/usr/include/openvdb/math/Operators.h is in libopenvdb-dev 5.0.0-1.
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//
// Copyright (c) 2012-2017 DreamWorks Animation LLC
//
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
//
// Redistributions of source code must retain the above copyright
// and license notice and the following restrictions and disclaimer.
//
// * Neither the name of DreamWorks Animation nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
// LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
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///////////////////////////////////////////////////////////////////////////
/// @file math/Operators.h
#ifndef OPENVDB_MATH_OPERATORS_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_OPERATORS_HAS_BEEN_INCLUDED
#include "FiniteDifference.h"
#include "Stencils.h"
#include "Maps.h"
#include "Transform.h"
#include <cmath> // for std::sqrt()
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
// Simple tools to help determine when type conversions are needed
template<typename Vec3T> struct is_vec3d { static const bool value = false; };
template<> struct is_vec3d<Vec3d> { static const bool value = true; };
template<typename T> struct is_double { static const bool value = false; };
template<> struct is_double<double> { static const bool value = true; };
/// @brief Adapter to associate a map with a world-space operator,
/// giving it the same call signature as an index-space operator
/// @todo For now, the operator's result type must be specified explicitly,
/// but eventually it should be possible, via traits, to derive the result type
/// from the operator type.
template<typename MapType, typename OpType, typename ResultType>
struct MapAdapter {
MapAdapter(const MapType& m): map(m) {}
template<typename AccessorType>
inline ResultType
result(const AccessorType& grid, const Coord& ijk) { return OpType::result(map, grid, ijk); }
template<typename StencilType>
inline ResultType
result(const StencilType& stencil) { return OpType::result(map, stencil); }
const MapType map;
};
/// Adapter for vector-valued index-space operators to return the vector magnitude
template<typename OpType>
struct ISOpMagnitude {
template<typename AccessorType>
static inline double result(const AccessorType& grid, const Coord& ijk) {
return double(OpType::result(grid, ijk).length());
}
template<typename StencilType>
static inline double result(const StencilType& stencil) {
return double(OpType::result(stencil).length());
}
};
/// Adapter for vector-valued world-space operators to return the vector magnitude
template<typename OpType, typename MapT>
struct OpMagnitude {
template<typename AccessorType>
static inline double result(const MapT& map, const AccessorType& grid, const Coord& ijk) {
return double(OpType::result(map, grid, ijk).length());
}
template<typename StencilType>
static inline double result(const MapT& map, const StencilType& stencil) {
return double(OpType::result(map, stencil).length());
}
};
namespace internal {
// This additional layer is necessary for Visual C++ to compile.
template<typename T>
struct ReturnValue {
using ValueType = typename T::ValueType;
using Vec3Type = math::Vec3<ValueType>;
};
} // namespace internal
// ---- Operators defined in index space
//@{
/// @brief Gradient operators defined in index space of various orders
template<DScheme DiffScheme>
struct ISGradient
{
// random access version
template<typename Accessor> static Vec3<typename Accessor::ValueType>
result(const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = Vec3<ValueType>;
return Vec3Type( D1<DiffScheme>::inX(grid, ijk),
D1<DiffScheme>::inY(grid, ijk),
D1<DiffScheme>::inZ(grid, ijk) );
}
// stencil access version
template<typename StencilT> static Vec3<typename StencilT::ValueType>
result(const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = Vec3<ValueType>;
return Vec3Type( D1<DiffScheme>::inX(stencil),
D1<DiffScheme>::inY(stencil),
D1<DiffScheme>::inZ(stencil) );
}
};
//@}
/// struct that relates the BiasedGradientScheme to the
/// forward and backward difference methods used, as well as to
/// the correct stencil type for index space use
template<BiasedGradientScheme bgs>
struct BIAS_SCHEME {
static const DScheme FD = FD_1ST;
static const DScheme BD = BD_1ST;
template<typename GridType, bool IsSafe = true>
struct ISStencil {
using StencilType = SevenPointStencil<GridType, IsSafe>;
};
};
template<> struct BIAS_SCHEME<FIRST_BIAS>
{
static const DScheme FD = FD_1ST;
static const DScheme BD = BD_1ST;
template<typename GridType, bool IsSafe = true>
struct ISStencil {
using StencilType = SevenPointStencil<GridType, IsSafe>;
};
};
template<> struct BIAS_SCHEME<SECOND_BIAS>
{
static const DScheme FD = FD_2ND;
static const DScheme BD = BD_2ND;
template<typename GridType, bool IsSafe = true>
struct ISStencil {
using StencilType = ThirteenPointStencil<GridType, IsSafe>;
};
};
template<> struct BIAS_SCHEME<THIRD_BIAS>
{
static const DScheme FD = FD_3RD;
static const DScheme BD = BD_3RD;
template<typename GridType, bool IsSafe = true>
struct ISStencil {
using StencilType = NineteenPointStencil<GridType, IsSafe>;
};
};
template<> struct BIAS_SCHEME<WENO5_BIAS>
{
static const DScheme FD = FD_WENO5;
static const DScheme BD = BD_WENO5;
template<typename GridType, bool IsSafe = true>
struct ISStencil {
using StencilType = NineteenPointStencil<GridType, IsSafe>;
};
};
template<> struct BIAS_SCHEME<HJWENO5_BIAS>
{
static const DScheme FD = FD_HJWENO5;
static const DScheme BD = BD_HJWENO5;
template<typename GridType, bool IsSafe = true>
struct ISStencil {
using StencilType = NineteenPointStencil<GridType, IsSafe>;
};
};
//@{
/// @brief Biased Gradient Operators, using upwinding defined by the @c Vec3Bias input
template<BiasedGradientScheme GradScheme, typename Vec3Bias>
struct ISGradientBiased
{
static const DScheme FD = BIAS_SCHEME<GradScheme>::FD;
static const DScheme BD = BIAS_SCHEME<GradScheme>::BD;
// random access version
template<typename Accessor>
static Vec3<typename Accessor::ValueType>
result(const Accessor& grid, const Coord& ijk, const Vec3Bias& V)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = Vec3<ValueType>;
return Vec3Type(V[0]<0 ? D1<FD>::inX(grid,ijk) : D1<BD>::inX(grid,ijk),
V[1]<0 ? D1<FD>::inY(grid,ijk) : D1<BD>::inY(grid,ijk),
V[2]<0 ? D1<FD>::inZ(grid,ijk) : D1<BD>::inZ(grid,ijk) );
}
// stencil access version
template<typename StencilT>
static Vec3<typename StencilT::ValueType>
result(const StencilT& stencil, const Vec3Bias& V)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = Vec3<ValueType>;
return Vec3Type(V[0]<0 ? D1<FD>::inX(stencil) : D1<BD>::inX(stencil),
V[1]<0 ? D1<FD>::inY(stencil) : D1<BD>::inY(stencil),
V[2]<0 ? D1<FD>::inZ(stencil) : D1<BD>::inZ(stencil) );
}
};
template<BiasedGradientScheme GradScheme>
struct ISGradientNormSqrd
{
static const DScheme FD = BIAS_SCHEME<GradScheme>::FD;
static const DScheme BD = BIAS_SCHEME<GradScheme>::BD;
// random access version
template<typename Accessor>
static typename Accessor::ValueType
result(const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = math::Vec3<ValueType>;
Vec3Type up = ISGradient<FD>::result(grid, ijk);
Vec3Type down = ISGradient<BD>::result(grid, ijk);
return math::GodunovsNormSqrd(grid.getValue(ijk)>0, down, up);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType
result(const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = math::Vec3<ValueType>;
Vec3Type up = ISGradient<FD>::result(stencil);
Vec3Type down = ISGradient<BD>::result(stencil);
return math::GodunovsNormSqrd(stencil.template getValue<0, 0, 0>()>0, down, up);
}
};
#ifdef DWA_OPENVDB // for SIMD - note will do the computations in float
template<>
struct ISGradientNormSqrd<HJWENO5_BIAS>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
{
struct GetValue
{
const Accessor& acc;
GetValue(const Accessor& acc_): acc(acc_) {}
// Return the grid value at ijk converted to simd::Float4::value_type (= float).
inline simd::Float4::value_type operator()(const Coord& ijk_) {
return static_cast<simd::Float4::value_type>(acc.getValue(ijk_));
}
}
valueAt(grid);
// SSE optimized
const simd::Float4
v1(valueAt(ijk.offsetBy(-2, 0, 0)) - valueAt(ijk.offsetBy(-3, 0, 0)),
valueAt(ijk.offsetBy( 0,-2, 0)) - valueAt(ijk.offsetBy( 0,-3, 0)),
valueAt(ijk.offsetBy( 0, 0,-2)) - valueAt(ijk.offsetBy( 0, 0,-3)), 0),
v2(valueAt(ijk.offsetBy(-1, 0, 0)) - valueAt(ijk.offsetBy(-2, 0, 0)),
valueAt(ijk.offsetBy( 0,-1, 0)) - valueAt(ijk.offsetBy( 0,-2, 0)),
valueAt(ijk.offsetBy( 0, 0,-1)) - valueAt(ijk.offsetBy( 0, 0,-2)), 0),
v3(valueAt(ijk ) - valueAt(ijk.offsetBy(-1, 0, 0)),
valueAt(ijk ) - valueAt(ijk.offsetBy( 0,-1, 0)),
valueAt(ijk ) - valueAt(ijk.offsetBy( 0, 0,-1)), 0),
v4(valueAt(ijk.offsetBy( 1, 0, 0)) - valueAt(ijk ),
valueAt(ijk.offsetBy( 0, 1, 0)) - valueAt(ijk ),
valueAt(ijk.offsetBy( 0, 0, 1)) - valueAt(ijk ), 0),
v5(valueAt(ijk.offsetBy( 2, 0, 0)) - valueAt(ijk.offsetBy( 1, 0, 0)),
valueAt(ijk.offsetBy( 0, 2, 0)) - valueAt(ijk.offsetBy( 0, 1, 0)),
valueAt(ijk.offsetBy( 0, 0, 2)) - valueAt(ijk.offsetBy( 0, 0, 1)), 0),
v6(valueAt(ijk.offsetBy( 3, 0, 0)) - valueAt(ijk.offsetBy( 2, 0, 0)),
valueAt(ijk.offsetBy( 0, 3, 0)) - valueAt(ijk.offsetBy( 0, 2, 0)),
valueAt(ijk.offsetBy( 0, 0, 3)) - valueAt(ijk.offsetBy( 0, 0, 2)), 0),
down = math::WENO5(v1, v2, v3, v4, v5),
up = math::WENO5(v6, v5, v4, v3, v2);
return math::GodunovsNormSqrd(grid.getValue(ijk)>0, down, up);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const StencilT& s)
{
using F4Val = simd::Float4::value_type;
// SSE optimized
const simd::Float4
v1(F4Val(s.template getValue<-2, 0, 0>()) - F4Val(s.template getValue<-3, 0, 0>()),
F4Val(s.template getValue< 0,-2, 0>()) - F4Val(s.template getValue< 0,-3, 0>()),
F4Val(s.template getValue< 0, 0,-2>()) - F4Val(s.template getValue< 0, 0,-3>()), 0),
v2(F4Val(s.template getValue<-1, 0, 0>()) - F4Val(s.template getValue<-2, 0, 0>()),
F4Val(s.template getValue< 0,-1, 0>()) - F4Val(s.template getValue< 0,-2, 0>()),
F4Val(s.template getValue< 0, 0,-1>()) - F4Val(s.template getValue< 0, 0,-2>()), 0),
v3(F4Val(s.template getValue< 0, 0, 0>()) - F4Val(s.template getValue<-1, 0, 0>()),
F4Val(s.template getValue< 0, 0, 0>()) - F4Val(s.template getValue< 0,-1, 0>()),
F4Val(s.template getValue< 0, 0, 0>()) - F4Val(s.template getValue< 0, 0,-1>()), 0),
v4(F4Val(s.template getValue< 1, 0, 0>()) - F4Val(s.template getValue< 0, 0, 0>()),
F4Val(s.template getValue< 0, 1, 0>()) - F4Val(s.template getValue< 0, 0, 0>()),
F4Val(s.template getValue< 0, 0, 1>()) - F4Val(s.template getValue< 0, 0, 0>()), 0),
v5(F4Val(s.template getValue< 2, 0, 0>()) - F4Val(s.template getValue< 1, 0, 0>()),
F4Val(s.template getValue< 0, 2, 0>()) - F4Val(s.template getValue< 0, 1, 0>()),
F4Val(s.template getValue< 0, 0, 2>()) - F4Val(s.template getValue< 0, 0, 1>()), 0),
v6(F4Val(s.template getValue< 3, 0, 0>()) - F4Val(s.template getValue< 2, 0, 0>()),
F4Val(s.template getValue< 0, 3, 0>()) - F4Val(s.template getValue< 0, 2, 0>()),
F4Val(s.template getValue< 0, 0, 3>()) - F4Val(s.template getValue< 0, 0, 2>()), 0),
down = math::WENO5(v1, v2, v3, v4, v5),
up = math::WENO5(v6, v5, v4, v3, v2);
return math::GodunovsNormSqrd(s.template getValue<0, 0, 0>()>0, down, up);
}
};
#endif //DWA_OPENVDB // for SIMD - note will do the computations in float
//@}
//@{
/// @brief Laplacian defined in index space, using various center-difference stencils
template<DDScheme DiffScheme>
struct ISLaplacian
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk);
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const StencilT& stencil);
};
template<>
struct ISLaplacian<CD_SECOND>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
{
return grid.getValue(ijk.offsetBy(1,0,0)) + grid.getValue(ijk.offsetBy(-1, 0, 0)) +
grid.getValue(ijk.offsetBy(0,1,0)) + grid.getValue(ijk.offsetBy(0, -1, 0)) +
grid.getValue(ijk.offsetBy(0,0,1)) + grid.getValue(ijk.offsetBy(0, 0,-1))
- 6*grid.getValue(ijk);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const StencilT& stencil)
{
return stencil.template getValue< 1, 0, 0>() + stencil.template getValue<-1, 0, 0>() +
stencil.template getValue< 0, 1, 0>() + stencil.template getValue< 0,-1, 0>() +
stencil.template getValue< 0, 0, 1>() + stencil.template getValue< 0, 0,-1>()
- 6*stencil.template getValue< 0, 0, 0>();
}
};
template<>
struct ISLaplacian<CD_FOURTH>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
{
using ValueT = typename Accessor::ValueType;
return static_cast<ValueT>(
(-1./12.)*(
grid.getValue(ijk.offsetBy(2,0,0)) + grid.getValue(ijk.offsetBy(-2, 0, 0)) +
grid.getValue(ijk.offsetBy(0,2,0)) + grid.getValue(ijk.offsetBy( 0,-2, 0)) +
grid.getValue(ijk.offsetBy(0,0,2)) + grid.getValue(ijk.offsetBy( 0, 0,-2)) )
+ (4./3.)*(
grid.getValue(ijk.offsetBy(1,0,0)) + grid.getValue(ijk.offsetBy(-1, 0, 0)) +
grid.getValue(ijk.offsetBy(0,1,0)) + grid.getValue(ijk.offsetBy( 0,-1, 0)) +
grid.getValue(ijk.offsetBy(0,0,1)) + grid.getValue(ijk.offsetBy( 0, 0,-1)) )
- 7.5*grid.getValue(ijk));
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const StencilT& stencil)
{
using ValueT = typename StencilT::ValueType;
return static_cast<ValueT>(
(-1./12.)*(
stencil.template getValue< 2, 0, 0>() + stencil.template getValue<-2, 0, 0>() +
stencil.template getValue< 0, 2, 0>() + stencil.template getValue< 0,-2, 0>() +
stencil.template getValue< 0, 0, 2>() + stencil.template getValue< 0, 0,-2>() )
+ (4./3.)*(
stencil.template getValue< 1, 0, 0>() + stencil.template getValue<-1, 0, 0>() +
stencil.template getValue< 0, 1, 0>() + stencil.template getValue< 0,-1, 0>() +
stencil.template getValue< 0, 0, 1>() + stencil.template getValue< 0, 0,-1>() )
- 7.5*stencil.template getValue< 0, 0, 0>());
}
};
template<>
struct ISLaplacian<CD_SIXTH>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
{
using ValueT = typename Accessor::ValueType;
return static_cast<ValueT>(
(1./90.)*(
grid.getValue(ijk.offsetBy(3,0,0)) + grid.getValue(ijk.offsetBy(-3, 0, 0)) +
grid.getValue(ijk.offsetBy(0,3,0)) + grid.getValue(ijk.offsetBy( 0,-3, 0)) +
grid.getValue(ijk.offsetBy(0,0,3)) + grid.getValue(ijk.offsetBy( 0, 0,-3)) )
- (3./20.)*(
grid.getValue(ijk.offsetBy(2,0,0)) + grid.getValue(ijk.offsetBy(-2, 0, 0)) +
grid.getValue(ijk.offsetBy(0,2,0)) + grid.getValue(ijk.offsetBy( 0,-2, 0)) +
grid.getValue(ijk.offsetBy(0,0,2)) + grid.getValue(ijk.offsetBy( 0, 0,-2)) )
+ 1.5 *(
grid.getValue(ijk.offsetBy(1,0,0)) + grid.getValue(ijk.offsetBy(-1, 0, 0)) +
grid.getValue(ijk.offsetBy(0,1,0)) + grid.getValue(ijk.offsetBy( 0,-1, 0)) +
grid.getValue(ijk.offsetBy(0,0,1)) + grid.getValue(ijk.offsetBy( 0, 0,-1)) )
- (3*49/18.)*grid.getValue(ijk));
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const StencilT& stencil)
{
using ValueT = typename StencilT::ValueType;
return static_cast<ValueT>(
(1./90.)*(
stencil.template getValue< 3, 0, 0>() + stencil.template getValue<-3, 0, 0>() +
stencil.template getValue< 0, 3, 0>() + stencil.template getValue< 0,-3, 0>() +
stencil.template getValue< 0, 0, 3>() + stencil.template getValue< 0, 0,-3>() )
- (3./20.)*(
stencil.template getValue< 2, 0, 0>() + stencil.template getValue<-2, 0, 0>() +
stencil.template getValue< 0, 2, 0>() + stencil.template getValue< 0,-2, 0>() +
stencil.template getValue< 0, 0, 2>() + stencil.template getValue< 0, 0,-2>() )
+ 1.5 *(
stencil.template getValue< 1, 0, 0>() + stencil.template getValue<-1, 0, 0>() +
stencil.template getValue< 0, 1, 0>() + stencil.template getValue< 0,-1, 0>() +
stencil.template getValue< 0, 0, 1>() + stencil.template getValue< 0, 0,-1>() )
- (3*49/18.)*stencil.template getValue< 0, 0, 0>());
}
};
//@}
//@{
/// Divergence operator defined in index space using various first derivative schemes
template<DScheme DiffScheme>
struct ISDivergence
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const Accessor& grid, const Coord& ijk)
{
return D1Vec<DiffScheme>::inX(grid, ijk, 0) +
D1Vec<DiffScheme>::inY(grid, ijk, 1) +
D1Vec<DiffScheme>::inZ(grid, ijk, 2);
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const StencilT& stencil)
{
return D1Vec<DiffScheme>::inX(stencil, 0) +
D1Vec<DiffScheme>::inY(stencil, 1) +
D1Vec<DiffScheme>::inZ(stencil, 2);
}
};
//@}
//@{
/// Curl operator defined in index space using various first derivative schemes
template<DScheme DiffScheme>
struct ISCurl
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename Accessor::ValueType;
return Vec3Type( D1Vec<DiffScheme>::inY(grid, ijk, 2) - //dw/dy - dv/dz
D1Vec<DiffScheme>::inZ(grid, ijk, 1),
D1Vec<DiffScheme>::inZ(grid, ijk, 0) - //du/dz - dw/dx
D1Vec<DiffScheme>::inX(grid, ijk, 2),
D1Vec<DiffScheme>::inX(grid, ijk, 1) - //dv/dx - du/dy
D1Vec<DiffScheme>::inY(grid, ijk, 0) );
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const StencilT& stencil)
{
using Vec3Type = typename StencilT::ValueType;
return Vec3Type( D1Vec<DiffScheme>::inY(stencil, 2) - //dw/dy - dv/dz
D1Vec<DiffScheme>::inZ(stencil, 1),
D1Vec<DiffScheme>::inZ(stencil, 0) - //du/dz - dw/dx
D1Vec<DiffScheme>::inX(stencil, 2),
D1Vec<DiffScheme>::inX(stencil, 1) - //dv/dx - du/dy
D1Vec<DiffScheme>::inY(stencil, 0) );
}
};
//@}
//@{
/// Compute the mean curvature in index space
template<DDScheme DiffScheme2, DScheme DiffScheme1>
struct ISMeanCurvature
{
/// @brief Random access version
/// @return @c true if the gradient is nonzero, in which case the mean curvature
/// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
/// in ∇ · (∇Φ / |∇Φ|) and @a beta is |∇Φ|.
template<typename Accessor>
static bool result(const Accessor& grid, const Coord& ijk,
typename Accessor::ValueType& alpha,
typename Accessor::ValueType& beta)
{
using ValueType = typename Accessor::ValueType;
const ValueType Dx = D1<DiffScheme1>::inX(grid, ijk);
const ValueType Dy = D1<DiffScheme1>::inY(grid, ijk);
const ValueType Dz = D1<DiffScheme1>::inZ(grid, ijk);
const ValueType Dx2 = Dx*Dx;
const ValueType Dy2 = Dy*Dy;
const ValueType Dz2 = Dz*Dz;
const ValueType normGrad = Dx2 + Dy2 + Dz2;
if (normGrad <= math::Tolerance<ValueType>::value()) {
alpha = beta = 0;
return false;
}
const ValueType Dxx = D2<DiffScheme2>::inX(grid, ijk);
const ValueType Dyy = D2<DiffScheme2>::inY(grid, ijk);
const ValueType Dzz = D2<DiffScheme2>::inZ(grid, ijk);
const ValueType Dxy = D2<DiffScheme2>::inXandY(grid, ijk);
const ValueType Dyz = D2<DiffScheme2>::inYandZ(grid, ijk);
const ValueType Dxz = D2<DiffScheme2>::inXandZ(grid, ijk);
// for return
alpha = (Dx2*(Dyy+Dzz)+Dy2*(Dxx+Dzz)+Dz2*(Dxx+Dyy)-2*(Dx*(Dy*Dxy+Dz*Dxz)+Dy*Dz*Dyz));
beta = ValueType(std::sqrt(double(normGrad))); // * 1/dx
return true;
}
/// @brief Stencil access version
/// @return @c true if the gradient is nonzero, in which case the mean curvature
/// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
/// in ∇ · (∇Φ / |∇Φ|) and @a beta is |∇Φ|.
template<typename StencilT>
static bool result(const StencilT& stencil,
typename StencilT::ValueType& alpha,
typename StencilT::ValueType& beta)
{
using ValueType = typename StencilT::ValueType;
const ValueType Dx = D1<DiffScheme1>::inX(stencil);
const ValueType Dy = D1<DiffScheme1>::inY(stencil);
const ValueType Dz = D1<DiffScheme1>::inZ(stencil);
const ValueType Dx2 = Dx*Dx;
const ValueType Dy2 = Dy*Dy;
const ValueType Dz2 = Dz*Dz;
const ValueType normGrad = Dx2 + Dy2 + Dz2;
if (normGrad <= math::Tolerance<ValueType>::value()) {
alpha = beta = 0;
return false;
}
const ValueType Dxx = D2<DiffScheme2>::inX(stencil);
const ValueType Dyy = D2<DiffScheme2>::inY(stencil);
const ValueType Dzz = D2<DiffScheme2>::inZ(stencil);
const ValueType Dxy = D2<DiffScheme2>::inXandY(stencil);
const ValueType Dyz = D2<DiffScheme2>::inYandZ(stencil);
const ValueType Dxz = D2<DiffScheme2>::inXandZ(stencil);
// for return
alpha = (Dx2*(Dyy+Dzz)+Dy2*(Dxx+Dzz)+Dz2*(Dxx+Dyy)-2*(Dx*(Dy*Dxy+Dz*Dxz)+Dy*Dz*Dyz));
beta = ValueType(std::sqrt(double(normGrad))); // * 1/dx
return true;
}
};
////////////////////////////////////////////////////////
// --- Operators defined in the Range of a given map
//@{
/// @brief Center difference gradient operators, defined with respect to
/// the range-space of the @c map
/// @note This will need to be divided by two in the case of CD_2NDT
template<typename MapType, DScheme DiffScheme>
struct Gradient
{
// random access version
template<typename Accessor>
static typename internal::ReturnValue<Accessor>::Vec3Type
result(const MapType& map, const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
Vec3d iGradient( ISGradient<DiffScheme>::result(grid, ijk) );
return Vec3Type(map.applyIJT(iGradient, ijk.asVec3d()));
}
// stencil access version
template<typename StencilT>
static typename internal::ReturnValue<StencilT>::Vec3Type
result(const MapType& map, const StencilT& stencil)
{
using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
Vec3d iGradient( ISGradient<DiffScheme>::result(stencil) );
return Vec3Type(map.applyIJT(iGradient, stencil.getCenterCoord().asVec3d()));
}
};
// Partial template specialization of Gradient
// translation, any order
template<DScheme DiffScheme>
struct Gradient<TranslationMap, DiffScheme>
{
// random access version
template<typename Accessor>
static typename internal::ReturnValue<Accessor>::Vec3Type
result(const TranslationMap&, const Accessor& grid, const Coord& ijk)
{
return ISGradient<DiffScheme>::result(grid, ijk);
}
// stencil access version
template<typename StencilT>
static typename internal::ReturnValue<StencilT>::Vec3Type
result(const TranslationMap&, const StencilT& stencil)
{
return ISGradient<DiffScheme>::result(stencil);
}
};
/// Full template specialization of Gradient
/// uniform scale, 2nd order
template<>
struct Gradient<UniformScaleMap, CD_2ND>
{
// random access version
template<typename Accessor>
static typename internal::ReturnValue<Accessor>::Vec3Type
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return iGradient * inv2dx;
}
// stencil access version
template<typename StencilT>
static typename internal::ReturnValue<StencilT>::Vec3Type
result(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return iGradient * inv2dx;
}
};
/// Full template specialization of Gradient
/// uniform scale translate, 2nd order
template<>
struct Gradient<UniformScaleTranslateMap, CD_2ND>
{
// random access version
template<typename Accessor>
static typename internal::ReturnValue<Accessor>::Vec3Type
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return iGradient * inv2dx;
}
// stencil access version
template<typename StencilT>
static typename internal::ReturnValue<StencilT>::Vec3Type
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return iGradient * inv2dx;
}
};
/// Full template specialization of Gradient
/// scale, 2nd order
template<>
struct Gradient<ScaleMap, CD_2ND>
{
// random access version
template<typename Accessor>
static typename internal::ReturnValue<Accessor>::Vec3Type
result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
return Vec3Type(ValueType(iGradient[0] * map.getInvTwiceScale()[0]),
ValueType(iGradient[1] * map.getInvTwiceScale()[1]),
ValueType(iGradient[2] * map.getInvTwiceScale()[2]) );
}
// stencil access version
template<typename StencilT>
static typename internal::ReturnValue<StencilT>::Vec3Type
result(const ScaleMap& map, const StencilT& stencil)
{
using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
return Vec3Type(ValueType(iGradient[0] * map.getInvTwiceScale()[0]),
ValueType(iGradient[1] * map.getInvTwiceScale()[1]),
ValueType(iGradient[2] * map.getInvTwiceScale()[2]) );
}
};
/// Full template specialization of Gradient
/// scale translate, 2nd order
template<>
struct Gradient<ScaleTranslateMap, CD_2ND>
{
// random access version
template<typename Accessor>
static typename internal::ReturnValue<Accessor>::Vec3Type
result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
return Vec3Type(ValueType(iGradient[0] * map.getInvTwiceScale()[0]),
ValueType(iGradient[1] * map.getInvTwiceScale()[1]),
ValueType(iGradient[2] * map.getInvTwiceScale()[2]) );
}
// Stencil access version
template<typename StencilT>
static typename internal::ReturnValue<StencilT>::Vec3Type
result(const ScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
return Vec3Type(ValueType(iGradient[0] * map.getInvTwiceScale()[0]),
ValueType(iGradient[1] * map.getInvTwiceScale()[1]),
ValueType(iGradient[2] * map.getInvTwiceScale()[2]) );
}
};
//@}
//@{
/// @brief Biased gradient operators, defined with respect to the range-space of the map
/// @note This will need to be divided by two in the case of CD_2NDT
template<typename MapType, BiasedGradientScheme GradScheme>
struct GradientBiased
{
// random access version
template<typename Accessor> static math::Vec3<typename Accessor::ValueType>
result(const MapType& map, const Accessor& grid, const Coord& ijk,
const Vec3<typename Accessor::ValueType>& V)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = math::Vec3<ValueType>;
Vec3d iGradient( ISGradientBiased<GradScheme, Vec3Type>::result(grid, ijk, V) );
return Vec3Type(map.applyIJT(iGradient, ijk.asVec3d()));
}
// stencil access version
template<typename StencilT> static math::Vec3<typename StencilT::ValueType>
result(const MapType& map, const StencilT& stencil,
const Vec3<typename StencilT::ValueType>& V)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = math::Vec3<ValueType>;
Vec3d iGradient( ISGradientBiased<GradScheme, Vec3Type>::result(stencil, V) );
return Vec3Type(map.applyIJT(iGradient, stencil.getCenterCoord().asVec3d()));
}
};
//@}
////////////////////////////////////////////////////////
// Computes |Grad[Phi]| using upwinding
template<typename MapType, BiasedGradientScheme GradScheme>
struct GradientNormSqrd
{
static const DScheme FD = BIAS_SCHEME<GradScheme>::FD;
static const DScheme BD = BIAS_SCHEME<GradScheme>::BD;
// random access version
template<typename Accessor>
static typename Accessor::ValueType
result(const MapType& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = math::Vec3<ValueType>;
Vec3Type up = Gradient<MapType, FD>::result(map, grid, ijk);
Vec3Type down = Gradient<MapType, BD>::result(map, grid, ijk);
return math::GodunovsNormSqrd(grid.getValue(ijk)>0, down, up);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType
result(const MapType& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = math::Vec3<ValueType>;
Vec3Type up = Gradient<MapType, FD>::result(map, stencil);
Vec3Type down = Gradient<MapType, BD>::result(map, stencil);
return math::GodunovsNormSqrd(stencil.template getValue<0, 0, 0>()>0, down, up);
}
};
/// Partial template specialization of GradientNormSqrd
template<BiasedGradientScheme GradScheme>
struct GradientNormSqrd<UniformScaleMap, GradScheme>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return invdxdx * ISGradientNormSqrd<GradScheme>::result(grid, ijk);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType
result(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return invdxdx * ISGradientNormSqrd<GradScheme>::result(stencil);
}
};
/// Partial template specialization of GradientNormSqrd
template<BiasedGradientScheme GradScheme>
struct GradientNormSqrd<UniformScaleTranslateMap, GradScheme>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return invdxdx * ISGradientNormSqrd<GradScheme>::result(grid, ijk);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return invdxdx * ISGradientNormSqrd<GradScheme>::result(stencil);
}
};
//@{
/// @brief Compute the divergence of a vector-valued grid using differencing
/// of various orders, the result defined with respect to the range-space of the map.
template<typename MapType, DScheme DiffScheme>
struct Divergence
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const MapType& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div(0);
for (int i=0; i < 3; i++) {
Vec3d vec( D1Vec<DiffScheme>::inX(grid, ijk, i),
D1Vec<DiffScheme>::inY(grid, ijk, i),
D1Vec<DiffScheme>::inZ(grid, ijk, i) );
div += ValueType(map.applyIJT(vec, ijk.asVec3d())[i]);
}
return div;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const MapType& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
for (int i=0; i < 3; i++) {
Vec3d vec( D1Vec<DiffScheme>::inX(stencil, i),
D1Vec<DiffScheme>::inY(stencil, i),
D1Vec<DiffScheme>::inZ(stencil, i) );
div += ValueType(map.applyIJT(vec, stencil.getCenterCoord().asVec3d())[i]);
}
return div;
}
};
/// Partial template specialization of Divergence
/// translation, any scheme
template<DScheme DiffScheme>
struct Divergence<TranslationMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const TranslationMap&, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div(0);
div =ISDivergence<DiffScheme>::result(grid, ijk);
return div;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const TranslationMap&, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div =ISDivergence<DiffScheme>::result(stencil);
return div;
}
};
/// Partial template specialization of Divergence
/// uniform scale, any scheme
template<DScheme DiffScheme>
struct Divergence<UniformScaleMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div(0);
div =ISDivergence<DiffScheme>::result(grid, ijk);
ValueType invdx = ValueType(map.getInvScale()[0]);
return div * invdx;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div =ISDivergence<DiffScheme>::result(stencil);
ValueType invdx = ValueType(map.getInvScale()[0]);
return div * invdx;
}
};
/// Partial template specialization of Divergence
/// uniform scale and translation, any scheme
template<DScheme DiffScheme>
struct Divergence<UniformScaleTranslateMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div(0);
div =ISDivergence<DiffScheme>::result(grid, ijk);
ValueType invdx = ValueType(map.getInvScale()[0]);
return div * invdx;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div =ISDivergence<DiffScheme>::result(stencil);
ValueType invdx = ValueType(map.getInvScale()[0]);
return div * invdx;
}
};
/// Full template specialization of Divergence
/// uniform scale 2nd order
template<>
struct Divergence<UniformScaleMap, CD_2ND>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div(0);
div =ISDivergence<CD_2NDT>::result(grid, ijk);
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return div * inv2dx;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div =ISDivergence<CD_2NDT>::result(stencil);
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return div * inv2dx;
}
};
/// Full template specialization of Divergence
/// uniform scale translate 2nd order
template<>
struct Divergence<UniformScaleTranslateMap, CD_2ND>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div(0);
div =ISDivergence<CD_2NDT>::result(grid, ijk);
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return div * inv2dx;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div =ISDivergence<CD_2NDT>::result(stencil);
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return div * inv2dx;
}
};
/// Partial template specialization of Divergence
/// scale, any scheme
template<DScheme DiffScheme>
struct Divergence<ScaleMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div = ValueType(
D1Vec<DiffScheme>::inX(grid, ijk, 0) * (map.getInvScale()[0]) +
D1Vec<DiffScheme>::inY(grid, ijk, 1) * (map.getInvScale()[1]) +
D1Vec<DiffScheme>::inZ(grid, ijk, 2) * (map.getInvScale()[2]));
return div;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const ScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div = ValueType(
D1Vec<DiffScheme>::inX(stencil, 0) * (map.getInvScale()[0]) +
D1Vec<DiffScheme>::inY(stencil, 1) * (map.getInvScale()[1]) +
D1Vec<DiffScheme>::inZ(stencil, 2) * (map.getInvScale()[2]) );
return div;
}
};
/// Partial template specialization of Divergence
/// scale translate, any scheme
template<DScheme DiffScheme>
struct Divergence<ScaleTranslateMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div = ValueType(
D1Vec<DiffScheme>::inX(grid, ijk, 0) * (map.getInvScale()[0]) +
D1Vec<DiffScheme>::inY(grid, ijk, 1) * (map.getInvScale()[1]) +
D1Vec<DiffScheme>::inZ(grid, ijk, 2) * (map.getInvScale()[2]));
return div;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const ScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div(0);
div = ValueType(
D1Vec<DiffScheme>::inX(stencil, 0) * (map.getInvScale()[0]) +
D1Vec<DiffScheme>::inY(stencil, 1) * (map.getInvScale()[1]) +
D1Vec<DiffScheme>::inZ(stencil, 2) * (map.getInvScale()[2]) );
return div;
}
};
/// Full template specialization Divergence
/// scale 2nd order
template<>
struct Divergence<ScaleMap, CD_2ND>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div = ValueType(
D1Vec<CD_2NDT>::inX(grid, ijk, 0) * (map.getInvTwiceScale()[0]) +
D1Vec<CD_2NDT>::inY(grid, ijk, 1) * (map.getInvTwiceScale()[1]) +
D1Vec<CD_2NDT>::inZ(grid, ijk, 2) * (map.getInvTwiceScale()[2]) );
return div;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const ScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div = ValueType(
D1Vec<CD_2NDT>::inX(stencil, 0) * (map.getInvTwiceScale()[0]) +
D1Vec<CD_2NDT>::inY(stencil, 1) * (map.getInvTwiceScale()[1]) +
D1Vec<CD_2NDT>::inZ(stencil, 2) * (map.getInvTwiceScale()[2]) );
return div;
}
};
/// Full template specialization of Divergence
/// scale and translate, 2nd order
template<>
struct Divergence<ScaleTranslateMap, CD_2ND>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType::value_type
result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType::value_type;
ValueType div = ValueType(
D1Vec<CD_2NDT>::inX(grid, ijk, 0) * (map.getInvTwiceScale()[0]) +
D1Vec<CD_2NDT>::inY(grid, ijk, 1) * (map.getInvTwiceScale()[1]) +
D1Vec<CD_2NDT>::inZ(grid, ijk, 2) * (map.getInvTwiceScale()[2]) );
return div;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType::value_type
result(const ScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType::value_type;
ValueType div = ValueType(
D1Vec<CD_2NDT>::inX(stencil, 0) * (map.getInvTwiceScale()[0]) +
D1Vec<CD_2NDT>::inY(stencil, 1) * (map.getInvTwiceScale()[1]) +
D1Vec<CD_2NDT>::inZ(stencil, 2) * (map.getInvTwiceScale()[2]) );
return div;
}
};
//@}
//@{
/// @brief Compute the curl of a vector-valued grid using differencing
/// of various orders in the space defined by the range of the map.
template<typename MapType, DScheme DiffScheme>
struct Curl
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const MapType& map, const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename Accessor::ValueType;
Vec3Type mat[3];
for (int i = 0; i < 3; i++) {
Vec3d vec(
D1Vec<DiffScheme>::inX(grid, ijk, i),
D1Vec<DiffScheme>::inY(grid, ijk, i),
D1Vec<DiffScheme>::inZ(grid, ijk, i));
// dF_i/dx_j (x_1 = x, x_2 = y, x_3 = z)
mat[i] = Vec3Type(map.applyIJT(vec, ijk.asVec3d()));
}
return Vec3Type(mat[2][1] - mat[1][2], // dF_3/dx_2 - dF_2/dx_3
mat[0][2] - mat[2][0], // dF_1/dx_3 - dF_3/dx_1
mat[1][0] - mat[0][1]); // dF_2/dx_1 - dF_1/dx_2
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const MapType& map, const StencilT& stencil)
{
using Vec3Type = typename StencilT::ValueType;
Vec3Type mat[3];
for (int i = 0; i < 3; i++) {
Vec3d vec(
D1Vec<DiffScheme>::inX(stencil, i),
D1Vec<DiffScheme>::inY(stencil, i),
D1Vec<DiffScheme>::inZ(stencil, i));
// dF_i/dx_j (x_1 = x, x_2 = y, x_3 = z)
mat[i] = Vec3Type(map.applyIJT(vec, stencil.getCenterCoord().asVec3d()));
}
return Vec3Type(mat[2][1] - mat[1][2], // dF_3/dx_2 - dF_2/dx_3
mat[0][2] - mat[2][0], // dF_1/dx_3 - dF_3/dx_1
mat[1][0] - mat[0][1]); // dF_2/dx_1 - dF_1/dx_2
}
};
/// Partial template specialization of Curl
template<DScheme DiffScheme>
struct Curl<UniformScaleMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename Accessor::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<DiffScheme>::result(grid, ijk) * ValueType(map.getInvScale()[0]);
}
// Stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleMap& map, const StencilT& stencil)
{
using Vec3Type = typename StencilT::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<DiffScheme>::result(stencil) * ValueType(map.getInvScale()[0]);
}
};
/// Partial template specialization of Curl
template<DScheme DiffScheme>
struct Curl<UniformScaleTranslateMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename Accessor::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<DiffScheme>::result(grid, ijk) * ValueType(map.getInvScale()[0]);
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using Vec3Type = typename StencilT::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<DiffScheme>::result(stencil) * ValueType(map.getInvScale()[0]);
}
};
/// Full template specialization of Curl
template<>
struct Curl<UniformScaleMap, CD_2ND>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename Accessor::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<CD_2NDT>::result(grid, ijk) * ValueType(map.getInvTwiceScale()[0]);
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleMap& map, const StencilT& stencil)
{
using Vec3Type = typename StencilT::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<CD_2NDT>::result(stencil) * ValueType(map.getInvTwiceScale()[0]);
}
};
/// Full template specialization of Curl
template<>
struct Curl<UniformScaleTranslateMap, CD_2ND>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using Vec3Type = typename Accessor::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<CD_2NDT>::result(grid, ijk) * ValueType(map.getInvTwiceScale()[0]);
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using Vec3Type = typename StencilT::ValueType;
using ValueType = typename Vec3Type::value_type;
return ISCurl<CD_2NDT>::result(stencil) * ValueType(map.getInvTwiceScale()[0]);
}
};
//@}
//@{
/// @brief Compute the Laplacian at a given location in a grid using finite differencing
/// of various orders. The result is defined in the range of the map.
template<typename MapType, DDScheme DiffScheme>
struct Laplacian
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const MapType& map,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
// all the second derivatives in index space
ValueType iddx = D2<DiffScheme>::inX(grid, ijk);
ValueType iddy = D2<DiffScheme>::inY(grid, ijk);
ValueType iddz = D2<DiffScheme>::inZ(grid, ijk);
ValueType iddxy = D2<DiffScheme>::inXandY(grid, ijk);
ValueType iddyz = D2<DiffScheme>::inYandZ(grid, ijk);
ValueType iddxz = D2<DiffScheme>::inXandZ(grid, ijk);
// second derivatives in index space
Mat3d d2_is(iddx, iddxy, iddxz,
iddxy, iddy, iddyz,
iddxz, iddyz, iddz);
Mat3d d2_rs; // to hold the second derivative matrix in range space
if (is_linear<MapType>::value) {
d2_rs = map.applyIJC(d2_is);
} else {
// compute the first derivatives with 2nd order accuracy.
Vec3d d1_is(static_cast<double>(D1<CD_2ND>::inX(grid, ijk)),
static_cast<double>(D1<CD_2ND>::inY(grid, ijk)),
static_cast<double>(D1<CD_2ND>::inZ(grid, ijk)));
d2_rs = map.applyIJC(d2_is, d1_is, ijk.asVec3d());
}
// the trace of the second derivative (range space) matrix is laplacian
return ValueType(d2_rs(0,0) + d2_rs(1,1) + d2_rs(2,2));
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const MapType& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
// all the second derivatives in index space
ValueType iddx = D2<DiffScheme>::inX(stencil);
ValueType iddy = D2<DiffScheme>::inY(stencil);
ValueType iddz = D2<DiffScheme>::inZ(stencil);
ValueType iddxy = D2<DiffScheme>::inXandY(stencil);
ValueType iddyz = D2<DiffScheme>::inYandZ(stencil);
ValueType iddxz = D2<DiffScheme>::inXandZ(stencil);
// second derivatives in index space
Mat3d d2_is(iddx, iddxy, iddxz,
iddxy, iddy, iddyz,
iddxz, iddyz, iddz);
Mat3d d2_rs; // to hold the second derivative matrix in range space
if (is_linear<MapType>::value) {
d2_rs = map.applyIJC(d2_is);
} else {
// compute the first derivatives with 2nd order accuracy.
Vec3d d1_is(D1<CD_2ND>::inX(stencil),
D1<CD_2ND>::inY(stencil),
D1<CD_2ND>::inZ(stencil) );
d2_rs = map.applyIJC(d2_is, d1_is, stencil.getCenterCoord().asVec3d());
}
// the trace of the second derivative (range space) matrix is laplacian
return ValueType(d2_rs(0,0) + d2_rs(1,1) + d2_rs(2,2));
}
};
template<DDScheme DiffScheme>
struct Laplacian<TranslationMap, DiffScheme>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const TranslationMap&,
const Accessor& grid, const Coord& ijk)
{
return ISLaplacian<DiffScheme>::result(grid, ijk);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const TranslationMap&, const StencilT& stencil)
{
return ISLaplacian<DiffScheme>::result(stencil);
}
};
// The Laplacian is invariant to rotation or reflection.
template<DDScheme DiffScheme>
struct Laplacian<UnitaryMap, DiffScheme>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const UnitaryMap&,
const Accessor& grid, const Coord& ijk)
{
return ISLaplacian<DiffScheme>::result(grid, ijk);
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const UnitaryMap&, const StencilT& stencil)
{
return ISLaplacian<DiffScheme>::result(stencil);
}
};
template<DDScheme DiffScheme>
struct Laplacian<UniformScaleMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ISLaplacian<DiffScheme>::result(grid, ijk) * invdxdx;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ISLaplacian<DiffScheme>::result(stencil) * invdxdx;
}
};
template<DDScheme DiffScheme>
struct Laplacian<UniformScaleTranslateMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ISLaplacian<DiffScheme>::result(grid, ijk) * invdxdx;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ISLaplacian<DiffScheme>::result(stencil) * invdxdx;
}
};
template<DDScheme DiffScheme>
struct Laplacian<ScaleMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
// compute the second derivatives in index space
ValueType iddx = D2<DiffScheme>::inX(grid, ijk);
ValueType iddy = D2<DiffScheme>::inY(grid, ijk);
ValueType iddz = D2<DiffScheme>::inZ(grid, ijk);
const Vec3d& invScaleSqr = map.getInvScaleSqr();
// scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
return ValueType(iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2]);
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const ScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
// compute the second derivatives in index space
ValueType iddx = D2<DiffScheme>::inX(stencil);
ValueType iddy = D2<DiffScheme>::inY(stencil);
ValueType iddz = D2<DiffScheme>::inZ(stencil);
const Vec3d& invScaleSqr = map.getInvScaleSqr();
// scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
return ValueType(iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2]);
}
};
template<DDScheme DiffScheme>
struct Laplacian<ScaleTranslateMap, DiffScheme>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
// compute the second derivatives in index space
ValueType iddx = D2<DiffScheme>::inX(grid, ijk);
ValueType iddy = D2<DiffScheme>::inY(grid, ijk);
ValueType iddz = D2<DiffScheme>::inZ(grid, ijk);
const Vec3d& invScaleSqr = map.getInvScaleSqr();
// scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
return ValueType(iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2]);
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const ScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
// compute the second derivatives in index space
ValueType iddx = D2<DiffScheme>::inX(stencil);
ValueType iddy = D2<DiffScheme>::inY(stencil);
ValueType iddz = D2<DiffScheme>::inZ(stencil);
const Vec3d& invScaleSqr = map.getInvScaleSqr();
// scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
return ValueType(iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2]);
}
};
/// @brief Compute the closest-point transform to a level set.
/// @return the closest point to the surface from which the level set was derived,
/// in the domain space of the map (e.g., voxel space).
template<typename MapType, DScheme DiffScheme>
struct CPT
{
// random access version
template<typename Accessor> static math::Vec3<typename Accessor::ValueType>
result(const MapType& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = Vec3<ValueType>;
// current distance
ValueType d = grid.getValue(ijk);
// compute gradient in physical space where it is a unit normal
// since the grid holds a distance level set.
Vec3d vectorFromSurface(d*Gradient<MapType,DiffScheme>::result(map, grid, ijk));
if (is_linear<MapType>::value) {
Vec3d result = ijk.asVec3d() - map.applyInverseMap(vectorFromSurface);
return Vec3Type(result);
} else {
Vec3d location = map.applyMap(ijk.asVec3d());
Vec3d result = map.applyInverseMap(location - vectorFromSurface);
return Vec3Type(result);
}
}
// stencil access version
template<typename StencilT> static math::Vec3<typename StencilT::ValueType>
result(const MapType& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = Vec3<ValueType>;
// current distance
ValueType d = stencil.template getValue<0, 0, 0>();
// compute gradient in physical space where it is a unit normal
// since the grid holds a distance level set.
Vec3d vectorFromSurface(d*Gradient<MapType, DiffScheme>::result(map, stencil));
if (is_linear<MapType>::value) {
Vec3d result = stencil.getCenterCoord().asVec3d()
- map.applyInverseMap(vectorFromSurface);
return Vec3Type(result);
} else {
Vec3d location = map.applyMap(stencil.getCenterCoord().asVec3d());
Vec3d result = map.applyInverseMap(location - vectorFromSurface);
return Vec3Type(result);
}
}
};
/// @brief Compute the closest-point transform to a level set.
/// @return the closest point to the surface from which the level set was derived,
/// in the range space of the map (e.g., in world space)
template<typename MapType, DScheme DiffScheme>
struct CPT_RANGE
{
// random access version
template<typename Accessor> static Vec3<typename Accessor::ValueType>
result(const MapType& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
using Vec3Type = Vec3<ValueType>;
// current distance
ValueType d = grid.getValue(ijk);
// compute gradient in physical space where it is a unit normal
// since the grid holds a distance level set.
Vec3Type vectorFromSurface =
d*Gradient<MapType,DiffScheme>::result(map, grid, ijk);
Vec3d result = map.applyMap(ijk.asVec3d()) - vectorFromSurface;
return Vec3Type(result);
}
// stencil access version
template<typename StencilT> static Vec3<typename StencilT::ValueType>
result(const MapType& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
using Vec3Type = Vec3<ValueType>;
// current distance
ValueType d = stencil.template getValue<0, 0, 0>();
// compute gradient in physical space where it is a unit normal
// since the grid holds a distance level set.
Vec3Type vectorFromSurface =
d*Gradient<MapType, DiffScheme>::result(map, stencil);
Vec3d result = map.applyMap(stencil.getCenterCoord().asVec3d()) - vectorFromSurface;
return Vec3Type(result);
}
};
/// @brief Compute the mean curvature.
/// @details The mean curvature is returned in two parts, @a alpha and @a beta,
/// where @a alpha is the numerator in ∇ · (∇Φ / |∇Φ|)
/// and @a beta is |∇Φ|.
template<typename MapType, DDScheme DiffScheme2, DScheme DiffScheme1>
struct MeanCurvature
{
/// @brief Random access version
/// @return @c true if the gradient is nonzero, in which case the mean curvature
/// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
/// in ∇ · (∇Φ / |∇Φ|) and @a beta is |∇Φ|.
template<typename Accessor>
static bool compute(const MapType& map, const Accessor& grid, const Coord& ijk,
double& alpha, double& beta)
{
using ValueType = typename Accessor::ValueType;
// compute the gradient in index and world space
Vec3d d1_is(static_cast<double>(D1<DiffScheme1>::inX(grid, ijk)),
static_cast<double>(D1<DiffScheme1>::inY(grid, ijk)),
static_cast<double>(D1<DiffScheme1>::inZ(grid, ijk))), d1_ws;
if (is_linear<MapType>::value) {//resolved at compiletime
d1_ws = map.applyIJT(d1_is);
} else {
d1_ws = map.applyIJT(d1_is, ijk.asVec3d());
}
const double Dx2 = d1_ws(0)*d1_ws(0);
const double Dy2 = d1_ws(1)*d1_ws(1);
const double Dz2 = d1_ws(2)*d1_ws(2);
const double normGrad = Dx2 + Dy2 + Dz2;
if (normGrad <= math::Tolerance<double>::value()) {
alpha = beta = 0;
return false;
}
// all the second derivatives in index space
ValueType iddx = D2<DiffScheme2>::inX(grid, ijk);
ValueType iddy = D2<DiffScheme2>::inY(grid, ijk);
ValueType iddz = D2<DiffScheme2>::inZ(grid, ijk);
ValueType iddxy = D2<DiffScheme2>::inXandY(grid, ijk);
ValueType iddyz = D2<DiffScheme2>::inYandZ(grid, ijk);
ValueType iddxz = D2<DiffScheme2>::inXandZ(grid, ijk);
// second derivatives in index space
Mat3d d2_is(iddx, iddxy, iddxz,
iddxy, iddy, iddyz,
iddxz, iddyz, iddz);
// convert second derivatives to world space
Mat3d d2_ws;
if (is_linear<MapType>::value) {//resolved at compiletime
d2_ws = map.applyIJC(d2_is);
} else {
d2_ws = map.applyIJC(d2_is, d1_is, ijk.asVec3d());
}
// assemble the nominator and denominator for mean curvature
alpha = (Dx2*(d2_ws(1,1)+d2_ws(2,2))+Dy2*(d2_ws(0,0)+d2_ws(2,2))
+Dz2*(d2_ws(0,0)+d2_ws(1,1))
-2*(d1_ws(0)*(d1_ws(1)*d2_ws(0,1)+d1_ws(2)*d2_ws(0,2))
+d1_ws(1)*d1_ws(2)*d2_ws(1,2)));
beta = std::sqrt(normGrad); // * 1/dx
return true;
}
template<typename Accessor>
static typename Accessor::ValueType result(const MapType& map,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
double alpha, beta;
return compute(map, grid, ijk, alpha, beta) ?
ValueType(alpha/(2. *math::Pow3(beta))) : 0;
}
template<typename Accessor>
static typename Accessor::ValueType normGrad(const MapType& map,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
double alpha, beta;
return compute(map, grid, ijk, alpha, beta) ?
ValueType(alpha/(2. *math::Pow2(beta))) : 0;
}
/// @brief Stencil access version
/// @return @c true if the gradient is nonzero, in which case the mean curvature
/// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
/// in ∇ · (∇Φ / |∇Φ|) and @a beta is |∇Φ|.
template<typename StencilT>
static bool compute(const MapType& map, const StencilT& stencil,
double& alpha, double& beta)
{
using ValueType = typename StencilT::ValueType;
// compute the gradient in index and world space
Vec3d d1_is(D1<DiffScheme1>::inX(stencil),
D1<DiffScheme1>::inY(stencil),
D1<DiffScheme1>::inZ(stencil) ), d1_ws;
if (is_linear<MapType>::value) {//resolved at compiletime
d1_ws = map.applyIJT(d1_is);
} else {
d1_ws = map.applyIJT(d1_is, stencil.getCenterCoord().asVec3d());
}
const double Dx2 = d1_ws(0)*d1_ws(0);
const double Dy2 = d1_ws(1)*d1_ws(1);
const double Dz2 = d1_ws(2)*d1_ws(2);
const double normGrad = Dx2 + Dy2 + Dz2;
if (normGrad <= math::Tolerance<double>::value()) {
alpha = beta = 0;
return false;
}
// all the second derivatives in index space
ValueType iddx = D2<DiffScheme2>::inX(stencil);
ValueType iddy = D2<DiffScheme2>::inY(stencil);
ValueType iddz = D2<DiffScheme2>::inZ(stencil);
ValueType iddxy = D2<DiffScheme2>::inXandY(stencil);
ValueType iddyz = D2<DiffScheme2>::inYandZ(stencil);
ValueType iddxz = D2<DiffScheme2>::inXandZ(stencil);
// second derivatives in index space
Mat3d d2_is(iddx, iddxy, iddxz,
iddxy, iddy, iddyz,
iddxz, iddyz, iddz);
// convert second derivatives to world space
Mat3d d2_ws;
if (is_linear<MapType>::value) {//resolved at compiletime
d2_ws = map.applyIJC(d2_is);
} else {
d2_ws = map.applyIJC(d2_is, d1_is, stencil.getCenterCoord().asVec3d());
}
// for return
alpha = (Dx2*(d2_ws(1,1)+d2_ws(2,2))+Dy2*(d2_ws(0,0)+d2_ws(2,2))
+Dz2*(d2_ws(0,0)+d2_ws(1,1))
-2*(d1_ws(0)*(d1_ws(1)*d2_ws(0,1)+d1_ws(2)*d2_ws(0,2))
+d1_ws(1)*d1_ws(2)*d2_ws(1,2)));
beta = std::sqrt(normGrad); // * 1/dx
return true;
}
template<typename StencilT>
static typename StencilT::ValueType
result(const MapType& map, const StencilT stencil)
{
using ValueType = typename StencilT::ValueType;
double alpha, beta;
return compute(map, stencil, alpha, beta) ?
ValueType(alpha/(2*math::Pow3(beta))) : 0;
}
template<typename StencilT>
static typename StencilT::ValueType normGrad(const MapType& map, const StencilT stencil)
{
using ValueType = typename StencilT::ValueType;
double alpha, beta;
return compute(map, stencil, alpha, beta) ?
ValueType(alpha/(2*math::Pow2(beta))) : 0;
}
};
template<DDScheme DiffScheme2, DScheme DiffScheme1>
struct MeanCurvature<TranslationMap, DiffScheme2, DiffScheme1>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const TranslationMap&,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType alpha, beta;
return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta) ?
ValueType(alpha /(2*math::Pow3(beta))) : 0;
}
template<typename Accessor>
static typename Accessor::ValueType normGrad(const TranslationMap&,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType alpha, beta;
return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta) ?
ValueType(alpha/(2*math::Pow2(beta))) : 0;
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const TranslationMap&, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType alpha, beta;
return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta) ?
ValueType(alpha /(2*math::Pow3(beta))) : 0;
}
template<typename StencilT>
static typename StencilT::ValueType normGrad(const TranslationMap&, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType alpha, beta;
return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta) ?
ValueType(alpha/(2*math::Pow2(beta))) : 0;
}
};
template<DDScheme DiffScheme2, DScheme DiffScheme1>
struct MeanCurvature<UniformScaleMap, DiffScheme2, DiffScheme1>
{
// random access version
template<typename Accessor>
static typename Accessor::ValueType result(const UniformScaleMap& map,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return ValueType(alpha*inv2dx/math::Pow3(beta));
}
return 0;
}
template<typename Accessor>
static typename Accessor::ValueType normGrad(const UniformScaleMap& map,
const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
}
return 0;
}
// stencil access version
template<typename StencilT>
static typename StencilT::ValueType result(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return ValueType(alpha*inv2dx/math::Pow3(beta));
}
return 0;
}
template<typename StencilT>
static typename StencilT::ValueType normGrad(const UniformScaleMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
}
return 0;
}
};
template<DDScheme DiffScheme2, DScheme DiffScheme1>
struct MeanCurvature<UniformScaleTranslateMap, DiffScheme2, DiffScheme1>
{
// random access version
template<typename Accessor> static typename Accessor::ValueType
result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return ValueType(alpha*inv2dx/math::Pow3(beta));
}
return 0;
}
template<typename Accessor> static typename Accessor::ValueType
normGrad(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
{
using ValueType = typename Accessor::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
}
return 0;
}
// stencil access version
template<typename StencilT> static typename StencilT::ValueType
result(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
return ValueType(alpha*inv2dx/math::Pow3(beta));
}
return 0;
}
template<typename StencilT> static typename StencilT::ValueType
normGrad(const UniformScaleTranslateMap& map, const StencilT& stencil)
{
using ValueType = typename StencilT::ValueType;
ValueType alpha, beta;
if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
}
return 0;
}
};
/// @brief A wrapper that holds a MapBase::ConstPtr and exposes a reduced set
/// of functionality needed by the mathematical operators
/// @details This may be used in some <tt>Map</tt>-templated code, when the overhead of
/// actually resolving the @c Map type is large compared to the map work to be done.
class GenericMap
{
public:
template<typename GridType>
GenericMap(const GridType& g): mMap(g.transform().baseMap()) {}
GenericMap(const Transform& t): mMap(t.baseMap()) {}
GenericMap(MapBase::Ptr map): mMap(ConstPtrCast<const MapBase>(map)) {}
GenericMap(MapBase::ConstPtr map): mMap(map) {}
~GenericMap() {}
Vec3d applyMap(const Vec3d& in) const { return mMap->applyMap(in); }
Vec3d applyInverseMap(const Vec3d& in) const { return mMap->applyInverseMap(in); }
Vec3d applyIJT(const Vec3d& in) const { return mMap->applyIJT(in); }
Vec3d applyIJT(const Vec3d& in, const Vec3d& pos) const { return mMap->applyIJT(in, pos); }
Mat3d applyIJC(const Mat3d& m) const { return mMap->applyIJC(m); }
Mat3d applyIJC(const Mat3d& m, const Vec3d& v, const Vec3d& pos) const
{ return mMap->applyIJC(m,v,pos); }
double determinant() const { return mMap->determinant(); }
double determinant(const Vec3d& in) const { return mMap->determinant(in); }
Vec3d voxelSize() const { return mMap->voxelSize(); }
Vec3d voxelSize(const Vec3d&v) const { return mMap->voxelSize(v); }
private:
MapBase::ConstPtr mMap;
};
} // end math namespace
} // namespace OPENVDB_VERSION_NAME
} // end openvdb namespace
#endif // OPENVDB_MATH_OPERATORS_HAS_BEEN_INCLUDED
// Copyright (c) 2012-2017 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
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