vtkm::Pow(neg1, s3) * vtkm::ACos(neg1 * ((vtkm::Dot(L3, L0)) / (l3 * l0))) * oneEightyOverPi) +
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(threeSixty * s3);
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const Scalar q = vtkm::Max(q0, vtkm::Max(q1, vtkm::Max(q2, q3)));
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return q;
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}
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} // namespace cellmetrics
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} // namespace worklet
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} // namespace vtkm
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#endif // vtk_m_worklet_cellmetrics_CellMaxAngleMetric_h
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