mirror of
https://gitlab.kitware.com/vtk/vtk-m
synced 2024-09-16 17:22:55 +00:00
1115 lines
41 KiB
C++
1115 lines
41 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 2015 Sandia Corporation.
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// Copyright 2015 UT-Battelle, LLC.
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// Copyright 2015 Los Alamos National Security.
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//
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// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
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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_exec_Derivative_h
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#define vtk_m_exec_Derivative_h
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#include <vtkm/Assert.h>
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#include <vtkm/CellShape.h>
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#include <vtkm/Math.h>
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#include <vtkm/Matrix.h>
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#include <vtkm/VecRectilinearPointCoordinates.h>
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#include <vtkm/VectorAnalysis.h>
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#include <vtkm/exec/CellInterpolate.h>
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#include <vtkm/exec/FunctorBase.h>
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namespace vtkm {
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namespace exec {
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namespace internal {
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// The derivative for a 2D polygon in 3D space is underdetermined since there
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// is no information in the direction perpendicular to the polygon. To compute
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// derivatives for general polygons, we build a 2D space for the polygon's
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// plane and solve the derivative there.
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template<typename T>
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struct Space2D
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{
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typedef vtkm::Vec<T,3> Vec3;
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typedef vtkm::Vec<T,2> Vec2;
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Vec3 Origin;
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Vec3 Basis0;
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Vec3 Basis1;
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VTKM_EXEC_EXPORT
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Space2D(const Vec3 &origin, const Vec3 &pointFirst, const Vec3 &pointLast)
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{
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this->Origin = origin;
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this->Basis0 = vtkm::Normal(pointFirst - this->Origin);
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Vec3 n = vtkm::Cross(this->Basis0, pointLast - this->Origin);
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this->Basis1 = vtkm::Normal(vtkm::Cross(this->Basis0, n));
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}
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VTKM_EXEC_EXPORT
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Vec2 ConvertCoordToSpace(const Vec3 coord) const {
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Vec3 vec = coord - this->Origin;
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return Vec2(vtkm::dot(vec, this->Basis0), vtkm::dot(vec, this->Basis1));
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}
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VTKM_EXEC_EXPORT
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Vec3 ConvertVecFromSpace(const Vec2 vec) const {
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return vec[0]*this->Basis0 + vec[1]*this->Basis1;
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}
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};
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#define VTKM_DERIVATIVE_WEIGHTS_HEXAHEDRON(pc, rc, call) \
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call(0, -rc[1]*rc[2], -rc[0]*rc[2], -rc[0]*rc[1]); \
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call(1, rc[1]*rc[2], -pc[0]*rc[2], -pc[0]*rc[1]); \
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call(2, pc[1]*rc[2], pc[0]*rc[2], -pc[0]*pc[1]); \
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call(3, -pc[1]*rc[2], rc[0]*rc[2], -rc[0]*pc[1]); \
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call(4, -rc[1]*pc[2], -rc[0]*pc[2], rc[0]*rc[1]); \
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call(5, rc[1]*pc[2], -pc[0]*pc[2], pc[0]*rc[1]); \
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call(6, pc[1]*pc[2], pc[0]*pc[2], pc[0]*pc[1]); \
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call(7, -pc[1]*pc[2], rc[0]*pc[2], rc[0]*pc[1])
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#define VTKM_DERIVATIVE_WEIGHTS_VOXEL(pc, rc, call) \
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call(0, -rc[1]*rc[2], -rc[0]*rc[2], -rc[0]*rc[1]); \
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call(1, rc[1]*rc[2], -pc[0]*rc[2], -pc[0]*rc[1]); \
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call(2, -pc[1]*rc[2], rc[0]*rc[2], -rc[0]*pc[1]); \
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call(3, pc[1]*rc[2], pc[0]*rc[2], -pc[0]*pc[1]); \
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call(4, -rc[1]*pc[2], -rc[0]*pc[2], rc[0]*rc[1]); \
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call(5, rc[1]*pc[2], -pc[0]*pc[2], pc[0]*rc[1]); \
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call(6, -pc[1]*pc[2], rc[0]*pc[2], rc[0]*pc[1]); \
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call(7, pc[1]*pc[2], pc[0]*pc[2], pc[0]*pc[1])
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#define VTKM_DERIVATIVE_WEIGHTS_WEDGE(pc, rc, call) \
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call(0, -rc[2], -rc[2], -1.0f+pc[0]+pc[1]); \
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call(1, 0.0f, rc[2], -pc[1]); \
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call(2, rc[2], 0.0f, -pc[0]); \
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call(3, -pc[2], -pc[2], 1.0f-pc[0]-pc[1]); \
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call(4, 0.0f, pc[2], pc[1]); \
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call(5, pc[2], 0.0f, pc[0])
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#define VTKM_DERIVATIVE_WEIGHTS_PYRAMID(pc, rc, call) \
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call(0, -rc[1]*rc[2], -rc[0]*rc[2], -rc[0]*rc[1]); \
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call(1, rc[1]*rc[2], -pc[0]*rc[2], -pc[0]*rc[1]); \
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call(2, pc[1]*rc[2], pc[0]*rc[2], -pc[0]*pc[1]); \
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call(3, -pc[1]*rc[2], rc[0]*rc[2], -rc[0]*pc[1]); \
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call(3, 0.0f, 0.0f, 1.0f)
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#define VTKM_DERIVATIVE_WEIGHTS_QUAD(pc, rc, call) \
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call(0, -rc[1], -rc[0]); \
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call(1, rc[1], -pc[0]); \
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call(2, pc[1], pc[0]); \
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call(3, -pc[1], rc[0])
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#define VTKM_DERIVATIVE_WEIGHTS_PIXEL(pc, rc, call) \
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call(0, -rc[1], -rc[0]); \
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call(1, rc[1], -pc[0]); \
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call(2, -pc[1], rc[0]); \
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call(3, pc[1], pc[0])
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// Given a series of point values for a wedge, return a new series of point
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// for a hexahedron that has the same interpolation within the wedge.
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template<typename FieldVecType>
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VTKM_EXEC_EXPORT
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vtkm::Vec<typename FieldVecType::ComponentType,8>
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PermuteWedgeToHex(const FieldVecType &field)
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{
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vtkm::Vec<typename FieldVecType::ComponentType,8> hexField;
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hexField[0] = field[0];
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hexField[1] = field[2];
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hexField[2] = field[2] + field[1] - field[0];
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hexField[3] = field[1];
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hexField[4] = field[3];
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hexField[5] = field[5];
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hexField[6] = field[5] + field[4] - field[3];
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hexField[7] = field[4];
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return hexField;
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}
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// Given a series of point values for a pyramid, return a new series of point
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// for a hexahedron that has the same interpolation within the pyramid.
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template<typename FieldVecType>
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VTKM_EXEC_EXPORT
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vtkm::Vec<typename FieldVecType::ComponentType,8>
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PermutePyramidToHex(const FieldVecType &field)
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{
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typedef typename FieldVecType::ComponentType T;
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vtkm::Vec<T,8> hexField;
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T baseCenter = T(0.25f)*(field[0]+field[1]+field[2]+field[3]);
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hexField[0] = field[0];
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hexField[1] = field[1];
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hexField[2] = field[2];
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hexField[3] = field[3];
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hexField[4] = field[4]+(field[0]-baseCenter);
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hexField[5] = field[4]+(field[1]-baseCenter);
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hexField[6] = field[4]+(field[2]-baseCenter);
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hexField[7] = field[4]+(field[3]-baseCenter);
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return hexField;
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}
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//-----------------------------------------------------------------------------
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// This returns the Jacobian of a hexahedron's (or other 3D cell's) coordinates
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// with respect to parametric coordinates. Explicitly, this is (d is partial
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// derivative):
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//
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// | |
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// | dx/du dx/dv dx/dw |
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// | |
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// | dy/du dy/dv dy/dw |
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// | |
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// | dz/du dz/dv dz/dw |
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// | |
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//
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#define VTKM_ACCUM_JACOBIAN_3D(pointIndex, weight0, weight1, weight2) \
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jacobian(0,0) += static_cast<JacobianType>(wCoords[pointIndex][0] * (weight0)); \
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jacobian(1,0) += static_cast<JacobianType>(wCoords[pointIndex][1] * (weight0)); \
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jacobian(2,0) += static_cast<JacobianType>(wCoords[pointIndex][2] * (weight0)); \
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jacobian(0,1) += static_cast<JacobianType>(wCoords[pointIndex][0] * (weight1)); \
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jacobian(1,1) += static_cast<JacobianType>(wCoords[pointIndex][1] * (weight1)); \
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jacobian(2,1) += static_cast<JacobianType>(wCoords[pointIndex][2] * (weight1)); \
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jacobian(0,2) += static_cast<JacobianType>(wCoords[pointIndex][0] * (weight2)); \
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jacobian(1,2) += static_cast<JacobianType>(wCoords[pointIndex][1] * (weight2)); \
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jacobian(2,2) += static_cast<JacobianType>(wCoords[pointIndex][2] * (weight2))
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template<typename WorldCoordType,
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typename ParametricCoordType,
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typename JacobianType>
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VTKM_EXEC_EXPORT
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void JacobianFor3DCell(const WorldCoordType &wCoords,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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vtkm::Matrix<JacobianType,3,3> &jacobian,
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vtkm::CellShapeTagHexahedron)
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{
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vtkm::Vec<JacobianType,3> pc(pcoords);
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vtkm::Vec<JacobianType,3> rc = vtkm::Vec<JacobianType,3>(1) - pc;
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jacobian = vtkm::Matrix<JacobianType,3,3>(0);
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VTKM_DERIVATIVE_WEIGHTS_HEXAHEDRON(pc, rc, VTKM_ACCUM_JACOBIAN_3D);
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}
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template<typename WorldCoordType,
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typename ParametricCoordType,
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typename JacobianType>
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VTKM_EXEC_EXPORT
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void JacobianFor3DCell(const WorldCoordType &wCoords,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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vtkm::Matrix<JacobianType,3,3> &jacobian,
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vtkm::CellShapeTagWedge)
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{
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#if 0
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// This is not working. Just leverage the hexahedron code that is working.
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vtkm::Vec<JacobianType,3> pc(pcoords);
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vtkm::Vec<JacobianType,3> rc = vtkm::Vec<JacobianType,3>(1) - pc;
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jacobian = vtkm::Matrix<JacobianType,3,3>(0);
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VTKM_DERIVATIVE_WEIGHTS_WEDGE(pc, rc, VTKM_ACCUM_JACOBIAN_3D);
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#else
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JacobianFor3DCell(vtkm::exec::internal::PermuteWedgeToHex(wCoords),
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pcoords,
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jacobian,
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vtkm::CellShapeTagHexahedron());
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#endif
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}
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template<typename WorldCoordType,
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typename ParametricCoordType,
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typename JacobianType>
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VTKM_EXEC_EXPORT
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void JacobianFor3DCell(const WorldCoordType &wCoords,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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vtkm::Matrix<JacobianType,3,3> &jacobian,
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vtkm::CellShapeTagPyramid)
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{
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#if 0
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// This is not working. Just leverage the hexahedron code that is working.
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vtkm::Vec<JacobianType,3> pc(pcoords);
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vtkm::Vec<JacobianType,3> rc = vtkm::Vec<JacobianType,3>(1) - pc;
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jacobian = vtkm::Matrix<JacobianType,3,3>(0);
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VTKM_DERIVATIVE_WEIGHTS_PYRAMID(pc, rc, VTKM_ACCUM_JACOBIAN_3D);
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#else
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JacobianFor3DCell(vtkm::exec::internal::PermutePyramidToHex(wCoords),
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pcoords,
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jacobian,
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vtkm::CellShapeTagHexahedron());
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#endif
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}
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#undef VTKM_ACCUM_JACOBIAN_3D
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// Derivatives in quadrilaterals are computed in much the same way as
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// hexahedra. Review the documentation for hexahedra derivatives for details
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// on the math. The major difference is that the equations are performed in
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// a 2D space built with make_SpaceForQuadrilateral.
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#define VTKM_ACCUM_JACOBIAN_2D(pointIndex, weight0, weight1) \
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wcoords2d = space.ConvertCoordToSpace(wCoords[pointIndex]); \
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jacobian(0,0) += wcoords2d[0] * (weight0); \
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jacobian(1,0) += wcoords2d[1] * (weight0); \
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jacobian(0,1) += wcoords2d[0] * (weight1); \
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jacobian(1,1) += wcoords2d[1] * (weight1)
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template<typename WorldCoordType,
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typename ParametricCoordType,
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typename JacobianType>
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VTKM_EXEC_EXPORT
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void JacobianFor2DCell(const WorldCoordType &wCoords,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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const vtkm::exec::internal::Space2D<JacobianType> &space,
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vtkm::Matrix<JacobianType,2,2> &jacobian,
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vtkm::CellShapeTagQuad)
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{
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vtkm::Vec<JacobianType,2> pc(static_cast<JacobianType>(pcoords[0]),
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static_cast<JacobianType>(pcoords[1]));
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vtkm::Vec<JacobianType,2> rc = vtkm::Vec<JacobianType,2>(1) - pc;
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vtkm::Vec<JacobianType,2> wcoords2d;
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jacobian = vtkm::Matrix<JacobianType,2,2>(0);
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VTKM_DERIVATIVE_WEIGHTS_QUAD(pc, rc, VTKM_ACCUM_JACOBIAN_2D);
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}
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#if 0
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// This code doesn't work, so I'm bailing on it. Instead, I'm just grabbing a
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// triangle and finding the derivative of that. If you can do better, please
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// implement it.
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template<typename WorldCoordType,
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typename ParametricCoordType,
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typename JacobianType>
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VTKM_EXEC_EXPORT
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void JacobianFor2DCell(const WorldCoordType &wCoords,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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const vtkm::exec::internal::Space2D<JacobianType> &space,
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vtkm::Matrix<JacobianType,2,2> &jacobian,
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vtkm::CellShapeTagPolygon)
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{
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const vtkm::IdComponent numPoints = wCoords.GetNumberOfComponents();
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vtkm::Vec<JacobianType,2> pc(pcoords[0], pcoords[1]);
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JacobianType deltaAngle = static_cast<JacobianType>(2*vtkm::Pi()/numPoints);
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jacobian = vtkm::Matrix<JacobianType,2,2>(0);
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for (vtkm::IdComponent pointIndex = 0; pointIndex < numPoints; pointIndex++)
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{
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JacobianType angle = pointIndex*deltaAngle;
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vtkm::Vec<JacobianType,2> nodePCoords(0.5f*(vtkm::Cos(angle)+1),
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0.5f*(vtkm::Sin(angle)+1));
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// This is the vector pointing from the user provided parametric coordinate
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// to the node at pointIndex in parametric space.
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vtkm::Vec<JacobianType,2> pvec = nodePCoords - pc;
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// The weight (the derivative of the interpolation factor) happens to be
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// pvec scaled by the cube root of pvec's magnitude.
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JacobianType magSqr = vtkm::MagnitudeSquared(pvec);
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JacobianType invMag = vtkm::RSqrt(magSqr);
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JacobianType scale = invMag*invMag*invMag;
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vtkm::Vec<JacobianType,2> weight = scale*pvec;
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vtkm::Vec<JacobianType,2> wcoords2d =
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space.ConvertCoordToSpace(wCoords[pointIndex]);
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jacobian(0,0) += wcoords2d[0] * weight[0];
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jacobian(1,0) += wcoords2d[1] * weight[0];
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jacobian(0,1) += wcoords2d[0] * weight[1];
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jacobian(1,1) += wcoords2d[1] * weight[1];
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}
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}
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#endif
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#undef VTKM_ACCUM_JACOBIAN_2D
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#define VTKM_ACCUM_PARAMETRIC_DERIVATIVE_3D(pointIndex,weight0,weight1,weight2)\
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parametricDerivative[0] += field[pointIndex] * weight0; \
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parametricDerivative[1] += field[pointIndex] * weight1; \
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parametricDerivative[2] += field[pointIndex] * weight2
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// Find the derivative of a field in parametric space. That is, find the
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// vector [ds/du, ds/dv, ds/dw].
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template<typename FieldVecType,
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typename ParametricCoordType>
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VTKM_EXEC_EXPORT
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vtkm::Vec<typename FieldVecType::ComponentType,3>
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ParametricDerivative(const FieldVecType &field,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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vtkm::CellShapeTagHexahedron)
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{
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typedef typename FieldVecType::ComponentType FieldType;
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typedef vtkm::Vec<FieldType,3> GradientType;
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GradientType pc(pcoords);
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GradientType rc = GradientType(1) - pc;
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GradientType parametricDerivative(0);
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VTKM_DERIVATIVE_WEIGHTS_HEXAHEDRON(pc,rc,VTKM_ACCUM_PARAMETRIC_DERIVATIVE_3D);
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return parametricDerivative;
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}
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template<typename FieldVecType,
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typename ParametricCoordType>
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VTKM_EXEC_EXPORT
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vtkm::Vec<typename FieldVecType::ComponentType,3>
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ParametricDerivative(const FieldVecType &field,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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vtkm::CellShapeTagWedge)
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{
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#if 0
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// This is not working. Just leverage the hexahedron code that is working.
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typedef typename FieldVecType::ComponentType FieldType;
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typedef vtkm::Vec<FieldType,3> GradientType;
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GradientType pc(pcoords);
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GradientType rc = GradientType(1) - pc;
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GradientType parametricDerivative(0);
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VTKM_DERIVATIVE_WEIGHTS_WEDGE(pc, rc, VTKM_ACCUM_PARAMETRIC_DERIVATIVE_3D);
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return parametricDerivative;
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#else
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return ParametricDerivative(vtkm::exec::internal::PermuteWedgeToHex(field),
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pcoords,
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vtkm::CellShapeTagHexahedron());
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#endif
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}
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template<typename FieldVecType,
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typename ParametricCoordType>
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VTKM_EXEC_EXPORT
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vtkm::Vec<typename FieldVecType::ComponentType,3>
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ParametricDerivative(const FieldVecType &field,
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const vtkm::Vec<ParametricCoordType,3> &pcoords,
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vtkm::CellShapeTagPyramid)
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{
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#if 0
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// This is not working. Just leverage the hexahedron code that is working.
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typedef typename FieldVecType::ComponentType FieldType;
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|
typedef vtkm::Vec<FieldType,3> GradientType;
|
|
|
|
GradientType pc(pcoords);
|
|
GradientType rc = GradientType(1) - pc;
|
|
|
|
GradientType parametricDerivative(0);
|
|
VTKM_DERIVATIVE_WEIGHTS_PYRAMID(pc, rc, VTKM_ACCUM_PARAMETRIC_DERIVATIVE_3D);
|
|
|
|
return parametricDerivative;
|
|
#else
|
|
return ParametricDerivative(vtkm::exec::internal::PermutePyramidToHex(field),
|
|
pcoords,
|
|
vtkm::CellShapeTagHexahedron());
|
|
#endif
|
|
}
|
|
|
|
#undef VTKM_ACCUM_PARAMETRIC_DERIVATIVE_3D
|
|
|
|
#define VTKM_ACCUM_PARAMETRIC_DERIVATIVE_2D(pointIndex, weight0, weight1) \
|
|
parametricDerivative[0] += field[pointIndex] * weight0; \
|
|
parametricDerivative[1] += field[pointIndex] * weight1
|
|
|
|
template<typename FieldVecType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,2>
|
|
ParametricDerivative(const FieldVecType &field,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagQuad)
|
|
{
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef vtkm::Vec<FieldType,2> GradientType;
|
|
|
|
GradientType pc(static_cast<FieldType>(pcoords[0]),
|
|
static_cast<FieldType>(pcoords[1]));
|
|
GradientType rc = GradientType(1) - pc;
|
|
|
|
GradientType parametricDerivative(0);
|
|
VTKM_DERIVATIVE_WEIGHTS_QUAD(pc, rc, VTKM_ACCUM_PARAMETRIC_DERIVATIVE_2D);
|
|
|
|
return parametricDerivative;
|
|
}
|
|
|
|
#if 0
|
|
// This code doesn't work, so I'm bailing on it. Instead, I'm just grabbing a
|
|
// triangle and finding the derivative of that. If you can do better, please
|
|
// implement it.
|
|
template<typename FieldVecType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,2>
|
|
ParametricDerivative(const FieldVecType &field,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagPolygon)
|
|
{
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef vtkm::Vec<FieldType,2> GradientType;
|
|
|
|
const vtkm::IdComponent numPoints = field.GetNumberOfComponents();
|
|
FieldType deltaAngle = static_cast<FieldType>(2*vtkm::Pi()/numPoints);
|
|
|
|
GradientType pc(pcoords[0], pcoords[1]);
|
|
|
|
GradientType parametricDerivative(0);
|
|
for (vtkm::IdComponent pointIndex = 0; pointIndex < numPoints; pointIndex++)
|
|
{
|
|
FieldType angle = pointIndex*deltaAngle;
|
|
vtkm::Vec<FieldType,2> nodePCoords(0.5f*(vtkm::Cos(angle)+1),
|
|
0.5f*(vtkm::Sin(angle)+1));
|
|
|
|
// This is the vector pointing from the user provided parametric coordinate
|
|
// to the node at pointIndex in parametric space.
|
|
vtkm::Vec<FieldType,2> pvec = nodePCoords - pc;
|
|
|
|
// The weight (the derivative of the interpolation factor) happens to be
|
|
// pvec scaled by the cube root of pvec's magnitude.
|
|
FieldType magSqr = vtkm::MagnitudeSquared(pvec);
|
|
FieldType invMag = vtkm::RSqrt(magSqr);
|
|
FieldType scale = invMag*invMag*invMag;
|
|
vtkm::Vec<FieldType,2> weight = scale*pvec;
|
|
|
|
parametricDerivative[0] += field[pointIndex] * weight[0];
|
|
parametricDerivative[1] += field[pointIndex] * weight[1];
|
|
}
|
|
|
|
return parametricDerivative;
|
|
}
|
|
#endif
|
|
|
|
#undef VTKM_ACCUM_PARAMETRIC_DERIVATIVE_2D
|
|
|
|
#undef VTKM_DERIVATIVE_WEIGHTS_HEXAHEDRON
|
|
#undef VTKM_DERIVATIVE_WEIGHTS_VOXEL
|
|
#undef VTKM_DERIVATIVE_WEIGHTS_WEDGE
|
|
#undef VTKM_DERIVATIVE_WEIGHTS_PYRAMID
|
|
#undef VTKM_DERIVATIVE_WEIGHTS_QUAD
|
|
#undef VTKM_DERIVATIVE_WEIGHTS_PIXEL
|
|
|
|
|
|
} // namespace internal
|
|
|
|
namespace detail {
|
|
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType,
|
|
typename CellShapeTag>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivativeFor3DCell(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
CellShapeTag)
|
|
{
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef vtkm::Vec<FieldType,3> GradientType;
|
|
|
|
// For reasons that should become apparent in a moment, we actually want
|
|
// the transpose of the Jacobian.
|
|
vtkm::Matrix<FieldType,3,3> jacobianTranspose;
|
|
vtkm::exec::internal::JacobianFor3DCell(
|
|
wCoords, pcoords, jacobianTranspose, CellShapeTag());
|
|
jacobianTranspose = vtkm::MatrixTranspose(jacobianTranspose);
|
|
|
|
GradientType parametricDerivative =
|
|
vtkm::exec::internal::ParametricDerivative(field,pcoords,CellShapeTag());
|
|
|
|
// If we write out the matrices below, it should become clear that the
|
|
// Jacobian transpose times the field derivative in world space equals
|
|
// the field derivative in parametric space.
|
|
//
|
|
// | | | | | |
|
|
// | dx/du dy/du dz/du | | ds/dx | | ds/du |
|
|
// | | | | | |
|
|
// | dx/dv dy/dv dz/dv | | ds/dy | = | ds/dv |
|
|
// | | | | | |
|
|
// | dx/dw dy/dw dz/dw | | ds/dz | | ds/dw |
|
|
// | | | | | |
|
|
//
|
|
// Now we just need to solve this linear system to find the derivative in
|
|
// world space.
|
|
|
|
bool valid; // Ignored.
|
|
return vtkm::SolveLinearSystem(jacobianTranspose,
|
|
parametricDerivative,
|
|
valid);
|
|
}
|
|
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType,
|
|
typename CellShapeTag>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivativeFor2DCell(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
CellShapeTag)
|
|
{
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
|
|
// We have an underdetermined system in 3D, so create a 2D space in the
|
|
// plane that the polygon sits.
|
|
vtkm::exec::internal::Space2D<FieldType> space(
|
|
wCoords[0], wCoords[1], wCoords[wCoords.GetNumberOfComponents()-1]);
|
|
|
|
// For reasons that should become apparent in a moment, we actually want
|
|
// the transpose of the Jacobian.
|
|
vtkm::Matrix<FieldType,2,2> jacobianTranspose;
|
|
vtkm::exec::internal::JacobianFor2DCell(
|
|
wCoords, pcoords, space, jacobianTranspose, CellShapeTag());
|
|
jacobianTranspose = vtkm::MatrixTranspose(jacobianTranspose);
|
|
|
|
// Find the derivative of the field in parametric coordinate space. That is,
|
|
// find the vector [ds/du, ds/dv].
|
|
vtkm::Vec<FieldType,2> parametricDerivative =
|
|
vtkm::exec::internal::ParametricDerivative(field,pcoords,CellShapeTag());
|
|
|
|
// If we write out the matrices below, it should become clear that the
|
|
// Jacobian transpose times the field derivative in world space equals
|
|
// the field derivative in parametric space.
|
|
//
|
|
// | | | | | |
|
|
// | db0/du db1/du | | ds/db0 | | ds/du |
|
|
// | | | | = | |
|
|
// | db0/dv db1/dv | | ds/db1 | | ds/dv |
|
|
// | | | | | |
|
|
//
|
|
// Now we just need to solve this linear system to find the derivative in
|
|
// world space.
|
|
|
|
bool valid; // Ignored.
|
|
vtkm::Vec<FieldType,2> gradient2D =
|
|
vtkm::SolveLinearSystem(jacobianTranspose, parametricDerivative, valid);
|
|
|
|
return space.ConvertVecFromSpace(gradient2D);
|
|
}
|
|
|
|
} // namespace detail
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// \brief Take the derivative (get the gradient) of a point field in a cell.
|
|
///
|
|
/// Given the point field values for each node and the parametric coordinates
|
|
/// of a point within the cell, finds the derivative with respect to each
|
|
/// coordinate (i.e. the gradient) at that point. The derivative is not always
|
|
/// constant in some "linear" cells.
|
|
///
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &pointFieldValues,
|
|
const WorldCoordType &worldCoordinateValues,
|
|
const vtkm::Vec<ParametricCoordType,3> ¶metricCoords,
|
|
vtkm::CellShapeTagGeneric shape,
|
|
const vtkm::exec::FunctorBase &worklet)
|
|
{
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3> result;
|
|
switch (shape.Id)
|
|
{
|
|
vtkmGenericCellShapeMacro(
|
|
result = CellDerivative(pointFieldValues,
|
|
worldCoordinateValues,
|
|
parametricCoords,
|
|
CellShapeTag(),
|
|
worklet));
|
|
default:
|
|
worklet.RaiseError("Unknown cell shape sent to derivative.");
|
|
return vtkm::Vec<typename FieldVecType::ComponentType,3>();
|
|
}
|
|
return result;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &,
|
|
const WorldCoordType &,
|
|
const vtkm::Vec<ParametricCoordType,3> &,
|
|
vtkm::CellShapeTagEmpty,
|
|
const vtkm::exec::FunctorBase &worklet)
|
|
{
|
|
worklet.RaiseError("Attempted to take derivative in empty cell.");
|
|
return vtkm::Vec<typename FieldVecType::ComponentType,3>();
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &,
|
|
vtkm::CellShapeTagVertex,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
(void)field;
|
|
(void)wCoords;
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 1);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 1);
|
|
|
|
typedef vtkm::Vec<typename FieldVecType::ComponentType,3> GradientType;
|
|
return GradientType(0,0,0);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &vtkmNotUsed(pcoords),
|
|
vtkm::CellShapeTagLine,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 2);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 2);
|
|
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef vtkm::Vec<FieldType,3> GradientType;
|
|
|
|
// The derivative of a line is in the direction of the line. Its length is
|
|
// equal to the difference of the scalar field divided by the length of the
|
|
// line segment. Thus, the derivative is characterized by
|
|
// (deltaField*vec)/mag(vec)^2.
|
|
|
|
FieldType deltaField = field[1] - field[0];
|
|
GradientType vec = wCoords[1] - wCoords[0];
|
|
|
|
return (deltaField/vtkm::MagnitudeSquared(vec))*vec;
|
|
}
|
|
|
|
template<typename FieldVecType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const vtkm::VecRectilinearPointCoordinates<1> &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &vtkmNotUsed(pcoords),
|
|
vtkm::CellShapeTagLine,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 2);
|
|
|
|
typedef typename FieldVecType::ComponentType T;
|
|
|
|
return vtkm::Vec<T,3>((field[1]-field[0])/wCoords.GetSpacing()[0], 0, 0);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &vtkmNotUsed(pcoords),
|
|
vtkm::CellShapeTagTriangle,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 3);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 3);
|
|
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef vtkm::Vec<FieldType,3> GradientType;
|
|
|
|
// The scalar values of the three points in a triangle completely specify a
|
|
// linear field (with constant gradient) assuming the field is constant in
|
|
// the normal direction to the triangle. The field, defined by the 3-vector
|
|
// gradient g and scalar value s_origin, can be found with this set of 4
|
|
// equations and 4 unknowns.
|
|
//
|
|
// dot(p0, g) + s_origin = s0
|
|
// dot(p1, g) + s_origin = s1
|
|
// dot(p2, g) + s_origin = s2
|
|
// dot(n, g) = 0
|
|
//
|
|
// Where the p's are point coordinates and n is the normal vector. But we
|
|
// don't really care about s_origin. We just want to find the gradient g.
|
|
// With some simple elimination we, we can get rid of s_origin and be left
|
|
// with 3 equations and 3 unknowns.
|
|
//
|
|
// dot(p1-p0, g) = s1 - s0
|
|
// dot(p2-p0, g) = s2 - s0
|
|
// dot(n, g) = 0
|
|
//
|
|
// We'll solve this by putting this in matrix form Ax = b where the rows of A
|
|
// are the differences in points and normal, b has the scalar differences,
|
|
// and x is really the gradient g.
|
|
|
|
GradientType v0 = wCoords[1] - wCoords[0];
|
|
GradientType v1 = wCoords[2] - wCoords[0];
|
|
GradientType n = vtkm::Cross(v0, v1);
|
|
|
|
vtkm::Matrix<FieldType,3,3> A;
|
|
vtkm::MatrixSetRow(A, 0, v0);
|
|
vtkm::MatrixSetRow(A, 1, v1);
|
|
vtkm::MatrixSetRow(A, 2, n);
|
|
|
|
GradientType b(field[1] - field[0], field[2] - field[0], 0);
|
|
|
|
// If we want to later change this method to take the gradient of multiple
|
|
// values (for example, to find the Jacobian of a vector field), then there
|
|
// are more efficient ways to solve them all than independently solving this
|
|
// equation for each component of the field. You could find the inverse of
|
|
// matrix A. Or you could alter the functions in vtkm/Matrix.h to
|
|
// simultaneously solve multiple equations.
|
|
|
|
// If the triangle is degenerate, then valid will be false. For now we are
|
|
// ignoring it. We could detect it if we determine we need to although I have
|
|
// seen singular matrices missed due to floating point error.
|
|
//
|
|
bool valid;
|
|
|
|
return vtkm::SolveLinearSystem(A, b, valid);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagPolygon,
|
|
const vtkm::exec::FunctorBase &worklet)
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == wCoords.GetNumberOfComponents());
|
|
|
|
const vtkm::IdComponent numPoints = field.GetNumberOfComponents();
|
|
VTKM_ASSERT(numPoints > 0);
|
|
|
|
switch (field.GetNumberOfComponents())
|
|
{
|
|
case 1: return CellDerivative(field,
|
|
wCoords,
|
|
pcoords,
|
|
vtkm::CellShapeTagVertex(),
|
|
worklet);
|
|
case 2: return CellDerivative(field,
|
|
wCoords,
|
|
pcoords,
|
|
vtkm::CellShapeTagLine(),
|
|
worklet);
|
|
case 3: return CellDerivative(field,
|
|
wCoords,
|
|
pcoords,
|
|
vtkm::CellShapeTagTriangle(),
|
|
worklet);
|
|
case 4: return CellDerivative(field,
|
|
wCoords,
|
|
pcoords,
|
|
vtkm::CellShapeTagQuad(),
|
|
worklet);
|
|
}
|
|
|
|
// If we are here, then there are 5 or more points on this polygon.
|
|
|
|
// Arrange the points such that they are on the circle circumscribed in the
|
|
// unit square from 0 to 1. That is, the point are on the circle centered at
|
|
// coordinate 0.5,0.5 with radius 0.5. The polygon is divided into regions
|
|
// defined by they triangle fan formed by the points around the center. This
|
|
// is C0 continuous but not necessarily C1 continuous. It is also possible to
|
|
// have a non 1 to 1 mapping between parametric coordinates world coordinates
|
|
// if the polygon is not planar or convex.
|
|
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef typename WorldCoordType::ComponentType WCoordType;
|
|
|
|
// Find the interpolation for the center point.
|
|
FieldType fieldCenter = field[0];
|
|
WCoordType wcoordCenter = wCoords[0];
|
|
for (vtkm::IdComponent pointIndex = 1; pointIndex < numPoints; pointIndex++)
|
|
{
|
|
fieldCenter = fieldCenter + field[pointIndex];
|
|
wcoordCenter = wcoordCenter + wCoords[pointIndex];
|
|
}
|
|
fieldCenter = fieldCenter*FieldType(1.0f/static_cast<float>(numPoints));
|
|
wcoordCenter = wcoordCenter*WCoordType(1.0f/static_cast<float>(numPoints));
|
|
|
|
ParametricCoordType angle;
|
|
if ((vtkm::Abs(pcoords[0]-0.5f) < 4*vtkm::Epsilon<ParametricCoordType>()) &&
|
|
(vtkm::Abs(pcoords[1]-0.5f) < 4*vtkm::Epsilon<ParametricCoordType>()))
|
|
{
|
|
angle = 0;
|
|
}
|
|
else
|
|
{
|
|
angle = vtkm::ATan2(pcoords[1]-0.5f, pcoords[0]-0.5f);
|
|
if (angle < 0)
|
|
{
|
|
angle += static_cast<ParametricCoordType>(2*vtkm::Pi());
|
|
}
|
|
}
|
|
|
|
const ParametricCoordType deltaAngle =
|
|
static_cast<ParametricCoordType>(2*vtkm::Pi()/numPoints);
|
|
vtkm::IdComponent firstPointIndex =
|
|
static_cast<vtkm::IdComponent>(vtkm::Floor(angle/deltaAngle));
|
|
vtkm::IdComponent secondPointIndex = firstPointIndex + 1;
|
|
if (secondPointIndex == numPoints)
|
|
{
|
|
secondPointIndex = 0;
|
|
}
|
|
|
|
// Set up parameters for triangle that pcoords is in
|
|
vtkm::Vec<FieldType,3> triangleField;
|
|
triangleField[0] = fieldCenter;
|
|
triangleField[1] = field[firstPointIndex];
|
|
triangleField[2] = field[secondPointIndex];
|
|
|
|
vtkm::Vec<WCoordType,3> triangleWCoords;
|
|
triangleWCoords[0] = wcoordCenter;
|
|
triangleWCoords[1] = wCoords[firstPointIndex];
|
|
triangleWCoords[2] = wCoords[secondPointIndex];
|
|
|
|
// Now use the triangle derivative. pcoords is actually invalid for the
|
|
// triangle, but that does not matter as the derivative for a triangle does
|
|
// not depend on it.
|
|
return vtkm::exec::CellDerivative(triangleField,
|
|
triangleWCoords,
|
|
pcoords,
|
|
vtkm::CellShapeTagTriangle(),
|
|
worklet);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagQuad,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 4);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 4);
|
|
|
|
return detail::CellDerivativeFor2DCell(
|
|
field, wCoords, pcoords, vtkm::CellShapeTagQuad());
|
|
}
|
|
|
|
template<typename FieldVecType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const vtkm::VecRectilinearPointCoordinates<2> &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagQuad,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 4);
|
|
|
|
typedef typename FieldVecType::ComponentType T;
|
|
typedef vtkm::Vec<T,2> VecT;
|
|
|
|
VecT pc(static_cast<T>(pcoords[0]),
|
|
static_cast<T>(pcoords[1]));
|
|
VecT rc = VecT(1) - pc;
|
|
|
|
VecT sum = field[0]*VecT(-rc[1], -rc[0]);
|
|
sum = sum + field[1]*VecT( rc[1], -pc[0]);
|
|
sum = sum + field[2]*VecT( pc[1], pc[0]);
|
|
sum = sum + field[3]*VecT(-pc[1], rc[0]);
|
|
|
|
return vtkm::Vec<T,3>(sum[0]/wCoords.GetSpacing()[0],
|
|
sum[1]/wCoords.GetSpacing()[1],
|
|
0);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &vtkmNotUsed(pcoords),
|
|
vtkm::CellShapeTagTetra,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 4);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 4);
|
|
|
|
typedef typename FieldVecType::ComponentType FieldType;
|
|
typedef vtkm::Vec<FieldType,3> GradientType;
|
|
|
|
// The scalar values of the four points in a tetrahedron completely specify a
|
|
// linear field (with constant gradient). The field, defined by the 3-vector
|
|
// gradient g and scalar value s_origin, can be found with this set of 4
|
|
// equations and 4 unknowns.
|
|
//
|
|
// dot(p0, g) + s_origin = s0
|
|
// dot(p1, g) + s_origin = s1
|
|
// dot(p2, g) + s_origin = s2
|
|
// dot(p3, g) + s_origin = s3
|
|
//
|
|
// Where the p's are point coordinates. But we don't really care about
|
|
// s_origin. We just want to find the gradient g. With some simple
|
|
// elimination we, we can get rid of s_origin and be left with 3 equations
|
|
// and 3 unknowns.
|
|
//
|
|
// dot(p1-p0, g) = s1 - s0
|
|
// dot(p2-p0, g) = s2 - s0
|
|
// dot(p3-p0, g) = s3 - s0
|
|
//
|
|
// We'll solve this by putting this in matrix form Ax = b where the rows of A
|
|
// are the differences in points and normal, b has the scalar differences,
|
|
// and x is really the gradient g.
|
|
|
|
GradientType v0 = wCoords[1] - wCoords[0];
|
|
GradientType v1 = wCoords[2] - wCoords[0];
|
|
GradientType v2 = wCoords[3] - wCoords[0];
|
|
|
|
vtkm::Matrix<FieldType,3,3> A;
|
|
vtkm::MatrixSetRow(A, 0, v0);
|
|
vtkm::MatrixSetRow(A, 1, v1);
|
|
vtkm::MatrixSetRow(A, 2, v2);
|
|
|
|
GradientType b(field[1]-field[0], field[2]-field[0], field[3]-field[0]);
|
|
|
|
// If we want to later change this method to take the gradient of multiple
|
|
// values (for example, to find the Jacobian of a vector field), then there
|
|
// are more efficient ways to solve them all than independently solving this
|
|
// equation for each component of the field. You could find the inverse of
|
|
// matrix A. Or you could alter the functions in vtkm/Matrix.h to
|
|
// simultaneously solve multiple equations.
|
|
|
|
// If the tetrahedron is degenerate, then valid will be false. For now we are
|
|
// ignoring it. We could detect it if we determine we need to although I have
|
|
// seen singular matrices missed due to floating point error.
|
|
//
|
|
bool valid;
|
|
|
|
return vtkm::SolveLinearSystem(A, b, valid);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagHexahedron,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 8);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 8);
|
|
|
|
return detail::CellDerivativeFor3DCell(
|
|
field, wCoords, pcoords, vtkm::CellShapeTagHexahedron());
|
|
}
|
|
|
|
template<typename FieldVecType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const vtkm::VecRectilinearPointCoordinates<3> &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagHexahedron,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 8);
|
|
|
|
typedef typename FieldVecType::ComponentType T;
|
|
typedef vtkm::Vec<T,3> VecT;
|
|
|
|
VecT pc(static_cast<T>(pcoords[0]),
|
|
static_cast<T>(pcoords[1]),
|
|
static_cast<T>(pcoords[2]));
|
|
VecT rc = VecT(1) - pc;
|
|
|
|
VecT sum = field[0]*VecT(-rc[1]*rc[2], -rc[0]*rc[2], -rc[0]*rc[1]);
|
|
sum = sum + field[1]*VecT( rc[1]*rc[2], -pc[0]*rc[2], -pc[0]*rc[1]);
|
|
sum = sum + field[2]*VecT( pc[1]*rc[2], pc[0]*rc[2], -pc[0]*pc[1]);
|
|
sum = sum + field[3]*VecT(-pc[1]*rc[2], rc[0]*rc[2], -rc[0]*pc[1]);
|
|
sum = sum + field[4]*VecT(-rc[1]*pc[2], -rc[0]*pc[2], rc[0]*rc[1]);
|
|
sum = sum + field[5]*VecT( rc[1]*pc[2], -pc[0]*pc[2], pc[0]*rc[1]);
|
|
sum = sum + field[6]*VecT( pc[1]*pc[2], pc[0]*pc[2], pc[0]*pc[1]);
|
|
sum = sum + field[7]*VecT(-pc[1]*pc[2], rc[0]*pc[2], rc[0]*pc[1]);
|
|
|
|
return sum/wCoords.GetSpacing();
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagWedge,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 6);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 6);
|
|
|
|
return detail::CellDerivativeFor3DCell(
|
|
field, wCoords, pcoords, vtkm::CellShapeTagWedge());
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template<typename FieldVecType,
|
|
typename WorldCoordType,
|
|
typename ParametricCoordType>
|
|
VTKM_EXEC_EXPORT
|
|
vtkm::Vec<typename FieldVecType::ComponentType,3>
|
|
CellDerivative(const FieldVecType &field,
|
|
const WorldCoordType &wCoords,
|
|
const vtkm::Vec<ParametricCoordType,3> &pcoords,
|
|
vtkm::CellShapeTagPyramid,
|
|
const vtkm::exec::FunctorBase &vtkmNotUsed(worklet))
|
|
{
|
|
VTKM_ASSERT(field.GetNumberOfComponents() == 5);
|
|
VTKM_ASSERT(wCoords.GetNumberOfComponents() == 5);
|
|
|
|
return detail::CellDerivativeFor3DCell(
|
|
field, wCoords, pcoords, vtkm::CellShapeTagPyramid());
|
|
}
|
|
|
|
|
|
}
|
|
} // namespace vtkm::exec
|
|
|
|
#endif //vtk_m_exec_Derivative_h
|