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Stencils.h
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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: MPL-2.0
//
/// @author Ken Museth
///
/// @date April 9, 2021
///
/// @file Stencils.h
///
/// @brief Defines various finite-difference stencils that allow for the
/// computation of gradients of order 1 to 5, mean curvatures,
/// gaussian curvatures, principal curvatures, tri-linear interpolation,
/// zero-crossing, laplacian, and closest point transform.
#ifndef NANOVDB_STENCILS_HAS_BEEN_INCLUDED
#define NANOVDB_STENCILS_HAS_BEEN_INCLUDED
#include "../NanoVDB.h"// for __hosedev__, Vec3, Min, Max, Pow2, Pow3, Pow4
namespace nanovdb {
// ---------------------------- WENO5 ----------------------------
/// @brief Implementation of nominally fifth-order finite-difference WENO
/// @details This function returns the numerical flux. See "High Order Finite Difference and
/// Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD" - Chi-Wang Shu
/// ICASE Report No 2001-11 (page 6). Also see ICASE No 97-65 for a more complete reference
/// (Shu, 1997).
/// Given v1 = f(x-2dx), v2 = f(x-dx), v3 = f(x), v4 = f(x+dx) and v5 = f(x+2dx),
/// return an interpolated value f(x+dx/2) with the special property that
/// ( f(x+dx/2) - f(x-dx/2) ) / dx = df/dx (x) + error,
/// where the error is fifth-order in smooth regions: O(dx) <= error <=O(dx^5)
template<typename ValueType, typename RealT = ValueType>
__hostdev__ inline ValueType
WENO5(const ValueType& v1,
const ValueType& v2,
const ValueType& v3,
const ValueType& v4,
const ValueType& v5,
RealT scale2 = 1.0)// openvdb uses scale2 = 0.01
{
static const RealT C = 13.0 / 12.0;
// WENO is formulated for non-dimensional equations, here the optional scale2
// is a reference value (squared) for the function being interpolated. For
// example if 'v' is of order 1000, then scale2 = 10^6 is ok. But in practice
// leave scale2 = 1.
const RealT eps = RealT(1.0e-6) * scale2;
// {\tilde \omega_k} = \gamma_k / ( \beta_k + \epsilon)^2 in Shu's ICASE report)
const RealT A1 = RealT(0.1)/Pow2(C*Pow2(v1-2*v2+v3)+RealT(0.25)*Pow2(v1-4*v2+3*v3)+eps),
A2 = RealT(0.6)/Pow2(C*Pow2(v2-2*v3+v4)+RealT(0.25)*Pow2(v2-v4)+eps),
A3 = RealT(0.3)/Pow2(C*Pow2(v3-2*v4+v5)+RealT(0.25)*Pow2(3*v3-4*v4+v5)+eps);
return static_cast<ValueType>((A1*(2*v1 - 7*v2 + 11*v3) +
A2*(5*v3 - v2 + 2*v4) +
A3*(2*v3 + 5*v4 - v5))/(6*(A1+A2+A3)));
}
// ---------------------------- GodunovsNormSqrd ----------------------------
template <typename RealT>
__hostdev__ inline RealT
GodunovsNormSqrd(bool isOutside,
RealT dP_xm, RealT dP_xp,
RealT dP_ym, RealT dP_yp,
RealT dP_zm, RealT dP_zp)
{
RealT dPLen2;
if (isOutside) { // outside
dPLen2 = Max(Pow2(Max(dP_xm, RealT(0))), Pow2(Min(dP_xp, RealT(0)))); // (dP/dx)2
dPLen2 += Max(Pow2(Max(dP_ym, RealT(0))), Pow2(Min(dP_yp, RealT(0)))); // (dP/dy)2
dPLen2 += Max(Pow2(Max(dP_zm, RealT(0))), Pow2(Min(dP_zp, RealT(0)))); // (dP/dz)2
} else { // inside
dPLen2 = Max(Pow2(Min(dP_xm, RealT(0))), Pow2(Max(dP_xp, RealT(0)))); // (dP/dx)2
dPLen2 += Max(Pow2(Min(dP_ym, RealT(0))), Pow2(Max(dP_yp, RealT(0)))); // (dP/dy)2
dPLen2 += Max(Pow2(Min(dP_zm, RealT(0))), Pow2(Max(dP_zp, RealT(0)))); // (dP/dz)2
}
return dPLen2; // |\nabla\phi|^2
}
template<typename RealT>
__hostdev__ inline RealT
GodunovsNormSqrd(bool isOutside,
const Vec3<RealT>& gradient_m,
const Vec3<RealT>& gradient_p)
{
return GodunovsNormSqrd<RealT>(isOutside,
gradient_m[0], gradient_p[0],
gradient_m[1], gradient_p[1],
gradient_m[2], gradient_p[2]);
}
// ---------------------------- BaseStencil ----------------------------
// BaseStencil uses curiously recurring template pattern (CRTP)
template<typename DerivedType, int SIZE, typename GridT>
class BaseStencil
{
public:
using ValueType = typename GridT::ValueType;
using GridType = GridT;
using TreeType = typename GridT::TreeType;
using AccessorType = typename GridT::AccessorType;// ReadAccessor<ValueType>;
/// @brief Initialize the stencil buffer with the values of voxel (i, j, k)
/// and its neighbors.
/// @param ijk Index coordinates of stencil center
__hostdev__ inline void moveTo(const Coord& ijk)
{
mCenter = ijk;
mValues[0] = mAcc.getValue(ijk);
static_cast<DerivedType&>(*this).init(mCenter);
}
/// @brief Initialize the stencil buffer with the values of voxel (i, j, k)
/// and its neighbors. The method also takes a value of the center
/// element of the stencil, assuming it is already known.
/// @param ijk Index coordinates of stencil center
/// @param centerValue Value of the center element of the stencil
__hostdev__ inline void moveTo(const Coord& ijk, const ValueType& centerValue)
{
mCenter = ijk;
mValues[0] = centerValue;
static_cast<DerivedType&>(*this).init(mCenter);
}
/// @brief Initialize the stencil buffer with the values of voxel
/// (x, y, z) and its neighbors.
///
/// @note This version is slightly faster than the one above, since
/// the center voxel's value is read directly from the iterator.
template<typename IterType>
__hostdev__ inline void moveTo(const IterType& iter)
{
mCenter = iter.getCoord();
mValues[0] = *iter;
static_cast<DerivedType&>(*this).init(mCenter);
}
/// @brief Initialize the stencil buffer with the values of voxel (x, y, z)
/// and its neighbors.
/// @param xyz Floating point voxel coordinates of stencil center
/// @details This method will check to see if it is necessary to
/// update the stencil based on the cached index coordinates of
/// the center point.
template<typename RealType>
__hostdev__ inline void moveTo(const Vec3<RealType>& xyz)
{
Coord ijk = RoundDown(xyz);
if (ijk != mCenter) this->moveTo(ijk);
}
/// @brief Return the value from the stencil buffer with linear
/// offset pos.
///
/// @note The default (@a pos = 0) corresponds to the first element
/// which is typically the center point of the stencil.
__hostdev__ inline const ValueType& getValue(unsigned int pos = 0) const
{
NANOVDB_ASSERT(pos < SIZE);
return mValues[pos];
}
/// @brief Return the value at the specified location relative to the center of the stencil
template<int i, int j, int k>
__hostdev__ inline const ValueType& getValue() const
{
return mValues[static_cast<const DerivedType&>(*this).template pos<i,j,k>()];
}
/// @brief Set the value at the specified location relative to the center of the stencil
template<int i, int j, int k>
__hostdev__ inline void setValue(const ValueType& value)
{
mValues[static_cast<const DerivedType&>(*this).template pos<i,j,k>()] = value;
}
/// @brief Return the size of the stencil buffer.
__hostdev__ static int size() { return SIZE; }
/// @brief Return the mean value of the current stencil.
__hostdev__ inline ValueType mean() const
{
ValueType sum = 0.0;
for (int i = 0; i < SIZE; ++i) sum += mValues[i];
return sum / ValueType(SIZE);
}
/// @brief Return the smallest value in the stencil buffer.
__hostdev__ inline ValueType min() const
{
ValueType v = mValues[0];
for (int i=1; i<SIZE; ++i) {
if (mValues[i] < v) v = mValues[i];
}
return v;
}
/// @brief Return the largest value in the stencil buffer.
__hostdev__ inline ValueType max() const
{
ValueType v = mValues[0];
for (int i=1; i<SIZE; ++i) {
if (mValues[i] > v) v = mValues[i];
}
return v;
}
/// @brief Return the coordinates of the center point of the stencil.
__hostdev__ inline const Coord& getCenterCoord() const { return mCenter; }
/// @brief Return the value at the center of the stencil
__hostdev__ inline const ValueType& getCenterValue() const { return mValues[0]; }
/// @brief Return true if the center of the stencil intersects the
/// iso-contour specified by the isoValue
__hostdev__ inline bool intersects(const ValueType &isoValue = ValueType(0) ) const
{
const bool less = this->getValue< 0, 0, 0>() < isoValue;
return (less ^ (this->getValue<-1, 0, 0>() < isoValue)) ||
(less ^ (this->getValue< 1, 0, 0>() < isoValue)) ||
(less ^ (this->getValue< 0,-1, 0>() < isoValue)) ||
(less ^ (this->getValue< 0, 1, 0>() < isoValue)) ||
(less ^ (this->getValue< 0, 0,-1>() < isoValue)) ||
(less ^ (this->getValue< 0, 0, 1>() < isoValue)) ;
}
struct Mask {
uint8_t bits;
__hostdev__ Mask() : bits(0u) {}
__hostdev__ void set(int i) { bits |= (1 << i); }
__hostdev__ bool test(int i) const { return bits & (1 << i); }
__hostdev__ bool any() const { return bits > 0u; }
__hostdev__ bool all() const { return bits == 255u; }
__hostdev__ bool none() const { return bits == 0u; }
__hostdev__ int count() const { return CountOn(bits); }
};// Mask
/// @brief Return true a bit-mask where the 6 lower bits indicates if the
/// center of the stencil intersects the iso-contour specified by the isoValue.
///
/// @note There are 2^6 = 64 different possible cases, including no intersections!
///
/// @details The ordering of bit mask is ( -x, +x, -y, +y, -z, +z ), so to
/// check if there is an intersection in -y use (mask & (1u<<2)) where mask is
/// ther return value from this function. To check if there are any
/// intersections use mask!=0u, and for no intersections use mask==0u.
/// To count the number of intersections use __builtin_popcount(mask).
__hostdev__ inline Mask intersectionMask(ValueType isoValue = ValueType(0)) const
{
Mask mask;
const bool less = this->getValue< 0, 0, 0>() < isoValue;
if (less ^ (this->getValue<-1, 0, 0>() < isoValue)) mask.set(0);// |= 1u;
if (less ^ (this->getValue< 1, 0, 0>() < isoValue)) mask.set(1);// |= 2u;
if (less ^ (this->getValue< 0,-1, 0>() < isoValue)) mask.set(2);// |= 4u;
if (less ^ (this->getValue< 0, 1, 0>() < isoValue)) mask.set(3);// |= 8u;
if (less ^ (this->getValue< 0, 0,-1>() < isoValue)) mask.set(4);// |= 16u;
if (less ^ (this->getValue< 0, 0, 1>() < isoValue)) mask.set(5);// |= 32u;
return mask;
}
/// @brief Return a const reference to the grid from which this
/// stencil was constructed.
__hostdev__ inline const GridType& grid() const { return *mGrid; }
/// @brief Return a const reference to the ValueAccessor
/// associated with this Stencil.
__hostdev__ inline const AccessorType& accessor() const { return mAcc; }
protected:
// Constructor is protected to prevent direct instantiation.
__hostdev__ BaseStencil(const GridType& grid)
: mGrid(&grid)
, mAcc(grid)
, mCenter(Coord::max())
{
}
const GridType* mGrid;
AccessorType mAcc;
ValueType mValues[SIZE];
Coord mCenter;
}; // BaseStencil class
// ---------------------------- BoxStencil ----------------------------
namespace { // anonymous namespace for stencil-layout map
// the eight point box stencil
template<int i, int j, int k> struct BoxPt {};
template<> struct BoxPt< 0, 0, 0> { enum { idx = 0 }; };
template<> struct BoxPt< 0, 0, 1> { enum { idx = 1 }; };
template<> struct BoxPt< 0, 1, 1> { enum { idx = 2 }; };
template<> struct BoxPt< 0, 1, 0> { enum { idx = 3 }; };
template<> struct BoxPt< 1, 0, 0> { enum { idx = 4 }; };
template<> struct BoxPt< 1, 0, 1> { enum { idx = 5 }; };
template<> struct BoxPt< 1, 1, 1> { enum { idx = 6 }; };
template<> struct BoxPt< 1, 1, 0> { enum { idx = 7 }; };
}
template<typename GridT>
class BoxStencil: public BaseStencil<BoxStencil<GridT>, 8, GridT>
{
using SelfT = BoxStencil<GridT>;
using BaseType = BaseStencil<SelfT, 8, GridT>;
public:
using GridType = GridT;
using TreeType = typename GridT::TreeType;
using ValueType = typename GridT::ValueType;
static constexpr int SIZE = 8;
__hostdev__ BoxStencil(const GridType& grid) : BaseType(grid) {}
/// Return linear offset for the specified stencil point relative to its center
template<int i, int j, int k>
__hostdev__ unsigned int pos() const { return BoxPt<i,j,k>::idx; }
/// @brief Return true if the center of the stencil intersects the
/// iso-contour specified by the isoValue
__hostdev__ inline bool intersects(ValueType isoValue = ValueType(0)) const
{
const bool less = mValues[0] < isoValue;
return (less ^ (mValues[1] < isoValue)) ||
(less ^ (mValues[2] < isoValue)) ||
(less ^ (mValues[3] < isoValue)) ||
(less ^ (mValues[4] < isoValue)) ||
(less ^ (mValues[5] < isoValue)) ||
(less ^ (mValues[6] < isoValue)) ||
(less ^ (mValues[7] < isoValue)) ;
}
/// @brief Return the trilinear interpolation at the normalized position.
/// @param xyz Floating point coordinate position. Index space and NOT world space.
/// @warning It is assumed that the stencil has already been moved
/// to the relevant voxel position, e.g. using moveTo(xyz).
/// @note Trilinear interpolation kernal reads as:
/// v000 (1-u)(1-v)(1-w) + v001 (1-u)(1-v)w + v010 (1-u)v(1-w) + v011 (1-u)vw
/// + v100 u(1-v)(1-w) + v101 u(1-v)w + v110 uv(1-w) + v111 uvw
__hostdev__ inline ValueType interpolation(const Vec3<ValueType>& xyz) const
{
const ValueType u = xyz[0] - mCenter[0];
const ValueType v = xyz[1] - mCenter[1];
const ValueType w = xyz[2] - mCenter[2];
NANOVDB_ASSERT(u>=0 && u<=1);
NANOVDB_ASSERT(v>=0 && v<=1);
NANOVDB_ASSERT(w>=0 && w<=1);
ValueType V = BaseType::template getValue<0,0,0>();
ValueType A = V + (BaseType::template getValue<0,0,1>() - V) * w;
V = BaseType::template getValue< 0, 1, 0>();
ValueType B = V + (BaseType::template getValue<0,1,1>() - V) * w;
ValueType C = A + (B - A) * v;
V = BaseType::template getValue<1,0,0>();
A = V + (BaseType::template getValue<1,0,1>() - V) * w;
V = BaseType::template getValue<1,1,0>();
B = V + (BaseType::template getValue<1,1,1>() - V) * w;
ValueType D = A + (B - A) * v;
return C + (D - C) * u;
}
/// @brief Return the gradient in world space of the trilinear interpolation kernel.
/// @param xyz Floating point coordinate position.
/// @warning It is assumed that the stencil has already been moved
/// to the relevant voxel position, e.g. using moveTo(xyz).
/// @note Computed as partial derivatives of the trilinear interpolation kernel:
/// v000 (1-u)(1-v)(1-w) + v001 (1-u)(1-v)w + v010 (1-u)v(1-w) + v011 (1-u)vw
/// + v100 u(1-v)(1-w) + v101 u(1-v)w + v110 uv(1-w) + v111 uvw
__hostdev__ inline Vec3<ValueType> gradient(const Vec3<ValueType>& xyz) const
{
const ValueType u = xyz[0] - mCenter[0];
const ValueType v = xyz[1] - mCenter[1];
const ValueType w = xyz[2] - mCenter[2];
NANOVDB_ASSERT(u>=0 && u<=1);
NANOVDB_ASSERT(v>=0 && v<=1);
NANOVDB_ASSERT(w>=0 && w<=1);
ValueType D[4]={BaseType::template getValue<0,0,1>()-BaseType::template getValue<0,0,0>(),
BaseType::template getValue<0,1,1>()-BaseType::template getValue<0,1,0>(),
BaseType::template getValue<1,0,1>()-BaseType::template getValue<1,0,0>(),
BaseType::template getValue<1,1,1>()-BaseType::template getValue<1,1,0>()};
// Z component
ValueType A = D[0] + (D[1]- D[0]) * v;
ValueType B = D[2] + (D[3]- D[2]) * v;
Vec3<ValueType> grad(0, 0, A + (B - A) * u);
D[0] = BaseType::template getValue<0,0,0>() + D[0] * w;
D[1] = BaseType::template getValue<0,1,0>() + D[1] * w;
D[2] = BaseType::template getValue<1,0,0>() + D[2] * w;
D[3] = BaseType::template getValue<1,1,0>() + D[3] * w;
// X component
A = D[0] + (D[1] - D[0]) * v;
B = D[2] + (D[3] - D[2]) * v;
grad[0] = B - A;
// Y component
A = D[1] - D[0];
B = D[3] - D[2];
grad[1] = A + (B - A) * u;
return BaseType::mGrid->map().applyIJT(grad);
}
private:
__hostdev__ inline void init(const Coord& ijk)
{
mValues[ 1] = mAcc.getValue(ijk.offsetBy( 0, 0, 1));
mValues[ 2] = mAcc.getValue(ijk.offsetBy( 0, 1, 1));
mValues[ 3] = mAcc.getValue(ijk.offsetBy( 0, 1, 0));
mValues[ 4] = mAcc.getValue(ijk.offsetBy( 1, 0, 0));
mValues[ 5] = mAcc.getValue(ijk.offsetBy( 1, 0, 1));
mValues[ 6] = mAcc.getValue(ijk.offsetBy( 1, 1, 1));
mValues[ 7] = mAcc.getValue(ijk.offsetBy( 1, 1, 0));
}
template<typename, int, typename> friend class BaseStencil; // allow base class to call init()
using BaseType::mAcc;
using BaseType::mValues;
using BaseType::mCenter;
};// BoxStencil class
// ---------------------------- GradStencil ----------------------------
namespace { // anonymous namespace for stencil-layout map
template<int i, int j, int k> struct GradPt {};
template<> struct GradPt< 0, 0, 0> { enum { idx = 0 }; };
template<> struct GradPt< 1, 0, 0> { enum { idx = 2 }; };
template<> struct GradPt< 0, 1, 0> { enum { idx = 4 }; };
template<> struct GradPt< 0, 0, 1> { enum { idx = 6 }; };
template<> struct GradPt<-1, 0, 0> { enum { idx = 1 }; };
template<> struct GradPt< 0,-1, 0> { enum { idx = 3 }; };
template<> struct GradPt< 0, 0,-1> { enum { idx = 5 }; };
}
/// This is a simple 7-point nearest neighbor stencil that supports
/// gradient by second-order central differencing, first-order upwinding,
/// Laplacian, closest-point transform and zero-crossing test.
///
/// @note For optimal random access performance this class
/// includes its own grid accessor.
template<typename GridT>
class GradStencil : public BaseStencil<GradStencil<GridT>, 7, GridT>
{
using SelfT = GradStencil<GridT>;
using BaseType = BaseStencil<SelfT, 7, GridT>;
public:
using GridType = GridT;
using TreeType = typename GridT::TreeType;
using ValueType = typename GridT::ValueType;
static constexpr int SIZE = 7;
__hostdev__ GradStencil(const GridType& grid)
: BaseType(grid)
, mInv2Dx(ValueType(0.5 / grid.voxelSize()[0]))
, mInvDx2(ValueType(4.0 * mInv2Dx * mInv2Dx))
{
}
__hostdev__ GradStencil(const GridType& grid, double dx)
: BaseType(grid)
, mInv2Dx(ValueType(0.5 / dx))
, mInvDx2(ValueType(4.0 * mInv2Dx * mInv2Dx))
{
}
/// @brief Return the norm square of the single-sided upwind gradient
/// (computed via Godunov's scheme) at the previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType normSqGrad() const
{
return mInvDx2 * GodunovsNormSqrd(mValues[0] > ValueType(0),
mValues[0] - mValues[1],
mValues[2] - mValues[0],
mValues[0] - mValues[3],
mValues[4] - mValues[0],
mValues[0] - mValues[5],
mValues[6] - mValues[0]);
}
/// @brief Return the gradient computed at the previously buffered
/// location by second order central differencing.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline Vec3<ValueType> gradient() const
{
return Vec3<ValueType>(mValues[2] - mValues[1],
mValues[4] - mValues[3],
mValues[6] - mValues[5])*mInv2Dx;
}
/// @brief Return the first-order upwind gradient corresponding to the direction V.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline Vec3<ValueType> gradient(const Vec3<ValueType>& V) const
{
return Vec3<ValueType>(
V[0]>0 ? mValues[0] - mValues[1] : mValues[2] - mValues[0],
V[1]>0 ? mValues[0] - mValues[3] : mValues[4] - mValues[0],
V[2]>0 ? mValues[0] - mValues[5] : mValues[6] - mValues[0])*2*mInv2Dx;
}
/// Return the Laplacian computed at the previously buffered
/// location by second-order central differencing.
__hostdev__ inline ValueType laplacian() const
{
return mInvDx2 * (mValues[1] + mValues[2] +
mValues[3] + mValues[4] +
mValues[5] + mValues[6] - 6*mValues[0]);
}
/// Return @c true if the sign of the value at the center point of the stencil
/// is different from the signs of any of its six nearest neighbors.
__hostdev__ inline bool zeroCrossing() const
{
return (mValues[0]>0 ? (mValues[1]<0 || mValues[2]<0 || mValues[3]<0 || mValues[4]<0 || mValues[5]<0 || mValues[6]<0)
: (mValues[1]>0 || mValues[2]>0 || mValues[3]>0 || mValues[4]>0 || mValues[5]>0 || mValues[6]>0));
}
/// @brief Compute the closest-point transform to a level set.
/// @return the closest point in index space to the surface
/// from which the level set was derived.
///
/// @note This method assumes that the grid represents a level set
/// with distances in world units and a simple affine transfrom
/// with uniform scaling.
__hostdev__ inline Vec3<ValueType> cpt()
{
const Coord& ijk = BaseType::getCenterCoord();
const ValueType d = ValueType(mValues[0] * 0.5 * mInvDx2); // distance in voxels / (2dx^2)
const auto value = Vec3<ValueType>(ijk[0] - d*(mValues[2] - mValues[1]),
ijk[1] - d*(mValues[4] - mValues[3]),
ijk[2] - d*(mValues[6] - mValues[5]));
return value;
}
/// Return linear offset for the specified stencil point relative to its center
template<int i, int j, int k>
__hostdev__ unsigned int pos() const { return GradPt<i,j,k>::idx; }
private:
__hostdev__ inline void init(const Coord& ijk)
{
mValues[ 1] = mAcc.getValue(ijk.offsetBy(-1, 0, 0));
mValues[ 2] = mAcc.getValue(ijk.offsetBy( 1, 0, 0));
mValues[ 3] = mAcc.getValue(ijk.offsetBy( 0,-1, 0));
mValues[ 4] = mAcc.getValue(ijk.offsetBy( 0, 1, 0));
mValues[ 5] = mAcc.getValue(ijk.offsetBy( 0, 0,-1));
mValues[ 6] = mAcc.getValue(ijk.offsetBy( 0, 0, 1));
}
template<typename, int, typename> friend class BaseStencil; // allow base class to call init()
using BaseType::mAcc;
using BaseType::mValues;
const ValueType mInv2Dx, mInvDx2;
}; // GradStencil class
// ---------------------------- WenoStencil ----------------------------
namespace { // anonymous namespace for stencil-layout map
template<int i, int j, int k> struct WenoPt {};
template<> struct WenoPt< 0, 0, 0> { enum { idx = 0 }; };
template<> struct WenoPt<-3, 0, 0> { enum { idx = 1 }; };
template<> struct WenoPt<-2, 0, 0> { enum { idx = 2 }; };
template<> struct WenoPt<-1, 0, 0> { enum { idx = 3 }; };
template<> struct WenoPt< 1, 0, 0> { enum { idx = 4 }; };
template<> struct WenoPt< 2, 0, 0> { enum { idx = 5 }; };
template<> struct WenoPt< 3, 0, 0> { enum { idx = 6 }; };
template<> struct WenoPt< 0,-3, 0> { enum { idx = 7 }; };
template<> struct WenoPt< 0,-2, 0> { enum { idx = 8 }; };
template<> struct WenoPt< 0,-1, 0> { enum { idx = 9 }; };
template<> struct WenoPt< 0, 1, 0> { enum { idx =10 }; };
template<> struct WenoPt< 0, 2, 0> { enum { idx =11 }; };
template<> struct WenoPt< 0, 3, 0> { enum { idx =12 }; };
template<> struct WenoPt< 0, 0,-3> { enum { idx =13 }; };
template<> struct WenoPt< 0, 0,-2> { enum { idx =14 }; };
template<> struct WenoPt< 0, 0,-1> { enum { idx =15 }; };
template<> struct WenoPt< 0, 0, 1> { enum { idx =16 }; };
template<> struct WenoPt< 0, 0, 2> { enum { idx =17 }; };
template<> struct WenoPt< 0, 0, 3> { enum { idx =18 }; };
}
/// @brief This is a special 19-point stencil that supports optimal fifth-order WENO
/// upwinding, second-order central differencing, Laplacian, and zero-crossing test.
///
/// @note For optimal random access performance this class
/// includes its own grid accessor.
template<typename GridT, typename RealT = typename GridT::ValueType>
class WenoStencil: public BaseStencil<WenoStencil<GridT>, 19, GridT>
{
using SelfT = WenoStencil<GridT>;
using BaseType = BaseStencil<SelfT, 19, GridT>;
public:
using GridType = GridT;
using TreeType = typename GridT::TreeType;
using ValueType = typename GridT::ValueType;
static constexpr int SIZE = 19;
__hostdev__ WenoStencil(const GridType& grid)
: BaseType(grid)
, mDx2(ValueType(Pow2(grid.voxelSize()[0])))
, mInv2Dx(ValueType(0.5 / grid.voxelSize()[0]))
, mInvDx2(ValueType(1.0 / mDx2))
{
}
__hostdev__ WenoStencil(const GridType& grid, double dx)
: BaseType(grid)
, mDx2(ValueType(dx * dx))
, mInv2Dx(ValueType(0.5 / dx))
, mInvDx2(ValueType(1.0 / mDx2))
{
}
/// @brief Return the norm-square of the WENO upwind gradient (computed via
/// WENO upwinding and Godunov's scheme) at the previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType normSqGrad(ValueType isoValue = ValueType(0)) const
{
const ValueType* v = mValues;
const RealT
dP_xm = WENO5<RealT>(v[ 2]-v[ 1],v[ 3]-v[ 2],v[ 0]-v[ 3],v[ 4]-v[ 0],v[ 5]-v[ 4],mDx2),
dP_xp = WENO5<RealT>(v[ 6]-v[ 5],v[ 5]-v[ 4],v[ 4]-v[ 0],v[ 0]-v[ 3],v[ 3]-v[ 2],mDx2),
dP_ym = WENO5<RealT>(v[ 8]-v[ 7],v[ 9]-v[ 8],v[ 0]-v[ 9],v[10]-v[ 0],v[11]-v[10],mDx2),
dP_yp = WENO5<RealT>(v[12]-v[11],v[11]-v[10],v[10]-v[ 0],v[ 0]-v[ 9],v[ 9]-v[ 8],mDx2),
dP_zm = WENO5<RealT>(v[14]-v[13],v[15]-v[14],v[ 0]-v[15],v[16]-v[ 0],v[17]-v[16],mDx2),
dP_zp = WENO5<RealT>(v[18]-v[17],v[17]-v[16],v[16]-v[ 0],v[ 0]-v[15],v[15]-v[14],mDx2);
return mInvDx2*static_cast<ValueType>(
GodunovsNormSqrd(v[0]>isoValue, dP_xm, dP_xp, dP_ym, dP_yp, dP_zm, dP_zp));
}
/// Return the optimal fifth-order upwind gradient corresponding to the
/// direction V.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline Vec3<ValueType> gradient(const Vec3<ValueType>& V) const
{
const ValueType* v = mValues;
return 2*mInv2Dx * Vec3<ValueType>(
V[0]>0 ? WENO5<RealT>(v[ 2]-v[ 1],v[ 3]-v[ 2],v[ 0]-v[ 3], v[ 4]-v[ 0],v[ 5]-v[ 4],mDx2)
: WENO5<RealT>(v[ 6]-v[ 5],v[ 5]-v[ 4],v[ 4]-v[ 0], v[ 0]-v[ 3],v[ 3]-v[ 2],mDx2),
V[1]>0 ? WENO5<RealT>(v[ 8]-v[ 7],v[ 9]-v[ 8],v[ 0]-v[ 9], v[10]-v[ 0],v[11]-v[10],mDx2)
: WENO5<RealT>(v[12]-v[11],v[11]-v[10],v[10]-v[ 0], v[ 0]-v[ 9],v[ 9]-v[ 8],mDx2),
V[2]>0 ? WENO5<RealT>(v[14]-v[13],v[15]-v[14],v[ 0]-v[15], v[16]-v[ 0],v[17]-v[16],mDx2)
: WENO5<RealT>(v[18]-v[17],v[17]-v[16],v[16]-v[ 0], v[ 0]-v[15],v[15]-v[14],mDx2));
}
/// Return the gradient computed at the previously buffered
/// location by second-order central differencing.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline Vec3<ValueType> gradient() const
{
return mInv2Dx * Vec3<ValueType>(mValues[ 4] - mValues[ 3],
mValues[10] - mValues[ 9],
mValues[16] - mValues[15]);
}
/// Return the Laplacian computed at the previously buffered
/// location by second-order central differencing.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType laplacian() const
{
return mInvDx2 * (
mValues[ 3] + mValues[ 4] +
mValues[ 9] + mValues[10] +
mValues[15] + mValues[16] - 6*mValues[0]);
}
/// Return @c true if the sign of the value at the center point of the stencil
/// differs from the sign of any of its six nearest neighbors
__hostdev__ inline bool zeroCrossing() const
{
const ValueType* v = mValues;
return (v[ 0]>0 ? (v[ 3]<0 || v[ 4]<0 || v[ 9]<0 || v[10]<0 || v[15]<0 || v[16]<0)
: (v[ 3]>0 || v[ 4]>0 || v[ 9]>0 || v[10]>0 || v[15]>0 || v[16]>0));
}
/// Return linear offset for the specified stencil point relative to its center
template<int i, int j, int k>
__hostdev__ unsigned int pos() const { return WenoPt<i,j,k>::idx; }
private:
__hostdev__ inline void init(const Coord& ijk)
{
mValues[ 1] = mAcc.getValue(ijk.offsetBy(-3, 0, 0));
mValues[ 2] = mAcc.getValue(ijk.offsetBy(-2, 0, 0));
mValues[ 3] = mAcc.getValue(ijk.offsetBy(-1, 0, 0));
mValues[ 4] = mAcc.getValue(ijk.offsetBy( 1, 0, 0));
mValues[ 5] = mAcc.getValue(ijk.offsetBy( 2, 0, 0));
mValues[ 6] = mAcc.getValue(ijk.offsetBy( 3, 0, 0));
mValues[ 7] = mAcc.getValue(ijk.offsetBy( 0, -3, 0));
mValues[ 8] = mAcc.getValue(ijk.offsetBy( 0, -2, 0));
mValues[ 9] = mAcc.getValue(ijk.offsetBy( 0, -1, 0));
mValues[10] = mAcc.getValue(ijk.offsetBy( 0, 1, 0));
mValues[11] = mAcc.getValue(ijk.offsetBy( 0, 2, 0));
mValues[12] = mAcc.getValue(ijk.offsetBy( 0, 3, 0));
mValues[13] = mAcc.getValue(ijk.offsetBy( 0, 0, -3));
mValues[14] = mAcc.getValue(ijk.offsetBy( 0, 0, -2));
mValues[15] = mAcc.getValue(ijk.offsetBy( 0, 0, -1));
mValues[16] = mAcc.getValue(ijk.offsetBy( 0, 0, 1));
mValues[17] = mAcc.getValue(ijk.offsetBy( 0, 0, 2));
mValues[18] = mAcc.getValue(ijk.offsetBy( 0, 0, 3));
}
template<typename, int, typename> friend class BaseStencil; // allow base class to call init()
using BaseType::mAcc;
using BaseType::mValues;
const ValueType mDx2, mInv2Dx, mInvDx2;
}; // WenoStencil class
// ---------------------------- CurvatureStencil ----------------------------
namespace { // anonymous namespace for stencil-layout map
template<int i, int j, int k> struct CurvPt {};
template<> struct CurvPt< 0, 0, 0> { enum { idx = 0 }; };
template<> struct CurvPt<-1, 0, 0> { enum { idx = 1 }; };
template<> struct CurvPt< 1, 0, 0> { enum { idx = 2 }; };
template<> struct CurvPt< 0,-1, 0> { enum { idx = 3 }; };
template<> struct CurvPt< 0, 1, 0> { enum { idx = 4 }; };
template<> struct CurvPt< 0, 0,-1> { enum { idx = 5 }; };
template<> struct CurvPt< 0, 0, 1> { enum { idx = 6 }; };
template<> struct CurvPt<-1,-1, 0> { enum { idx = 7 }; };
template<> struct CurvPt< 1,-1, 0> { enum { idx = 8 }; };
template<> struct CurvPt<-1, 1, 0> { enum { idx = 9 }; };
template<> struct CurvPt< 1, 1, 0> { enum { idx =10 }; };
template<> struct CurvPt<-1, 0,-1> { enum { idx =11 }; };
template<> struct CurvPt< 1, 0,-1> { enum { idx =12 }; };
template<> struct CurvPt<-1, 0, 1> { enum { idx =13 }; };
template<> struct CurvPt< 1, 0, 1> { enum { idx =14 }; };
template<> struct CurvPt< 0,-1,-1> { enum { idx =15 }; };
template<> struct CurvPt< 0, 1,-1> { enum { idx =16 }; };
template<> struct CurvPt< 0,-1, 1> { enum { idx =17 }; };
template<> struct CurvPt< 0, 1, 1> { enum { idx =18 }; };
}
template<typename GridT, typename RealT = typename GridT::ValueType>
class CurvatureStencil: public BaseStencil<CurvatureStencil<GridT>, 19, GridT>
{
using SelfT = CurvatureStencil<GridT>;
using BaseType = BaseStencil<SelfT, 19, GridT>;
public:
using GridType = GridT;
using TreeType = typename GridT::TreeType;
using ValueType = typename GridT::ValueType;
static constexpr int SIZE = 19;
__hostdev__ CurvatureStencil(const GridType& grid)
: BaseType(grid)
, mInv2Dx(ValueType(0.5 / grid.voxelSize()[0]))
, mInvDx2(ValueType(4.0 * mInv2Dx * mInv2Dx))
{
}
__hostdev__ CurvatureStencil(const GridType& grid, double dx)
: BaseType(grid)
, mInv2Dx(ValueType(0.5 / dx))
, mInvDx2(ValueType(4.0 * mInv2Dx * mInv2Dx))
{
}
/// @brief Return the mean curvature at the previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType meanCurvature() const
{
RealT alpha, normGrad;
return this->meanCurvature(alpha, normGrad) ?
ValueType(alpha*mInv2Dx/Pow3(normGrad)) : 0;
}
/// @brief Return the Gaussian curvature at the previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType gaussianCurvature() const
{
RealT alpha, normGrad;
return this->gaussianCurvature(alpha, normGrad) ?
ValueType(alpha*mInvDx2/Pow4(normGrad)) : 0;
}
/// @brief Return both the mean and the Gaussian curvature at the
/// previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline void curvatures(ValueType &mean, ValueType& gauss) const
{
RealT alphaM, alphaG, normGrad;
if (this->curvatures(alphaM, alphaG, normGrad)) {
mean = ValueType(alphaM*mInv2Dx/Pow3(normGrad));
gauss = ValueType(alphaG*mInvDx2/Pow4(normGrad));
} else {
mean = gauss = 0;
}
}
/// Return the mean curvature multiplied by the norm of the
/// central-difference gradient. This method is very useful for
/// mean-curvature flow of level sets!
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType meanCurvatureNormGrad() const
{
RealT alpha, normGrad;
return this->meanCurvature(alpha, normGrad) ?
ValueType(alpha*mInvDx2/(2*Pow2(normGrad))) : 0;
}
/// Return the mean Gaussian multiplied by the norm of the
/// central-difference gradient.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType gaussianCurvatureNormGrad() const
{
RealT alpha, normGrad;
return this->gaussianCurvature(alpha, normGrad) ?
ValueType(2*alpha*mInv2Dx*mInvDx2/Pow3(normGrad)) : 0;
}
/// @brief Return both the mean and the Gaussian curvature at the
/// previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline void curvaturesNormGrad(ValueType &mean, ValueType& gauss) const
{
RealT alphaM, alphaG, normGrad;
if (this->curvatures(alphaM, alphaG, normGrad)) {
mean = ValueType(alphaM*mInvDx2/(2*Pow2(normGrad)));
gauss = ValueType(2*alphaG*mInv2Dx*mInvDx2/Pow3(normGrad));
} else {
mean = gauss = 0;
}
}
/// @brief Computes the minimum and maximum principal curvature at the
/// previously buffered location.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline void principalCurvatures(ValueType &min, ValueType &max) const
{
min = max = 0;
RealT alphaM, alphaG, normGrad;
if (this->curvatures(alphaM, alphaG, normGrad)) {
const RealT mean = alphaM*mInv2Dx/Pow3(normGrad);
const RealT tmp = Sqrt(mean*mean - alphaG*mInvDx2/Pow4(normGrad));
min = ValueType(mean - tmp);
max = ValueType(mean + tmp);
}
}
/// Return the Laplacian computed at the previously buffered
/// location by second-order central differencing.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline ValueType laplacian() const
{
return mInvDx2 * (
mValues[1] + mValues[2] +
mValues[3] + mValues[4] +
mValues[5] + mValues[6] - 6*mValues[0]);
}
/// Return the gradient computed at the previously buffered
/// location by second-order central differencing.
///
/// @note This method should not be called until the stencil
/// buffer has been populated via a call to moveTo(ijk).
__hostdev__ inline Vec3<ValueType> gradient() const
{
return Vec3<ValueType>(
mValues[2] - mValues[1],
mValues[4] - mValues[3],
mValues[6] - mValues[5])*mInv2Dx;
}
/// Return linear offset for the specified stencil point relative to its center
template<int i, int j, int k>
__hostdev__ unsigned int pos() const { return CurvPt<i,j,k>::idx; }
private:
__hostdev__ inline void init(const Coord &ijk)
{
mValues[ 1] = mAcc.getValue(ijk.offsetBy(-1, 0, 0));
mValues[ 2] = mAcc.getValue(ijk.offsetBy( 1, 0, 0));
mValues[ 3] = mAcc.getValue(ijk.offsetBy( 0, -1, 0));
mValues[ 4] = mAcc.getValue(ijk.offsetBy( 0, 1, 0));
mValues[ 5] = mAcc.getValue(ijk.offsetBy( 0, 0, -1));
mValues[ 6] = mAcc.getValue(ijk.offsetBy( 0, 0, 1));
mValues[ 7] = mAcc.getValue(ijk.offsetBy(-1, -1, 0));
mValues[ 8] = mAcc.getValue(ijk.offsetBy( 1, -1, 0));
mValues[ 9] = mAcc.getValue(ijk.offsetBy(-1, 1, 0));
mValues[10] = mAcc.getValue(ijk.offsetBy( 1, 1, 0));
mValues[11] = mAcc.getValue(ijk.offsetBy(-1, 0, -1));
mValues[12] = mAcc.getValue(ijk.offsetBy( 1, 0, -1));
mValues[13] = mAcc.getValue(ijk.offsetBy(-1, 0, 1));
mValues[14] = mAcc.getValue(ijk.offsetBy( 1, 0, 1));
mValues[15] = mAcc.getValue(ijk.offsetBy( 0, -1, -1));
mValues[16] = mAcc.getValue(ijk.offsetBy( 0, 1, -1));
mValues[17] = mAcc.getValue(ijk.offsetBy( 0, -1, 1));
mValues[18] = mAcc.getValue(ijk.offsetBy( 0, 1, 1));
}
__hostdev__ inline RealT Dx() const { return 0.5*(mValues[2] - mValues[1]); }// * 1/dx
__hostdev__ inline RealT Dy() const { return 0.5*(mValues[4] - mValues[3]); }// * 1/dx
__hostdev__ inline RealT Dz() const { return 0.5*(mValues[6] - mValues[5]); }// * 1/dx
__hostdev__ inline RealT Dxx() const { return mValues[2] - 2 * mValues[0] + mValues[1]; }// * 1/dx2
__hostdev__ inline RealT Dyy() const { return mValues[4] - 2 * mValues[0] + mValues[3]; }// * 1/dx2}
__hostdev__ inline RealT Dzz() const { return mValues[6] - 2 * mValues[0] + mValues[5]; }// * 1/dx2
__hostdev__ inline RealT Dxy() const { return 0.25 * (mValues[10] - mValues[ 8] + mValues[ 7] - mValues[ 9]); }// * 1/dx2
__hostdev__ inline RealT Dxz() const { return 0.25 * (mValues[14] - mValues[12] + mValues[11] - mValues[13]); }// * 1/dx2
__hostdev__ inline RealT Dyz() const { return 0.25 * (mValues[18] - mValues[16] + mValues[15] - mValues[17]); }// * 1/dx2
__hostdev__ inline bool meanCurvature(RealT& alpha, RealT& normGrad) const
{
// For performance all finite differences are unscaled wrt dx
const RealT Dx = this->Dx(), Dy = this->Dy(), Dz = this->Dz(),
Dx2 = Dx*Dx, Dy2 = Dy*Dy, Dz2 = Dz*Dz, normGrad2 = Dx2 + Dy2 + Dz2;
if (normGrad2 <= Tolerance<RealT>::value()) {
alpha = normGrad = 0;
return false;
}
const RealT Dxx = this->Dxx(), Dyy = this->Dyy(), Dzz = this->Dzz();
alpha = Dx2*(Dyy + Dzz) + Dy2*(Dxx + Dzz) + Dz2*(Dxx + Dyy) -
2*(Dx*(Dy*this->Dxy() + Dz*this->Dxz()) + Dy*Dz*this->Dyz());// * 1/dx^4
normGrad = Sqrt(normGrad2); // * 1/dx
return true;
}
__hostdev__ inline bool gaussianCurvature(RealT& alpha, RealT& normGrad) const
{
// For performance all finite differences are unscaled wrt dx
const RealT Dx = this->Dx(), Dy = this->Dy(), Dz = this->Dz(),
Dx2 = Dx*Dx, Dy2 = Dy*Dy, Dz2 = Dz*Dz, normGrad2 = Dx2 + Dy2 + Dz2;
if (normGrad2 <= Tolerance<RealT>::value()) {
alpha = normGrad = 0;
return false;
}
const RealT Dxx = this->Dxx(), Dyy = this->Dyy(), Dzz = this->Dzz(),
Dxy = this->Dxy(), Dxz = this->Dxz(), Dyz = this->Dyz();
alpha = Dx2*(Dyy*Dzz - Dyz*Dyz) + Dy2*(Dxx*Dzz - Dxz*Dxz) + Dz2*(Dxx*Dyy - Dxy*Dxy) +
2*( Dy*Dz*(Dxy*Dxz - Dyz*Dxx) + Dx*Dz*(Dxy*Dyz - Dxz*Dyy) + Dx*Dy*(Dxz*Dyz - Dxy*Dzz) );// * 1/dx^6
normGrad = Sqrt(normGrad2); // * 1/dx
return true;
}
__hostdev__ inline bool curvatures(RealT& alphaM, RealT& alphaG, RealT& normGrad) const
{
// For performance all finite differences are unscaled wrt dx
const RealT Dx = this->Dx(), Dy = this->Dy(), Dz = this->Dz(),
Dx2 = Dx*Dx, Dy2 = Dy*Dy, Dz2 = Dz*Dz, normGrad2 = Dx2 + Dy2 + Dz2;
if (normGrad2 <= Tolerance<RealT>::value()) {
alphaM = alphaG =normGrad = 0;
return false;
}
const RealT Dxx = this->Dxx(), Dyy = this->Dyy(), Dzz = this->Dzz(),
Dxy = this->Dxy(), Dxz = this->Dxz(), Dyz = this->Dyz();
alphaM = Dx2*(Dyy + Dzz) + Dy2*(Dxx + Dzz) + Dz2*(Dxx + Dyy) -
2*(Dx*(Dy*Dxy + Dz*Dxz) + Dy*Dz*Dyz);// *1/dx^4
alphaG = Dx2*(Dyy*Dzz - Dyz*Dyz) + Dy2*(Dxx*Dzz - Dxz*Dxz) + Dz2*(Dxx*Dyy - Dxy*Dxy) +
2*( Dy*Dz*(Dxy*Dxz - Dyz*Dxx) + Dx*Dz*(Dxy*Dyz - Dxz*Dyy) + Dx*Dy*(Dxz*Dyz - Dxy*Dzz) );// *1/dx^6
normGrad = Sqrt(normGrad2); // * 1/dx
return true;
}
template<typename, int, typename> friend class BaseStencil; // allow base class to call init()
using BaseType::mAcc;
using BaseType::mValues;
const ValueType mInv2Dx, mInvDx2;
}; // CurvatureStencil class
} // end nanovdb namespace
#endif // NANOVDB_STENCILS_HAS_BEEN_INCLUDED
value
ValueT value
Definition GridBuilder.h:1290
NanoVDB.h
Implements a light-weight self-contained VDB data-structure in a single file! In other words,...
__hostdev__
#define __hostdev__
Definition NanoVDB.h:192
NANOVDB_ASSERT
#define NANOVDB_ASSERT(x)
Definition NanoVDB.h:173
nanovdb::BaseStencil::min
ValueType min() const
Return the smallest value in the stencil buffer.
Definition Stencils.h:189
nanovdb::BaseStencil::moveTo
void moveTo(const Vec3< RealType > &xyz)
Initialize the stencil buffer with the values of voxel (x, y, z) and its neighbors.
Definition Stencils.h:146
nanovdb::BaseStencil< SelfT, 8, GridT >::mValues
ValueType mValues[SIZE]
Definition Stencils.h:279
nanovdb::BaseStencil::accessor
const AccessorType & accessor() const
Return a const reference to the ValueAccessor associated with this Stencil.
Definition Stencils.h:266
nanovdb::BaseStencil::moveTo
void moveTo(const IterType &iter)
Initialize the stencil buffer with the values of voxel (x, y, z) and its neighbors.
Definition Stencils.h:132
nanovdb::BaseStencil::getValue
const ValueType & getValue(unsigned int pos=0) const
Return the value from the stencil buffer with linear offset pos.
Definition Stencils.h:157
nanovdb::BaseStencil::intersects
bool intersects(const ValueType &isoValue=ValueType(0)) const
Return true if the center of the stencil intersects the iso-contour specified by the isoValue.
Definition Stencils.h:216
nanovdb::BaseStencil::mean
ValueType mean() const
Return the mean value of the current stencil.
Definition Stencils.h:181
nanovdb::BaseStencil::setValue
void setValue(const ValueType &value)
Set the value at the specified location relative to the center of the stencil.
Definition Stencils.h:172
nanovdb::BaseStencil::moveTo
void moveTo(const Coord &ijk, const ValueType &centerValue)
Initialize the stencil buffer with the values of voxel (i, j, k) and its neighbors....
Definition Stencils.h:119
nanovdb::BaseStencil::AccessorType
typename GridT::AccessorType AccessorType
Definition Stencils.h:102
nanovdb::BaseStencil::moveTo
void moveTo(const Coord &ijk)
Initialize the stencil buffer with the values of voxel (i, j, k) and its neighbors.
Definition Stencils.h:107
nanovdb::BaseStencil< SelfT, 8, GridT >::mCenter
Coord mCenter
Definition Stencils.h:280
nanovdb::BaseStencil< SelfT, 8, GridT >::mGrid
const GridType * mGrid
Definition Stencils.h:277
nanovdb::BaseStencil::getCenterValue
const ValueType & getCenterValue() const
Return the value at the center of the stencil.
Definition Stencils.h:212
nanovdb::BaseStencil::getValue
const ValueType & getValue() const
Return the value at the specified location relative to the center of the stencil.
Definition Stencils.h:165
nanovdb::BaseStencil::getCenterCoord
const Coord & getCenterCoord() const
Return the coordinates of the center point of the stencil.
Definition Stencils.h:209
nanovdb::BaseStencil::TreeType
typename GridT::TreeType TreeType
Definition Stencils.h:101
nanovdb::BaseStencil::ValueType
typename GridT::ValueType ValueType
Definition Stencils.h:99
nanovdb::BaseStencil::BaseStencil
BaseStencil(const GridType &grid)
Definition Stencils.h:270
nanovdb::BaseStencil::grid
const GridType & grid() const
Return a const reference to the grid from which this stencil was constructed.
Definition Stencils.h:262
nanovdb::BaseStencil::size
static int size()
Return the size of the stencil buffer.
Definition Stencils.h:178
nanovdb::BaseStencil::max
ValueType max() const
Return the largest value in the stencil buffer.
Definition Stencils.h:199
nanovdb::BaseStencil< SelfT, 8, GridT >::mAcc
AccessorType mAcc
Definition Stencils.h:278
nanovdb::BaseStencil::intersectionMask
Mask intersectionMask(ValueType isoValue=ValueType(0)) const
Return true a bit-mask where the 6 lower bits indicates if the center of the stencil intersects the i...
Definition Stencils.h:247
nanovdb::BaseStencil::GridType
GridT GridType
Definition Stencils.h:100
nanovdb::BoxStencil::SIZE
static constexpr int SIZE
Definition Stencils.h:313
nanovdb::BoxStencil::gradient
Vec3< ValueType > gradient(const Vec3< ValueType > &xyz) const
Return the gradient in world space of the trilinear interpolation kernel.
Definition Stencils.h:374
nanovdb::BoxStencil::interpolation
ValueType interpolation(const Vec3< ValueType > &xyz) const
Return the trilinear interpolation at the normalized position.
Definition Stencils.h:342
nanovdb::BoxStencil::intersects
bool intersects(ValueType isoValue=ValueType(0)) const
Return true if the center of the stencil intersects the.
Definition Stencils.h:323
nanovdb::BoxStencil::BoxStencil
BoxStencil(const GridType &grid)
Definition Stencils.h:315
nanovdb::BoxStencil::TreeType
typename GridT::TreeType TreeType
Definition Stencils.h:310
nanovdb::BoxStencil::ValueType
typename GridT::ValueType ValueType
Definition Stencils.h:311
nanovdb::BoxStencil::BaseStencil
friend class BaseStencil
Definition Stencils.h:426
nanovdb::BoxStencil::pos
unsigned int pos() const
Return linear offset for the specified stencil point relative to its center.
Definition Stencils.h:319
nanovdb::BoxStencil::GridType
GridT GridType
Definition Stencils.h:309
nanovdb::Coord
Signed (i, j, k) 32-bit integer coordinate class, similar to openvdb::math::Coord.
Definition NanoVDB.h:967
nanovdb::Coord::offsetBy
Coord offsetBy(ValueType dx, ValueType dy, ValueType dz) const
Definition NanoVDB.h:1116
nanovdb::CurvatureStencil::curvaturesNormGrad
void curvaturesNormGrad(ValueType &mean, ValueType &gauss) const
Return both the mean and the Gaussian curvature at the previously buffered location.
Definition Stencils.h:872
nanovdb::CurvatureStencil::SIZE
static constexpr int SIZE
Definition Stencils.h:788
nanovdb::CurvatureStencil::CurvatureStencil
CurvatureStencil(const GridType &grid)
Definition Stencils.h:790
nanovdb::CurvatureStencil::meanCurvature
ValueType meanCurvature() const
Return the mean curvature at the previously buffered location.
Definition Stencils.h:808
nanovdb::CurvatureStencil::gradient
Vec3< ValueType > gradient() const
Definition Stencils.h:918
nanovdb::CurvatureStencil::gaussianCurvatureNormGrad
ValueType gaussianCurvatureNormGrad() const
Definition Stencils.h:860
nanovdb::CurvatureStencil::principalCurvatures
void principalCurvatures(ValueType &min, ValueType &max) const
Computes the minimum and maximum principal curvature at the previously buffered location.
Definition Stencils.h:888
nanovdb::CurvatureStencil::curvatures
void curvatures(ValueType &mean, ValueType &gauss) const
Return both the mean and the Gaussian curvature at the previously buffered location.
Definition Stencils.h:831
nanovdb::CurvatureStencil::laplacian
ValueType laplacian() const
Definition Stencils.h:905
nanovdb::CurvatureStencil::TreeType
typename GridT::TreeType TreeType
Definition Stencils.h:785
nanovdb::CurvatureStencil::ValueType
typename GridT::ValueType ValueType
Definition Stencils.h:786
nanovdb::CurvatureStencil::BaseStencil
friend class BaseStencil
Definition Stencils.h:1020
nanovdb::CurvatureStencil::meanCurvatureNormGrad
ValueType meanCurvatureNormGrad() const
Definition Stencils.h:848
nanovdb::CurvatureStencil::gaussianCurvature
ValueType gaussianCurvature() const
Return the Gaussian curvature at the previously buffered location.
Definition Stencils.h:819
nanovdb::CurvatureStencil::pos
unsigned int pos() const
Return linear offset for the specified stencil point relative to its center.
Definition Stencils.h:928
nanovdb::CurvatureStencil::GridType
GridT GridType
Definition Stencils.h:784
nanovdb::CurvatureStencil::CurvatureStencil
CurvatureStencil(const GridType &grid, double dx)
Definition Stencils.h:797
nanovdb::GradStencil::SIZE
static constexpr int SIZE
Definition Stencils.h:463
nanovdb::GradStencil::GradStencil
GradStencil(const GridType &grid, double dx)
Definition Stencils.h:472
nanovdb::GradStencil::GradStencil
GradStencil(const GridType &grid)
Definition Stencils.h:465
nanovdb::GradStencil::gradient
Vec3< ValueType > gradient() const
Return the gradient computed at the previously buffered location by second order central differencing...
Definition Stencils.h:500
nanovdb::GradStencil::cpt
Vec3< ValueType > cpt()
Compute the closest-point transform to a level set.
Definition Stencils.h:542
nanovdb::GradStencil::laplacian
ValueType laplacian() const
Definition Stencils.h:520
nanovdb::GradStencil::gradient
Vec3< ValueType > gradient(const Vec3< ValueType > &V) const
Return the first-order upwind gradient corresponding to the direction V.
Definition Stencils.h:510
nanovdb::GradStencil::zeroCrossing
bool zeroCrossing() const
Definition Stencils.h:529
nanovdb::GradStencil::TreeType
typename GridT::TreeType TreeType
Definition Stencils.h:460
nanovdb::GradStencil::ValueType
typename GridT::ValueType ValueType
Definition Stencils.h:461
nanovdb::GradStencil::BaseStencil
friend class BaseStencil
Definition Stencils.h:570
nanovdb::GradStencil::pos
unsigned int pos() const
Return linear offset for the specified stencil point relative to its center.
Definition Stencils.h:554
nanovdb::GradStencil::normSqGrad
ValueType normSqGrad() const
Return the norm square of the single-sided upwind gradient (computed via Godunov's scheme) at the pre...
Definition Stencils.h:484
nanovdb::GradStencil::GridType
GridT GridType
Definition Stencils.h:459
nanovdb::Vec3
A simple vector class with three double components, similar to openvdb::math::Vec3.
Definition NanoVDB.h:1158
nanovdb::WenoStencil::SIZE
static constexpr int SIZE
Definition Stencils.h:622
nanovdb::WenoStencil::gradient
Vec3< ValueType > gradient() const
Definition Stencils.h:680
nanovdb::WenoStencil::WenoStencil
WenoStencil(const GridType &grid)
Definition Stencils.h:624
nanovdb::WenoStencil::WenoStencil
WenoStencil(const GridType &grid, double dx)
Definition Stencils.h:632
nanovdb::WenoStencil::laplacian
ValueType laplacian() const
Definition Stencils.h:692
nanovdb::WenoStencil::gradient
Vec3< ValueType > gradient(const Vec3< ValueType > &V) const
Definition Stencils.h:664
nanovdb::WenoStencil::zeroCrossing
bool zeroCrossing() const
Definition Stencils.h:702
nanovdb::WenoStencil::TreeType
typename GridT::TreeType TreeType
Definition Stencils.h:619
nanovdb::WenoStencil::ValueType
typename GridT::ValueType ValueType
Definition Stencils.h:620
nanovdb::WenoStencil::BaseStencil
friend class BaseStencil
Definition Stencils.h:738
nanovdb::WenoStencil::pos
unsigned int pos() const
Return linear offset for the specified stencil point relative to its center.
Definition Stencils.h:711
nanovdb::WenoStencil::GridType
GridT GridType
Definition Stencils.h:618
nanovdb::WenoStencil::normSqGrad
ValueType normSqGrad(ValueType isoValue=ValueType(0)) const
Return the norm-square of the WENO upwind gradient (computed via WENO upwinding and Godunov's scheme)...
Definition Stencils.h:645
nanovdb
Definition NanoVDB.h:208
nanovdb::CountOn
uint32_t CountOn(uint64_t v)
Definition NanoVDB.h:1931
nanovdb::Min
Type Min(Type a, Type b)
Definition NanoVDB.h:758
nanovdb::Pow4
T Pow4(T x)
Definition NanoVDB.h:849
nanovdb::Sqrt
float Sqrt(float x)
Return the square root of a floating-point value.
Definition NanoVDB.h:902
nanovdb::WENO5
ValueType WENO5(const ValueType &v1, const ValueType &v2, const ValueType &v3, const ValueType &v4, const ValueType &v5, RealT scale2=1.0)
Implementation of nominally fifth-order finite-difference WENO.
Definition Stencils.h:35
nanovdb::Pow3
T Pow3(T x)
Definition NanoVDB.h:843
nanovdb::RoundDown
CoordT RoundDown(const Vec3T< RealT > &xyz)
Definition NanoVDB.h:895
nanovdb::Pow2
T Pow2(T x)
Definition NanoVDB.h:837
nanovdb::Max
Type Max(Type a, Type b)
Definition NanoVDB.h:779
nanovdb::GodunovsNormSqrd
RealT GodunovsNormSqrd(bool isOutside, RealT dP_xm, RealT dP_xp, RealT dP_ym, RealT dP_yp, RealT dP_zm, RealT dP_zp)
Definition Stencils.h:62
nanovdb::BaseStencil::Mask::count
int count() const
Definition Stencils.h:234
nanovdb::BaseStencil::Mask::test
bool test(int i) const
Definition Stencils.h:230
nanovdb::BaseStencil::Mask::none
bool none() const
Definition Stencils.h:233
nanovdb::BaseStencil::Mask::bits
uint8_t bits
Definition Stencils.h:227
nanovdb::BaseStencil::Mask::all
bool all() const
Definition Stencils.h:232
nanovdb::BaseStencil::Mask::set
void set(int i)
Definition Stencils.h:229
nanovdb::BaseStencil::Mask::any
bool any() const
Definition Stencils.h:231
nanovdb::BaseStencil::Mask::Mask
Mask()
Definition Stencils.h:228