mirror of
https://gitlab.kitware.com/vtk/vtk-m
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236 lines
9.5 KiB
C++
236 lines
9.5 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_Oddy_h
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#define vtk_m_worklet_cellmetrics_Oddy_h
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/*
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* Mesh quality metric functions that compute the Oddy of mesh cells.
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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 CellOddyMetric(const vtkm::IdComponent& numPts,
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const PointCoordVecType& pts,
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CellShapeType shape,
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vtkm::ErrorCode&)
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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 Oddy of a quadrilateral.
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// Formula: for i 0 to 3: max{[(||Li||^2 - ||Li+1||^2)^2 + 4((Li * Li+1)^2)] / (2||Ni+1||^2)}
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// - L4 = L0
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// - '*' symbolizes the dot product of two vectors
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// - Ni is the normal vector associated with each point
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// Equals 0 for a unit square
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// Acceptable range: [0,0.5]
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// Normal range: [0,FLOAT_MAX]
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// Full range: [0,FLOAT_MAX]
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// Note, for loop avoided because L4 = L0
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template <typename Scalar, typename Vector>
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VTKM_EXEC Scalar GetQuadOddyQi(const Vector& Li, const Vector& LiPlus1, const Vector& NiPlus1)
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{
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const Scalar two(2.0);
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const Scalar four(4.0);
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const Scalar liMagnitudeSquared = vtkm::MagnitudeSquared(Li);
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const Scalar liPlus1MagnitudeSquared = vtkm::MagnitudeSquared(LiPlus1);
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const Scalar niPlus1MagnitudeSquared = vtkm::MagnitudeSquared(NiPlus1);
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const Scalar q = (((liMagnitudeSquared - liPlus1MagnitudeSquared) *
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(liMagnitudeSquared - liPlus1MagnitudeSquared)) +
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(four * (vtkm::Dot(Li, LiPlus1) * vtkm::Dot(Li, LiPlus1)))) /
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(two * niPlus1MagnitudeSquared);
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return q;
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}
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template <typename OutType, typename PointCoordVecType>
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VTKM_EXEC OutType CellOddyMetric(const vtkm::IdComponent& numPts,
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const PointCoordVecType& pts,
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vtkm::CellShapeTagQuad,
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vtkm::ErrorCode& ec)
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{
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if (numPts != 4)
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{
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ec = vtkm::ErrorCode::InvalidNumberOfPoints;
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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 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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const Vector N0 = GetQuadN0<Scalar, Vector, CollectionOfPoints>(pts);
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const Vector N1 = GetQuadN1<Scalar, Vector, CollectionOfPoints>(pts);
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const Vector N2 = GetQuadN2<Scalar, Vector, CollectionOfPoints>(pts);
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const Vector N3 = GetQuadN3<Scalar, Vector, CollectionOfPoints>(pts);
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if (vtkm::MagnitudeSquared(N0) <= Scalar(0.0) || vtkm::MagnitudeSquared(N1) <= Scalar(0.0) ||
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vtkm::MagnitudeSquared(N2) <= Scalar(0.0) || vtkm::MagnitudeSquared(N3) <= Scalar(0.0))
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{
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return vtkm::Infinity<Scalar>();
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}
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const Scalar q0 = GetQuadOddyQi<Scalar, Vector>(L0, L1, N1);
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const Scalar q1 = GetQuadOddyQi<Scalar, Vector>(L1, L2, N2);
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const Scalar q2 = GetQuadOddyQi<Scalar, Vector>(L2, L3, N3);
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const Scalar q3 = GetQuadOddyQi<Scalar, Vector>(L3, L0, N0);
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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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// ============================= 3D Volume cells ==================================
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// Compute the Oddy of a hexahedron.
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// Formula:
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// Equals 0 for a unit cube
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// Acceptable Range: [0, 0.5]
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// Normal range: [0,FLOAT_MAX]
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// Full range: [0,FLOAT_MAX]
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template <typename OutType, typename PointCoordVecType>
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VTKM_EXEC OutType CellOddyMetric(const vtkm::IdComponent& numPts,
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const PointCoordVecType& pts,
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vtkm::CellShapeTagHexahedron,
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vtkm::ErrorCode& ec)
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{
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if (numPts != 8)
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{
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ec = vtkm::ErrorCode::InvalidNumberOfPoints;
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return OutType(0.0);
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}
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//The 12 points of a hexahedron
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using Edge = typename PointCoordVecType::ComponentType;
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const Edge HexEdges[12] = {
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pts[1] - pts[0], // 0
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pts[2] - pts[1], pts[3] - pts[2],
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pts[3] - pts[0], // 3
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pts[4] - pts[0], pts[5] - pts[1],
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pts[6] - pts[2], // 6
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pts[7] - pts[3], pts[5] - pts[4],
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pts[6] - pts[5], // 9
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pts[7] - pts[6],
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pts[7] - pts[4] // 11
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};
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Edge principleXAxis = HexEdges[0] + (pts[2] - pts[3]) + HexEdges[8] + (pts[6] - pts[7]);
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Edge principleYAxis = (pts[3] - pts[0]) + HexEdges[1] + (pts[7] - pts[4]) + HexEdges[9];
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Edge principleZAxis = HexEdges[4] + HexEdges[5] + HexEdges[6] + HexEdges[7];
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Edge hexJacobianMatrices[9][3] = {
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{ HexEdges[0], HexEdges[3], HexEdges[4] },
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{ HexEdges[1], (-1 * HexEdges[0]), HexEdges[5] },
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{ HexEdges[2], (-1 * HexEdges[1]), HexEdges[6] },
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{ (-1 * HexEdges[3]), (-1 * HexEdges[2]), HexEdges[7] },
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{ HexEdges[11], HexEdges[8], (-1 * HexEdges[4]) },
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{ (-1 * HexEdges[8]), HexEdges[9], (-1 * HexEdges[5]) },
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{ (-1 * HexEdges[9]), HexEdges[10], (-1 * HexEdges[6]) },
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{ (-1 * HexEdges[10]), (-1 * HexEdges[11]), (-1 * HexEdges[7]) },
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{ principleXAxis, principleYAxis, principleZAxis }
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};
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OutType third = (OutType)(1.0 / 3.0);
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OutType negativeInfinity = vtkm::NegativeInfinity<OutType>();
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OutType tempMatrix1_1, tempMatrix1_2, tempMatrix1_3, tempMatrix2_2, tempMatrix2_3, tempMatrix3_3,
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determinant;
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OutType firstPartOfNumerator, secondPartOfNumerator, currentOddy, maxOddy = negativeInfinity;
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for (vtkm::IdComponent matrixNumber = 0; matrixNumber < 9; matrixNumber++)
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{
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/*
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// these computations equal the value at X_Y for the matrix B,
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// where B = matrix A multiplied by its transpose.
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// the values at X_X are also used for the matrix multiplication AA.
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// Note that the values 1_2 = 2_1, 1_3 = 3_1, and 2_3 = 3_2.
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// This fact is used to optimize the computation
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*/
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tempMatrix1_1 =
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vtkm::Dot(hexJacobianMatrices[matrixNumber][0], hexJacobianMatrices[matrixNumber][0]);
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tempMatrix1_2 =
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vtkm::Dot(hexJacobianMatrices[matrixNumber][0], hexJacobianMatrices[matrixNumber][1]);
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tempMatrix1_3 =
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vtkm::Dot(hexJacobianMatrices[matrixNumber][0], hexJacobianMatrices[matrixNumber][2]);
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tempMatrix2_2 =
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vtkm::Dot(hexJacobianMatrices[matrixNumber][1], hexJacobianMatrices[matrixNumber][1]);
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tempMatrix2_3 =
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vtkm::Dot(hexJacobianMatrices[matrixNumber][1], hexJacobianMatrices[matrixNumber][2]);
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tempMatrix3_3 =
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vtkm::Dot(hexJacobianMatrices[matrixNumber][2], hexJacobianMatrices[matrixNumber][2]);
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determinant = vtkm::Dot(
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hexJacobianMatrices[matrixNumber][0],
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vtkm::Cross(hexJacobianMatrices[matrixNumber][1], hexJacobianMatrices[matrixNumber][2]));
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if (determinant <= OutType(0.0))
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{
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return vtkm::Infinity<OutType>();
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}
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else
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{
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firstPartOfNumerator = (tempMatrix1_1 * tempMatrix1_1) + 2 * (tempMatrix1_2 * tempMatrix1_2) +
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2 * (tempMatrix1_3 * tempMatrix1_3) + (tempMatrix2_2 * tempMatrix2_2) +
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2 * (tempMatrix2_3 * tempMatrix2_3) + (tempMatrix3_3 * tempMatrix3_3);
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secondPartOfNumerator = tempMatrix1_1 + tempMatrix2_2 + tempMatrix3_3;
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secondPartOfNumerator *= secondPartOfNumerator;
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secondPartOfNumerator *= third;
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currentOddy = (firstPartOfNumerator - secondPartOfNumerator) /
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(vtkm::Pow(determinant, OutType(4.0 * third)));
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maxOddy = currentOddy > maxOddy ? currentOddy : maxOddy;
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}
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}
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if (maxOddy > 0)
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{
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return vtkm::Min(maxOddy, vtkm::Infinity<OutType>()); //normal case
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}
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return vtkm::Max(maxOddy, negativeInfinity);
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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_Oddy_h
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