mirror of
https://gitlab.kitware.com/vtk/vtk-m
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240 lines
11 KiB
C++
240 lines
11 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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//
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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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#ifndef vtk_m_exec_Jacobian_h
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#define vtk_m_exec_Jacobian_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/VectorAnalysis.h>
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namespace vtkm
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{
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namespace exec
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{
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namespace internal
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{
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template <typename T>
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struct Space2D
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{
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using Vec3 = vtkm::Vec<T, 3>;
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using Vec2 = vtkm::Vec<T, 2>;
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Vec3 Origin;
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Vec3 Basis0;
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Vec3 Basis1;
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VTKM_EXEC
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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
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Vec2 ConvertCoordToSpace(const Vec3 coord) const
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{
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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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template <typename U>
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VTKM_EXEC vtkm::Vec<U, 3> ConvertVecFromSpace(const vtkm::Vec<U, 2> vec) const
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{
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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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} //namespace internal
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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_WEDGE(pc, rc, call) \
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call(0, (-rc[2]), (-rc[2]), (pc[0] - rc[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]), (rc[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(4, (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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//-----------------------------------------------------------------------------
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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, typename ParametricCoordType, typename JacobianType>
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VTKM_EXEC 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>(JacobianType(1)) - pc;
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jacobian = vtkm::Matrix<JacobianType, 3, 3>(JacobianType(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, typename ParametricCoordType, typename JacobianType>
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VTKM_EXEC 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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vtkm::Vec<JacobianType, 3> pc(pcoords);
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vtkm::Vec<JacobianType, 3> rc = vtkm::Vec<JacobianType, 3>(JacobianType(1)) - pc;
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jacobian = vtkm::Matrix<JacobianType, 3, 3>(JacobianType(0));
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VTKM_DERIVATIVE_WEIGHTS_WEDGE(pc, rc, VTKM_ACCUM_JACOBIAN_3D);
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}
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template <typename WorldCoordType, typename ParametricCoordType, typename JacobianType>
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VTKM_EXEC 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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vtkm::Vec<JacobianType, 3> pc(pcoords);
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vtkm::Vec<JacobianType, 3> rc = vtkm::Vec<JacobianType, 3>(JacobianType(1)) - pc;
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jacobian = vtkm::Matrix<JacobianType, 3, 3>(JacobianType(0));
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VTKM_DERIVATIVE_WEIGHTS_PYRAMID(pc, rc, VTKM_ACCUM_JACOBIAN_3D);
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}
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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 SpaceType,
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typename JacobianType>
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VTKM_EXEC void JacobianFor2DCell(const WorldCoordType& wCoords,
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const vtkm::Vec<ParametricCoordType, 3>& pcoords,
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const vtkm::exec::internal::Space2D<SpaceType>& 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>(JacobianType(1)) - pc;
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vtkm::Vec<SpaceType, 2> wcoords2d;
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jacobian = vtkm::Matrix<JacobianType, 2, 2>(JacobianType(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
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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 = 2*vtkm::Pi<JacobianType>()/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_3D
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#undef VTKM_ACCUM_JACOBIAN_2D
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}
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} // namespace vtkm::exec
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#endif //vtk_m_exec_Jacobian_h
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