text: //============================================================================
  //  Copyright (c) Kitware, Inc.
  //  All rights reserved.
  //  See LICENSE.txt for details.
  //  This software is distributed WITHOUT ANY WARRANTY; without even
  //  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
  //  PURPOSE.  See the above copyright notice for more information.
  //
  //  Copyright 2018 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
  //  Copyright 2018 UT-Battelle, LLC.
  //  Copyright 2018 Los Alamos National Security.
  //
  //  Under the terms of Contract DE-NA0003525 with NTESS,
  //  the U.S. Government retains certain rights in this software.
  //
  //  Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
  //  Laboratory (LANL), the U.S. Government retains certain rights in
  //  this software.
  //============================================================================
  #ifndef vtk_m_worklet_cellmetrics_CellMinAngleMetric_h
  #define vtk_m_worklet_cellmetrics_CellMinAngleMetric_h
  
  /*
  * Mesh quality metric functions that compute the minimum angle of cell in a mesh.
  ** These metric computations are adapted from the VTK implementation of the Verdict library,
  * which provides a set of mesh/cell metrics for evaluating the geometric qualities of regions
  * of mesh spaces.
  ** See: The Verdict Library Reference Manual (for per-cell-type metric formulae)
  * See: vtk/ThirdParty/verdict/vtkverdict (for VTK code implementation of this metric)
  */
  
  #include "vtkm/CellShape.h"
  #include "vtkm/CellTraits.h"
  #include "vtkm/VecTraits.h"
  #include "vtkm/VectorAnalysis.h"
  #include "vtkm/exec/FunctorBase.h"
  
  #define UNUSED(expr) (void)(expr);
  
  namespace vtkm
  {
  namespace worklet
  {
  namespace cellmetrics
  {
  
  // ========================= Unsupported cells ==================================
  
  // By default, cells have zero shape unless the shape type template is specialized below.
  template <typename OutType, typename PointCoordVecType, typename CellShapeType>
  VTKM_EXEC OutType CellMinAngleMetric(const vtkm::IdComponent& numPts,
                                       const PointCoordVecType& pts,
                                       CellShapeType shape,
                                       vtkm::ErrorCode&)
  {
    UNUSED(numPts);
    UNUSED(pts);
    UNUSED(shape);
    return OutType(-1.0);
  }
  
  // ========================= 2D cells ==================================
  // Compute the minimum angle of a triangle.
  // Formula: q = min( arccos((Ln dot Ln+1)/(||Ln|| * ||Ln+1||))(180º/π) for n 0,1, and 2 )
  //   - L3 = L0
  //   - if any edge has length 0, return q = 360º
  //   - All angle measurements are in degrees
  // q equals 60 for a unit triangle
  // Acceptable range: [30º, 60º]
  // Normal Range: [0º, 360º]
  // Full range: [0º, 360º]
  template <typename OutType, typename PointCoordVecType>
  VTKM_EXEC OutType CellMinAngleMetric(const vtkm::IdComponent& numPts,
                                       const PointCoordVecType& pts,
                                       vtkm::CellShapeTagTriangle,
                                       vtkm::ErrorCode& ec)
  {
    if (numPts != 3)
    {
      ec = vtkm::ErrorCode::InvalidNumberOfPoints;
      return OutType(0.0);
    }
  
    using Scalar = OutType;
    using CollectionOfPoints = PointCoordVecType;
    using Vector = typename PointCoordVecType::ComponentType;
  
    const Scalar l0 = GetTriangleL0Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar l1 = GetTriangleL1Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar l2 = GetTriangleL2Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
  
    if (l0 <= Scalar(0.0) || l1 <= Scalar(0.0) || l2 <= Scalar(0.0))
    {
      return Scalar(0.0);
    }
  
    const Scalar oneEightyOverPi = (Scalar)57.2957795131;
    const Scalar two(2.0);
    const Scalar q0 = vtkm::ACos(((l1 * l1) + (l2 * l2) - (l0 * l0)) / (two * l1 * l2));
    const Scalar q1 = vtkm::ACos(((l2 * l2) + (l0 * l0) - (l1 * l1)) / (two * l2 * l0));
    const Scalar q2 = vtkm::ACos(((l0 * l0) + (l1 * l1) - (l2 * l2)) / (two * l0 * l1));
  
    const Scalar q = vtkm::Min(q0, vtkm::Min(q1, q2));
  
    const Scalar qInDegrees = q * oneEightyOverPi;
  
    return qInDegrees;
  }
  // Compute the min angle of a quadrilateral.
  // Formula: q = min( Ai for i 0,1,2, and 3 )
  //   - L4 = L0
  //   - Ai = -1^Si arccos(-1(Li dot Li+1)/(||Li||||Li+1||) )(180/π) + 360º*Si
  //   - if ||Li|| <= FLOAT_MIN or ||Li+1|| <= FLOAT_MIN, return q = 360º
  // q = 90º for a unit square
  // Acceptable range: [45º, 90º]
  // Normal Range: [0º, 90º]
  // Full range: [0º, 360º]
  template <typename OutType, typename PointCoordVecType>
  VTKM_EXEC OutType CellMinAngleMetric(const vtkm::IdComponent& numPts,
                                       const PointCoordVecType& pts,
                                       vtkm::CellShapeTagQuad,
                                       vtkm::ErrorCode& ec)
  {
    if (numPts != 4)
    {
      ec = vtkm::ErrorCode::InvalidNumberOfPoints;
      return OutType(0.0);
    }
    using Scalar = OutType;
    using CollectionOfPoints = PointCoordVecType;
    using Vector = typename PointCoordVecType::ComponentType;
  
    const Scalar l0 = GetQuadL0Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar l1 = GetQuadL1Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar l2 = GetQuadL2Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar l3 = GetQuadL3Magnitude<Scalar, Vector, CollectionOfPoints>(pts);
  
    if (l0 <= Scalar(0.0) || l1 <= Scalar(0.0) || l2 <= Scalar(0.0) || l3 <= Scalar(0.0))
    {
      return Scalar(0.0);
    }
  
    const Scalar alpha0 = GetQuadAlpha0<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar alpha1 = GetQuadAlpha1<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar alpha2 = GetQuadAlpha2<Scalar, Vector, CollectionOfPoints>(pts);
    const Scalar alpha3 = GetQuadAlpha3<Scalar, Vector, CollectionOfPoints>(pts);
  
    const Scalar s0 = alpha0 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
    const Scalar s1 = alpha1 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
    const Scalar s2 = alpha2 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
    const Scalar s3 = alpha3 < Scalar(0.0) ? Scalar(1.0) : Scalar(0.0);
  
    const Vector L0 = GetQuadL0<Scalar, Vector, CollectionOfPoints>(pts);
    const Vector L1 = GetQuadL1<Scalar, Vector, CollectionOfPoints>(pts);
    const Vector L2 = GetQuadL2<Scalar, Vector, CollectionOfPoints>(pts);
    const Vector L3 = GetQuadL3<Scalar, Vector, CollectionOfPoints>(pts);
  
    // 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.
    // Further, it combines steps 1 & 2 into a single expression using clever (-1)^power flags.
    const Scalar neg1(-1.0);
    const Scalar oneEightyOverPi = (Scalar)57.2957795131; // ~ 180/pi
    const Scalar threeSixty(360.0);
    const Scalar q0 =
      (vtkm::Pow(neg1, s0) * vtkm::ACos(neg1 * (static_cast<Scalar>(vtkm::Dot(L0, L1)) / (l0 * l1))) *
       oneEightyOverPi) +
      (threeSixty * s0);
    const Scalar q1 =
      (vtkm::Pow(neg1, s1) * vtkm::ACos(neg1 * (static_cast<Scalar>(vtkm::Dot(L1, L2)) / (l1 * l2))) *
       oneEightyOverPi) +
      (threeSixty * s1);
    const Scalar q2 =
      (vtkm::Pow(neg1, s2) * vtkm::ACos(neg1 * (static_cast<Scalar>(vtkm::Dot(L2, L3)) / (l2 * l3))) *
       oneEightyOverPi) +
      (threeSixty * s2);
    const Scalar q3 =
      (vtkm::Pow(neg1, s3) * vtkm::ACos(neg1 * (static_cast<Scalar>(vtkm::Dot(L3, L0)) / (l3 * l0))) *
       oneEightyOverPi) +
      (threeSixty * s3);
  
    const Scalar q = vtkm::Min(q0, vtkm::Min(q1, vtkm::Min(q2, q3)));
    return q;
  }
  } // namespace cellmetrics
  } // namespace worklet
  } // namespace vtkm
  #endif // vtk_m_worklet_cellmetrics_CellMinAngleMetric_h
  