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//
// Copyright (c) 2012-2016 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.
//
///////////////////////////////////////////////////////////////////////////
//
/// @file Maps.h
#ifndef OPENVDB_MATH_MAPS_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_MAPS_HAS_BEEN_INCLUDED
#include "Math.h"
#include "Mat4.h"
#include "Vec3.h"
#include "BBox.h"
#include "Coord.h"
#include <openvdb/io/io.h> // for io::getFormatVersion()
#include <openvdb/util/Name.h>
#include <openvdb/Types.h>
#include <boost/shared_ptr.hpp>
#include <map>
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
////////////////////////////////////////
/// Forward declarations of the different map types
class MapBase;
class ScaleMap;
class TranslationMap;
class ScaleTranslateMap;
class UniformScaleMap;
class UniformScaleTranslateMap;
class AffineMap;
class UnitaryMap;
class NonlinearFrustumMap;
template<typename T1, typename T2> class CompoundMap;
typedef CompoundMap<UnitaryMap, TranslationMap> UnitaryAndTranslationMap;
typedef CompoundMap<CompoundMap<UnitaryMap, ScaleMap>, UnitaryMap> SpectralDecomposedMap;
typedef SpectralDecomposedMap SymmetricMap;
typedef CompoundMap<SymmetricMap, UnitaryAndTranslationMap> FullyDecomposedMap;
typedef CompoundMap<SymmetricMap, UnitaryMap> PolarDecomposedMap;
////////////////////////////////////////
/// Map traits
template<typename T> struct is_linear { static const bool value = false; };
template<> struct is_linear<AffineMap> { static const bool value = true; };
template<> struct is_linear<ScaleMap> { static const bool value = true; };
template<> struct is_linear<UniformScaleMap> { static const bool value = true; };
template<> struct is_linear<UnitaryMap> { static const bool value = true; };
template<> struct is_linear<TranslationMap> { static const bool value = true; };
template<> struct is_linear<ScaleTranslateMap> { static const bool value = true; };
template<> struct is_linear<UniformScaleTranslateMap> { static const bool value = true; };
template<typename T1, typename T2> struct is_linear<CompoundMap<T1, T2> > {
static const bool value = is_linear<T1>::value && is_linear<T2>::value;
};
template<typename T> struct is_uniform_scale { static const bool value = false; };
template<> struct is_uniform_scale<UniformScaleMap> { static const bool value = true; };
template<typename T> struct is_uniform_scale_translate { static const bool value = false; };
template<> struct is_uniform_scale_translate<TranslationMap> { static const bool value = true; };
template<> struct is_uniform_scale_translate<UniformScaleTranslateMap> {
static const bool value = true;
};
template<typename T> struct is_scale { static const bool value = false; };
template<> struct is_scale<ScaleMap> { static const bool value = true; };
template<typename T> struct is_scale_translate { static const bool value = false; };
template<> struct is_scale_translate<ScaleTranslateMap> { static const bool value = true; };
template<typename T> struct is_uniform_diagonal_jacobian {
static const bool value = is_uniform_scale<T>::value || is_uniform_scale_translate<T>::value;
};
template<typename T> struct is_diagonal_jacobian {
static const bool value = is_scale<T>::value || is_scale_translate<T>::value;
};
////////////////////////////////////////
/// Utility methods
/// @brief Create a SymmetricMap from a symmetric matrix.
/// Decomposes the map into Rotation Diagonal Rotation^T
OPENVDB_API boost::shared_ptr<SymmetricMap> createSymmetricMap(const Mat3d& m);
/// @brief General decomposition of a Matrix into a Unitary (e.g. rotation)
/// following a Symmetric (e.g. stretch & shear)
OPENVDB_API boost::shared_ptr<FullyDecomposedMap> createFullyDecomposedMap(const Mat4d& m);
/// @brief Decomposes a general linear into translation following polar decomposition.
///
/// T U S where:
///
/// T: Translation
/// U: Unitary (rotation or reflection)
/// S: Symmetric
///
/// @note: the Symmetric is automatically decomposed into Q D Q^T, where
/// Q is rotation and D is diagonal.
OPENVDB_API boost::shared_ptr<PolarDecomposedMap> createPolarDecomposedMap(const Mat3d& m);
/// @brief reduces an AffineMap to a ScaleMap or a ScaleTranslateMap when it can
OPENVDB_API boost::shared_ptr<MapBase> simplify(boost::shared_ptr<AffineMap> affine);
/// @brief Returns the left pseudoInverse of the input matrix when the 3x3 part is symmetric
/// otherwise it zeros the 3x3 and reverses the translation.
OPENVDB_API Mat4d approxInverse(const Mat4d& mat);
////////////////////////////////////////
/// @brief Abstract base class for maps
class OPENVDB_API MapBase
{
public:
typedef boost::shared_ptr<MapBase> Ptr;
typedef boost::shared_ptr<const MapBase> ConstPtr;
typedef Ptr (*MapFactory)();
virtual ~MapBase(){}
virtual boost::shared_ptr<AffineMap> getAffineMap() const = 0;
/// Return the name of this map's concrete type (e.g., @c "AffineMap").
virtual Name type() const = 0;
/// Return @c true if this map is of concrete type @c MapT (e.g., AffineMap).
template<typename MapT> bool isType() const { return this->type() == MapT::mapType(); }
/// Return @c true if this map is equal to the given map.
virtual bool isEqual(const MapBase& other) const = 0;
/// Return @c true if this map is linear.
virtual bool isLinear() const = 0;
/// Return @c true if the spacing between the image of latice is uniform in all directions
virtual bool hasUniformScale() const = 0;
virtual Vec3d applyMap(const Vec3d& in) const = 0;
virtual Vec3d applyInverseMap(const Vec3d& in) const = 0;
//@{
/// @brief Apply the Inverse Jacobian Transpose of this map to a vector.
/// For a linear map this is equivalent to applying the transpose of
/// inverse map excluding translation.
virtual Vec3d applyIJT(const Vec3d& in) const = 0;
virtual Vec3d applyIJT(const Vec3d& in, const Vec3d& domainPos) const = 0;
//@}
virtual Mat3d applyIJC(const Mat3d& m) const = 0;
virtual Mat3d applyIJC(const Mat3d& m, const Vec3d& v, const Vec3d& domainPos) const = 0;
virtual double determinant() const = 0;
virtual double determinant(const Vec3d&) const = 0;
//@{
/// @brief Method to return the local size of a voxel.
/// When a location is specified as an argument, it is understood to be
/// be in the domain of the map (i.e. index space)
virtual Vec3d voxelSize() const = 0;
virtual Vec3d voxelSize(const Vec3d&) const = 0;
//@}
virtual void read(std::istream&) = 0;
virtual void write(std::ostream&) const = 0;
virtual std::string str() const = 0;
virtual MapBase::Ptr copy() const = 0;
//@{
/// @brief Methods to update the map
virtual MapBase::Ptr preRotate(double radians, Axis axis = X_AXIS) const = 0;
virtual MapBase::Ptr preTranslate(const Vec3d&) const = 0;
virtual MapBase::Ptr preScale(const Vec3d&) const = 0;
virtual MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const = 0;
virtual MapBase::Ptr postRotate(double radians, Axis axis = X_AXIS) const = 0;
virtual MapBase::Ptr postTranslate(const Vec3d&) const = 0;
virtual MapBase::Ptr postScale(const Vec3d&) const = 0;
virtual MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const = 0;
//@}
//@{
/// @brief Apply the Jacobian of this map to a vector.
/// For a linear map this is equivalent to applying the map excluding translation.
/// @warning Houdini 12.5 uses an earlier version of OpenVDB, and maps created
/// with that version lack a virtual table entry for this method. Do not call
/// this method from Houdini 12.5.
virtual Vec3d applyJacobian(const Vec3d& in) const = 0;
virtual Vec3d applyJacobian(const Vec3d& in, const Vec3d& domainPos) const = 0;
//@}
//@{
/// @brief Apply the InverseJacobian of this map to a vector.
/// For a linear map this is equivalent to applying the map inverse excluding translation.
/// @warning Houdini 12.5 uses an earlier version of OpenVDB, and maps created
/// with that version lack a virtual table entry for this method. Do not call
/// this method from Houdini 12.5.
virtual Vec3d applyInverseJacobian(const Vec3d& in) const = 0;
virtual Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d& domainPos) const = 0;
//@}
//@{
/// @brief Apply the Jacobian transpose of this map to a vector.
/// For a linear map this is equivalent to applying the transpose of the map
/// excluding translation.
/// @warning Houdini 12.5 uses an earlier version of OpenVDB, and maps created
/// with that version lack a virtual table entry for this method. Do not call
/// this method from Houdini 12.5.
virtual Vec3d applyJT(const Vec3d& in) const = 0;
virtual Vec3d applyJT(const Vec3d& in, const Vec3d& domainPos) const = 0;
//@}
/// @brief Return a new map representing the inverse of this map.
/// @throw NotImplementedError if the map is a NonlinearFrustumMap.
/// @warning Houdini 12.5 uses an earlier version of OpenVDB, and maps created
/// with that version lack a virtual table entry for this method. Do not call
/// this method from Houdini 12.5.
virtual MapBase::Ptr inverseMap() const = 0;
protected:
MapBase() {}
template<typename MapT>
static bool isEqualBase(const MapT& self, const MapBase& other)
{
return other.isType<MapT>() && (self == *static_cast<const MapT*>(&other));
}
};
////////////////////////////////////////
/// @brief Threadsafe singleton object for accessing the map type-name dictionary.
/// Associates a map type-name with a factory function.
class OPENVDB_API MapRegistry
{
public:
typedef std::map<Name, MapBase::MapFactory> MapDictionary;
static MapRegistry* instance();
/// Create a new map of the given (registered) type name.
static MapBase::Ptr createMap(const Name&);
/// Return @c true if the given map type name is registered.
static bool isRegistered(const Name&);
/// Register a map type along with a factory function.
static void registerMap(const Name&, MapBase::MapFactory);
/// Remove a map type from the registry.
static void unregisterMap(const Name&);
/// Clear the map type registry.
static void clear();
private:
MapRegistry() {}
static MapRegistry* staticInstance();
static MapRegistry* mInstance;
MapDictionary mMap;
};
////////////////////////////////////////
/// @brief A general linear transform using homogeneous coordinates to perform
/// rotation, scaling, shear and translation
class OPENVDB_API AffineMap: public MapBase
{
public:
typedef boost::shared_ptr<AffineMap> Ptr;
typedef boost::shared_ptr<const AffineMap> ConstPtr;
AffineMap():
mMatrix(Mat4d::identity()),
mMatrixInv(Mat4d::identity()),
mJacobianInv(Mat3d::identity()),
mDeterminant(1),
mVoxelSize(Vec3d(1,1,1)),
mIsDiagonal(true),
mIsIdentity(true)
// the default constructor for translation is zero
{
}
AffineMap(const Mat3d& m)
{
Mat4d mat4(Mat4d::identity());
mat4.setMat3(m);
mMatrix = mat4;
updateAcceleration();
}
AffineMap(const Mat4d& m): mMatrix(m)
{
if (!isAffine(m)) {
OPENVDB_THROW(ArithmeticError,
"Tried to initialize an affine transform from a non-affine 4x4 matrix");
}
updateAcceleration();
}
AffineMap(const AffineMap& other):
MapBase(other),
mMatrix(other.mMatrix),
mMatrixInv(other.mMatrixInv),
mJacobianInv(other.mJacobianInv),
mDeterminant(other.mDeterminant),
mVoxelSize(other.mVoxelSize),
mIsDiagonal(other.mIsDiagonal),
mIsIdentity(other.mIsIdentity)
{
}
/// @brief constructor that merges the matrixes for two affine maps
AffineMap(const AffineMap& first, const AffineMap& second):
mMatrix(first.mMatrix * second.mMatrix)
{
updateAcceleration();
}
~AffineMap() {}
/// Return a MapBase::Ptr to a new AffineMap
static MapBase::Ptr create() { return MapBase::Ptr(new AffineMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new AffineMap(*this)); }
MapBase::Ptr inverseMap() const { return MapBase::Ptr(new AffineMap(mMatrixInv)); }
static bool isRegistered() { return MapRegistry::isRegistered(AffineMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
AffineMap::mapType(),
AffineMap::create);
}
Name type() const { return mapType(); }
static Name mapType() { return Name("AffineMap"); }
/// Return @c true (an AffineMap is always linear).
bool isLinear() const { return true; }
/// Return @c false ( test if this is unitary with translation )
bool hasUniformScale() const
{
Mat3d mat = mMatrix.getMat3();
const double det = mat.det();
if (isApproxEqual(det, double(0))) {
return false;
} else {
mat *= (1.f / pow(std::abs(det),1./3.));
return isUnitary(mat);
}
}
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const AffineMap& other) const
{
// the Mat.eq() is approximate
if (!mMatrix.eq(other.mMatrix)) { return false; }
if (!mMatrixInv.eq(other.mMatrixInv)) { return false; }
return true;
}
bool operator!=(const AffineMap& other) const { return !(*this == other); }
AffineMap& operator=(const AffineMap& other)
{
mMatrix = other.mMatrix;
mMatrixInv = other.mMatrixInv;
mJacobianInv = other.mJacobianInv;
mDeterminant = other.mDeterminant;
mVoxelSize = other.mVoxelSize;
mIsDiagonal = other.mIsDiagonal;
mIsIdentity = other.mIsIdentity;
return *this;
}
/// Return the image of @c in under the map
Vec3d applyMap(const Vec3d& in) const { return in * mMatrix; }
/// Return the pre-image of @c in under the map
Vec3d applyInverseMap(const Vec3d& in) const {return in * mMatrixInv; }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in, const Vec3d&) const { return applyJacobian(in); }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in) const { return mMatrix.transform3x3(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d&) const { return applyInverseJacobian(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in) const { return mMatrixInv.transform3x3(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
/// This tranforms range-space gradients to domain-space gradients
Vec3d applyJT(const Vec3d& in, const Vec3d&) const { return applyJT(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
Vec3d applyJT(const Vec3d& in) const {
const double* m = mMatrix.asPointer();
return Vec3d( m[ 0] * in[0] + m[ 1] * in[1] + m[ 2] * in[2],
m[ 4] * in[0] + m[ 5] * in[1] + m[ 6] * in[2],
m[ 8] * in[0] + m[ 9] * in[1] + m[10] * in[2] );
}
/// Return the transpose of the inverse Jacobian of the map applied to @a in.
Vec3d applyIJT(const Vec3d& in, const Vec3d&) const { return applyIJT(in); }
/// Return the transpose of the inverse Jacobian of the map applied to @c in
Vec3d applyIJT(const Vec3d& in) const { return in * mJacobianInv; }
/// Return the Jacobian Curvature: zero for a linear map
Mat3d applyIJC(const Mat3d& m) const {
return mJacobianInv.transpose()* m * mJacobianInv;
}
Mat3d applyIJC(const Mat3d& in, const Vec3d& , const Vec3d& ) const {
return applyIJC(in);
}
/// Return the determinant of the Jacobian, ignores argument
double determinant(const Vec3d& ) const { return determinant(); }
/// Return the determinant of the Jacobian
double determinant() const { return mDeterminant; }
//@{
/// @brief Return the lengths of the images of the segments
/// (0,0,0)-(1,0,0), (0,0,0)-(0,1,0) and (0,0,0)-(0,0,1).
Vec3d voxelSize() const { return mVoxelSize; }
Vec3d voxelSize(const Vec3d&) const { return voxelSize(); }
//@}
/// Return @c true if the underlying matrix is approximately an identity
bool isIdentity() const { return mIsIdentity; }
/// Return @c true if the underylying matrix is diagonal
bool isDiagonal() const { return mIsDiagonal; }
/// Return @c true if the map is equivalent to a ScaleMap
bool isScale() const { return isDiagonal(); }
/// Return @c true if the map is equivalent to a ScaleTranslateMap
bool isScaleTranslate() const { return math::isDiagonal(mMatrix.getMat3()); }
// Methods that modify the existing affine map
//@{
/// @brief Modify the existing affine map by pre-applying the given operation.
void accumPreRotation(Axis axis, double radians)
{
mMatrix.preRotate(axis, radians);
updateAcceleration();
}
void accumPreScale(const Vec3d& v)
{
mMatrix.preScale(v);
updateAcceleration();
}
void accumPreTranslation(const Vec3d& v)
{
mMatrix.preTranslate(v);
updateAcceleration();
}
void accumPreShear(Axis axis0, Axis axis1, double shear)
{
mMatrix.preShear(axis0, axis1, shear);
updateAcceleration();
}
//@}
//@{
/// @brief Modify the existing affine map by post-applying the given operation.
void accumPostRotation(Axis axis, double radians)
{
mMatrix.postRotate(axis, radians);
updateAcceleration();
}
void accumPostScale(const Vec3d& v)
{
mMatrix.postScale(v);
updateAcceleration();
}
void accumPostTranslation(const Vec3d& v)
{
mMatrix.postTranslate(v);
updateAcceleration();
}
void accumPostShear(Axis axis0, Axis axis1, double shear)
{
mMatrix.postShear(axis0, axis1, shear);
updateAcceleration();
}
//@}
/// read serialization
void read(std::istream& is)
{
mMatrix.read(is);
updateAcceleration();
}
/// write serialization
void write(std::ostream& os) const
{
mMatrix.write(os);
}
/// string serialization, useful for debugging
std::string str() const
{
std::ostringstream buffer;
buffer << " - mat4:\n" << mMatrix.str() << std::endl;
buffer << " - voxel dimensions: " << mVoxelSize << std::endl;
return buffer.str();
}
/// on-demand decomposition of the affine map
boost::shared_ptr<FullyDecomposedMap> createDecomposedMap()
{
return createFullyDecomposedMap(mMatrix);
}
/// Return AffineMap::Ptr to a deep copy of the current AffineMap
AffineMap::Ptr getAffineMap() const { return AffineMap::Ptr(new AffineMap(*this)); }
/// Return AffineMap::Ptr to the inverse of this map
AffineMap::Ptr inverse() const { return AffineMap::Ptr(new AffineMap(mMatrixInv)); }
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropraite operation.
MapBase::Ptr preRotate(double radians, Axis axis = X_AXIS) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr preTranslate(const Vec3d& t) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreTranslation(t);
return boost::static_pointer_cast<MapBase, AffineMap>(affineMap);
}
MapBase::Ptr preScale(const Vec3d& s) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreScale(s);
return boost::static_pointer_cast<MapBase, AffineMap>(affineMap);
}
MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of postfixing the appropraite operation.
MapBase::Ptr postRotate(double radians, Axis axis = X_AXIS) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr postTranslate(const Vec3d& t) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostTranslation(t);
return boost::static_pointer_cast<MapBase, AffineMap>(affineMap);
}
MapBase::Ptr postScale(const Vec3d& s) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostScale(s);
return boost::static_pointer_cast<MapBase, AffineMap>(affineMap);
}
MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
/// Return the matrix representation of this AffineMap
Mat4d getMat4() const { return mMatrix;}
const Mat4d& getConstMat4() const {return mMatrix;}
const Mat3d& getConstJacobianInv() const {return mJacobianInv;}
private:
void updateAcceleration() {
Mat3d mat3 = mMatrix.getMat3();
mDeterminant = mat3.det();
if (std::abs(mDeterminant) < (3.0 * math::Tolerance<double>::value())) {
OPENVDB_THROW(ArithmeticError,
"Tried to initialize an affine transform from a nearly singular matrix");
}
mMatrixInv = mMatrix.inverse();
mJacobianInv = mat3.inverse().transpose();
mIsDiagonal = math::isDiagonal(mMatrix);
mIsIdentity = math::isIdentity(mMatrix);
Vec3d pos = applyMap(Vec3d(0,0,0));
mVoxelSize(0) = (applyMap(Vec3d(1,0,0)) - pos).length();
mVoxelSize(1) = (applyMap(Vec3d(0,1,0)) - pos).length();
mVoxelSize(2) = (applyMap(Vec3d(0,0,1)) - pos).length();
}
// the underlying matrix
Mat4d mMatrix;
// stored for acceleration
Mat4d mMatrixInv;
Mat3d mJacobianInv;
double mDeterminant;
Vec3d mVoxelSize;
bool mIsDiagonal, mIsIdentity;
}; // class AffineMap
////////////////////////////////////////
/// @brief A specialized Affine transform that scales along the principal axis
/// the scaling need not be uniform in the three-directions
class OPENVDB_API ScaleMap: public MapBase
{
public:
typedef boost::shared_ptr<ScaleMap> Ptr;
typedef boost::shared_ptr<const ScaleMap> ConstPtr;
ScaleMap(): MapBase(), mScaleValues(Vec3d(1,1,1)), mVoxelSize(Vec3d(1,1,1)),
mScaleValuesInverse(Vec3d(1,1,1)),
mInvScaleSqr(1,1,1), mInvTwiceScale(0.5,0.5,0.5){}
ScaleMap(const Vec3d& scale):
MapBase(),
mScaleValues(scale),
mVoxelSize(Vec3d(std::abs(scale(0)),std::abs(scale(1)), std::abs(scale(2))))
{
double determinant = scale[0]* scale[1] * scale[2];
if (std::abs(determinant) < 3.0 * math::Tolerance<double>::value()) {
OPENVDB_THROW(ArithmeticError, "Non-zero scale values required");
}
mScaleValuesInverse = 1.0 / mScaleValues;
mInvScaleSqr = mScaleValuesInverse * mScaleValuesInverse;
mInvTwiceScale = mScaleValuesInverse / 2;
}
ScaleMap(const ScaleMap& other):
MapBase(),
mScaleValues(other.mScaleValues),
mVoxelSize(other.mVoxelSize),
mScaleValuesInverse(other.mScaleValuesInverse),
mInvScaleSqr(other.mInvScaleSqr),
mInvTwiceScale(other.mInvTwiceScale)
{
}
~ScaleMap() {}
/// Return a MapBase::Ptr to a new ScaleMap
static MapBase::Ptr create() { return MapBase::Ptr(new ScaleMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new ScaleMap(*this)); }
MapBase::Ptr inverseMap() const { return MapBase::Ptr(new ScaleMap(mScaleValuesInverse)); }
static bool isRegistered() { return MapRegistry::isRegistered(ScaleMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
ScaleMap::mapType(),
ScaleMap::create);
}
Name type() const { return mapType(); }
static Name mapType() { return Name("ScaleMap"); }
/// Return @c true (a ScaleMap is always linear).
bool isLinear() const { return true; }
/// Return @c true if the values have the same magitude (eg. -1, 1, -1 would be a rotation).
bool hasUniformScale() const
{
bool value = isApproxEqual(
std::abs(mScaleValues.x()), std::abs(mScaleValues.y()), double(5e-7));
value = value && isApproxEqual(
std::abs(mScaleValues.x()), std::abs(mScaleValues.z()), double(5e-7));
return value;
}
/// Return the image of @c in under the map
Vec3d applyMap(const Vec3d& in) const
{
return Vec3d(
in.x() * mScaleValues.x(),
in.y() * mScaleValues.y(),
in.z() * mScaleValues.z());
}
/// Return the pre-image of @c in under the map
Vec3d applyInverseMap(const Vec3d& in) const
{
return Vec3d(
in.x() * mScaleValuesInverse.x(),
in.y() * mScaleValuesInverse.y(),
in.z() * mScaleValuesInverse.z());
}
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in, const Vec3d&) const { return applyJacobian(in); }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in) const { return applyMap(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d&) const { return applyInverseJacobian(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in) const { return applyInverseMap(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
/// This tranforms range-space gradients to domain-space gradients
Vec3d applyJT(const Vec3d& in, const Vec3d&) const { return applyJT(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
Vec3d applyJT(const Vec3d& in) const { return applyMap(in); }
/// @brief Return the transpose of the inverse Jacobian of the map applied to @a in.
/// @details Ignores second argument
Vec3d applyIJT(const Vec3d& in, const Vec3d&) const { return applyIJT(in);}
/// Return the transpose of the inverse Jacobian of the map applied to @c in
Vec3d applyIJT(const Vec3d& in) const { return applyInverseMap(in); }
/// Return the Jacobian Curvature: zero for a linear map
Mat3d applyIJC(const Mat3d& in) const
{
Mat3d tmp;
for (int i = 0; i < 3; i++) {
tmp.setRow(i, in.row(i) * mScaleValuesInverse(i));
}
for (int i = 0; i < 3; i++) {
tmp.setCol(i, tmp.col(i) * mScaleValuesInverse(i));
}
return tmp;
}
Mat3d applyIJC(const Mat3d& in, const Vec3d&, const Vec3d&) const { return applyIJC(in); }
/// Return the product of the scale values, ignores argument
double determinant(const Vec3d&) const { return determinant(); }
/// Return the product of the scale values
double determinant() const { return mScaleValues.x() * mScaleValues.y() * mScaleValues.z(); }
/// Return the scale values that define the map
const Vec3d& getScale() const {return mScaleValues;}
/// Return the square of the scale. Used to optimize some finite difference calculations
const Vec3d& getInvScaleSqr() const { return mInvScaleSqr; }
/// Return 1/(2 scale). Used to optimize some finite difference calculations
const Vec3d& getInvTwiceScale() const { return mInvTwiceScale; }
/// Return 1/(scale)
const Vec3d& getInvScale() const { return mScaleValuesInverse; }
//@{
/// @brief Returns the lengths of the images
/// of the segments
/// \f$(0,0,0)-(1,0,0)\f$, \f$(0,0,0)-(0,1,0)\f$, \f$(0,0,0)-(0,0,1)\f$
/// this is equivalent to the absolute values of the scale values
Vec3d voxelSize() const { return mVoxelSize; }
Vec3d voxelSize(const Vec3d&) const { return voxelSize(); }
//@}
/// read serialization
void read(std::istream& is)
{
mScaleValues.read(is);
mVoxelSize.read(is);
mScaleValuesInverse.read(is);
mInvScaleSqr.read(is);
mInvTwiceScale.read(is);
}
/// write serialization
void write(std::ostream& os) const
{
mScaleValues.write(os);
mVoxelSize.write(os);
mScaleValuesInverse.write(os);
mInvScaleSqr.write(os);
mInvTwiceScale.write(os);
}
/// string serialization, useful for debuging
std::string str() const
{
std::ostringstream buffer;
buffer << " - scale: " << mScaleValues << std::endl;
buffer << " - voxel dimensions: " << mVoxelSize << std::endl;
return buffer.str();
}
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const ScaleMap& other) const
{
// ::eq() uses a tolerance
if (!mScaleValues.eq(other.mScaleValues)) { return false; }
return true;
}
bool operator!=(const ScaleMap& other) const { return !(*this == other); }
/// Return a AffineMap equivalent to this map
AffineMap::Ptr getAffineMap() const
{
return AffineMap::Ptr(new AffineMap(math::scale<Mat4d>(mScaleValues)));
}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropraite operation to the existing map
MapBase::Ptr preRotate(double radians, Axis axis) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr preTranslate(const Vec3d& tr) const;
MapBase::Ptr preScale(const Vec3d& v) const;
MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropraite operation to the existing map.
MapBase::Ptr postRotate(double radians, Axis axis) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr postTranslate(const Vec3d& tr) const;
MapBase::Ptr postScale(const Vec3d& v) const;
MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
private:
Vec3d mScaleValues, mVoxelSize, mScaleValuesInverse, mInvScaleSqr, mInvTwiceScale;
}; // class ScaleMap
/// @brief A specialized Affine transform that scales along the principal axis
/// the scaling is uniform in the three-directions
class OPENVDB_API UniformScaleMap: public ScaleMap
{
public:
typedef boost::shared_ptr<UniformScaleMap> Ptr;
typedef boost::shared_ptr<const UniformScaleMap> ConstPtr;
UniformScaleMap(): ScaleMap(Vec3d(1,1,1)) {}
UniformScaleMap(double scale): ScaleMap(Vec3d(scale, scale, scale)) {}
UniformScaleMap(const UniformScaleMap& other): ScaleMap(other) {}
~UniformScaleMap() {}
/// Return a MapBase::Ptr to a new UniformScaleMap
static MapBase::Ptr create() { return MapBase::Ptr(new UniformScaleMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new UniformScaleMap(*this)); }
MapBase::Ptr inverseMap() const
{
const Vec3d& invScale = getInvScale();
return MapBase::Ptr(new UniformScaleMap( invScale[0]));
}
static bool isRegistered() { return MapRegistry::isRegistered(UniformScaleMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
UniformScaleMap::mapType(),
UniformScaleMap::create);
}
Name type() const { return mapType(); }
static Name mapType() { return Name("UniformScaleMap"); }
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const UniformScaleMap& other) const { return ScaleMap::operator==(other); }
bool operator!=(const UniformScaleMap& other) const { return !(*this == other); }
/// Return a MapBase::Ptr to a UniformScaleTraslateMap that is the result of
/// pre-translation on this map
MapBase::Ptr preTranslate(const Vec3d& tr) const;
/// Return a MapBase::Ptr to a UniformScaleTraslateMap that is the result of
/// post-translation on this map
MapBase::Ptr postTranslate(const Vec3d& tr) const;
}; // class UniformScaleMap
////////////////////////////////////////
inline MapBase::Ptr
ScaleMap::preScale(const Vec3d& v) const
{
const Vec3d new_scale(v * mScaleValues);
if (isApproxEqual(new_scale[0],new_scale[1]) && isApproxEqual(new_scale[0],new_scale[2])) {
return MapBase::Ptr(new UniformScaleMap(new_scale[0]));
} else {
return MapBase::Ptr(new ScaleMap(new_scale));
}
}
inline MapBase::Ptr
ScaleMap::postScale(const Vec3d& v) const
{ // pre-post Scale are the same for a scale map
return preScale(v);
}
/// @brief A specialized linear transform that performs a translation
class OPENVDB_API TranslationMap: public MapBase
{
public:
typedef boost::shared_ptr<TranslationMap> Ptr;
typedef boost::shared_ptr<const TranslationMap> ConstPtr;
// default constructor is a translation by zero.
TranslationMap(): MapBase(), mTranslation(Vec3d(0,0,0)) {}
TranslationMap(const Vec3d& t): MapBase(), mTranslation(t) {}
TranslationMap(const TranslationMap& other): MapBase(), mTranslation(other.mTranslation) {}
~TranslationMap() {}
/// Return a MapBase::Ptr to a new TranslationMap
static MapBase::Ptr create() { return MapBase::Ptr(new TranslationMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new TranslationMap(*this)); }
MapBase::Ptr inverseMap() const { return MapBase::Ptr(new TranslationMap(-mTranslation)); }
static bool isRegistered() { return MapRegistry::isRegistered(TranslationMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
TranslationMap::mapType(),
TranslationMap::create);
}
Name type() const { return mapType(); }
static Name mapType() { return Name("TranslationMap"); }
/// Return @c true (a TranslationMap is always linear).
bool isLinear() const { return true; }
/// Return @c false (by convention true)
bool hasUniformScale() const { return true; }
/// Return the image of @c in under the map
Vec3d applyMap(const Vec3d& in) const { return in + mTranslation; }
/// Return the pre-image of @c in under the map
Vec3d applyInverseMap(const Vec3d& in) const { return in - mTranslation; }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in, const Vec3d&) const { return applyJacobian(in); }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in) const { return in; }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d&) const { return applyInverseJacobian(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in) const { return in; }
/// Return the Jacobian Transpose of the map applied to @a in.
/// This tranforms range-space gradients to domain-space gradients
Vec3d applyJT(const Vec3d& in, const Vec3d&) const { return applyJT(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
Vec3d applyJT(const Vec3d& in) const { return in; }
/// @brief Return the transpose of the inverse Jacobian (Identity for TranslationMap)
/// of the map applied to @c in, ignores second argument
Vec3d applyIJT(const Vec3d& in, const Vec3d& ) const { return applyIJT(in);}
/// @brief Return the transpose of the inverse Jacobian (Identity for TranslationMap)
/// of the map applied to @c in
Vec3d applyIJT(const Vec3d& in) const {return in;}
/// Return the Jacobian Curvature: zero for a linear map
Mat3d applyIJC(const Mat3d& mat) const {return mat;}
Mat3d applyIJC(const Mat3d& mat, const Vec3d&, const Vec3d&) const { return applyIJC(mat); }
/// Return @c 1
double determinant(const Vec3d& ) const { return determinant(); }
/// Return @c 1
double determinant() const { return 1.0; }
/// Return \f$ (1,1,1) \f$
Vec3d voxelSize() const { return Vec3d(1,1,1);}
/// Return \f$ (1,1,1) \f$
Vec3d voxelSize(const Vec3d&) const { return voxelSize();}
/// Return the translation vector
const Vec3d& getTranslation() const { return mTranslation; }
/// read serialization
void read(std::istream& is) { mTranslation.read(is); }
/// write serialization
void write(std::ostream& os) const { mTranslation.write(os); }
/// string serialization, useful for debuging
std::string str() const
{
std::ostringstream buffer;
buffer << " - translation: " << mTranslation << std::endl;
return buffer.str();
}
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const TranslationMap& other) const
{
// ::eq() uses a tolerance
return mTranslation.eq(other.mTranslation);
}
bool operator!=(const TranslationMap& other) const { return !(*this == other); }
/// Return AffineMap::Ptr to an AffineMap equivalent to *this
AffineMap::Ptr getAffineMap() const
{
Mat4d matrix(Mat4d::identity());
matrix.setTranslation(mTranslation);
AffineMap::Ptr affineMap(new AffineMap(matrix));
return affineMap;
}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropriate operation.
MapBase::Ptr preRotate(double radians, Axis axis) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr preTranslate(const Vec3d& t) const
{
return MapBase::Ptr(new TranslationMap(t + mTranslation));
}
MapBase::Ptr preScale(const Vec3d& v) const;
MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of postfixing the appropriate operation.
MapBase::Ptr postRotate(double radians, Axis axis) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr postTranslate(const Vec3d& t) const
{ // post and pre are the same for this
return MapBase::Ptr(new TranslationMap(t + mTranslation));
}
MapBase::Ptr postScale(const Vec3d& v) const;
MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
private:
Vec3d mTranslation;
}; // class TranslationMap
////////////////////////////////////////
/// @brief A specialized Affine transform that scales along the principal axis
/// the scaling need not be uniform in the three-directions, and then
/// translates the result.
class OPENVDB_API ScaleTranslateMap: public MapBase
{
public:
typedef boost::shared_ptr<ScaleTranslateMap> Ptr;
typedef boost::shared_ptr<const ScaleTranslateMap> ConstPtr;
ScaleTranslateMap():
MapBase(),
mTranslation(Vec3d(0,0,0)),
mScaleValues(Vec3d(1,1,1)),
mVoxelSize(Vec3d(1,1,1)),
mScaleValuesInverse(Vec3d(1,1,1)),
mInvScaleSqr(1,1,1),
mInvTwiceScale(0.5,0.5,0.5)
{
}
ScaleTranslateMap(const Vec3d& scale, const Vec3d& translate):
MapBase(),
mTranslation(translate),
mScaleValues(scale),
mVoxelSize(std::abs(scale(0)), std::abs(scale(1)), std::abs(scale(2)))
{
const double determinant = scale[0]* scale[1] * scale[2];
if (std::abs(determinant) < 3.0 * math::Tolerance<double>::value()) {
OPENVDB_THROW(ArithmeticError, "Non-zero scale values required");
}
mScaleValuesInverse = 1.0 / mScaleValues;
mInvScaleSqr = mScaleValuesInverse * mScaleValuesInverse;
mInvTwiceScale = mScaleValuesInverse / 2;
}
ScaleTranslateMap(const ScaleMap& scale, const TranslationMap& translate):
MapBase(),
mTranslation(translate.getTranslation()),
mScaleValues(scale.getScale()),
mVoxelSize(std::abs(mScaleValues(0)),
std::abs(mScaleValues(1)),
std::abs(mScaleValues(2))),
mScaleValuesInverse(1.0 / scale.getScale())
{
mInvScaleSqr = mScaleValuesInverse * mScaleValuesInverse;
mInvTwiceScale = mScaleValuesInverse / 2;
}
ScaleTranslateMap(const ScaleTranslateMap& other):
MapBase(),
mTranslation(other.mTranslation),
mScaleValues(other.mScaleValues),
mVoxelSize(other.mVoxelSize),
mScaleValuesInverse(other.mScaleValuesInverse),
mInvScaleSqr(other.mInvScaleSqr),
mInvTwiceScale(other.mInvTwiceScale)
{}
~ScaleTranslateMap() {}
/// Return a MapBase::Ptr to a new ScaleTranslateMap
static MapBase::Ptr create() { return MapBase::Ptr(new ScaleTranslateMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new ScaleTranslateMap(*this)); }
MapBase::Ptr inverseMap() const
{
return MapBase::Ptr(new ScaleTranslateMap(
mScaleValuesInverse, -mScaleValuesInverse * mTranslation));
}
static bool isRegistered() { return MapRegistry::isRegistered(ScaleTranslateMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
ScaleTranslateMap::mapType(),
ScaleTranslateMap::create);
}
Name type() const { return mapType(); }
static Name mapType() { return Name("ScaleTranslateMap"); }
/// Return @c true (a ScaleTranslateMap is always linear).
bool isLinear() const { return true; }
/// @brief Return @c true if the scale values have the same magnitude
/// (eg. -1, 1, -1 would be a rotation).
bool hasUniformScale() const
{
bool value = isApproxEqual(
std::abs(mScaleValues.x()), std::abs(mScaleValues.y()), double(5e-7));
value = value && isApproxEqual(
std::abs(mScaleValues.x()), std::abs(mScaleValues.z()), double(5e-7));
return value;
}
/// Return the image of @c under the map
Vec3d applyMap(const Vec3d& in) const
{
return Vec3d(
in.x() * mScaleValues.x() + mTranslation.x(),
in.y() * mScaleValues.y() + mTranslation.y(),
in.z() * mScaleValues.z() + mTranslation.z());
}
/// Return the pre-image of @c under the map
Vec3d applyInverseMap(const Vec3d& in) const
{
return Vec3d(
(in.x() - mTranslation.x() ) * mScaleValuesInverse.x(),
(in.y() - mTranslation.y() ) * mScaleValuesInverse.y(),
(in.z() - mTranslation.z() ) * mScaleValuesInverse.z());
}
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in, const Vec3d&) const { return applyJacobian(in); }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in) const { return in * mScaleValues; }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d&) const { return applyInverseJacobian(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in) const { return in * mScaleValuesInverse; }
/// Return the Jacobian Transpose of the map applied to @a in.
/// This tranforms range-space gradients to domain-space gradients
Vec3d applyJT(const Vec3d& in, const Vec3d&) const { return applyJT(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
Vec3d applyJT(const Vec3d& in) const { return applyJacobian(in); }
/// @brief Return the transpose of the inverse Jacobian of the map applied to @a in
/// @details Ignores second argument
Vec3d applyIJT(const Vec3d& in, const Vec3d& ) const { return applyIJT(in);}
/// Return the transpose of the inverse Jacobian of the map applied to @c in
Vec3d applyIJT(const Vec3d& in) const
{
return Vec3d(
in.x() * mScaleValuesInverse.x(),
in.y() * mScaleValuesInverse.y(),
in.z() * mScaleValuesInverse.z());
}
/// Return the Jacobian Curvature: zero for a linear map
Mat3d applyIJC(const Mat3d& in) const
{
Mat3d tmp;
for (int i=0; i<3; i++){
tmp.setRow(i, in.row(i)*mScaleValuesInverse(i));
}
for (int i=0; i<3; i++){
tmp.setCol(i, tmp.col(i)*mScaleValuesInverse(i));
}
return tmp;
}
Mat3d applyIJC(const Mat3d& in, const Vec3d&, const Vec3d& ) const { return applyIJC(in); }
/// Return the product of the scale values, ignores argument
double determinant(const Vec3d& ) const { return determinant(); }
/// Return the product of the scale values
double determinant() const { return mScaleValues.x()*mScaleValues.y()*mScaleValues.z(); }
/// Return the absolute values of the scale values
Vec3d voxelSize() const { return mVoxelSize;}
/// Return the absolute values of the scale values, ignores
///argument
Vec3d voxelSize(const Vec3d&) const { return voxelSize();}
/// Returns the scale values
const Vec3d& getScale() const { return mScaleValues; }
/// Returns the translation
const Vec3d& getTranslation() const { return mTranslation; }
/// Return the square of the scale. Used to optimize some finite difference calculations
const Vec3d& getInvScaleSqr() const {return mInvScaleSqr;}
/// Return 1/(2 scale). Used to optimize some finite difference calculations
const Vec3d& getInvTwiceScale() const {return mInvTwiceScale;}
/// Return 1/(scale)
const Vec3d& getInvScale() const {return mScaleValuesInverse; }
/// read serialization
void read(std::istream& is)
{
mTranslation.read(is);
mScaleValues.read(is);
mVoxelSize.read(is);
mScaleValuesInverse.read(is);
mInvScaleSqr.read(is);
mInvTwiceScale.read(is);
}
/// write serialization
void write(std::ostream& os) const
{
mTranslation.write(os);
mScaleValues.write(os);
mVoxelSize.write(os);
mScaleValuesInverse.write(os);
mInvScaleSqr.write(os);
mInvTwiceScale.write(os);
}
/// string serialization, useful for debuging
std::string str() const
{
std::ostringstream buffer;
buffer << " - translation: " << mTranslation << std::endl;
buffer << " - scale: " << mScaleValues << std::endl;
buffer << " - voxel dimensions: " << mVoxelSize << std::endl;
return buffer.str();
}
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const ScaleTranslateMap& other) const
{
// ::eq() uses a tolerance
if (!mScaleValues.eq(other.mScaleValues)) { return false; }
if (!mTranslation.eq(other.mTranslation)) { return false; }
return true;
}
bool operator!=(const ScaleTranslateMap& other) const { return !(*this == other); }
/// Return AffineMap::Ptr to an AffineMap equivalent to *this
AffineMap::Ptr getAffineMap() const
{
AffineMap::Ptr affineMap(new AffineMap(math::scale<Mat4d>(mScaleValues)));
affineMap->accumPostTranslation(mTranslation);
return affineMap;
}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropraite operation.
MapBase::Ptr preRotate(double radians, Axis axis) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr preTranslate(const Vec3d& t) const
{
const Vec3d& s = mScaleValues;
const Vec3d scaled_trans( t.x() * s.x(),
t.y() * s.y(),
t.z() * s.z() );
return MapBase::Ptr( new ScaleTranslateMap(mScaleValues, mTranslation + scaled_trans));
}
MapBase::Ptr preScale(const Vec3d& v) const;
MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of postfixing the appropraite operation.
MapBase::Ptr postRotate(double radians, Axis axis) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostRotation(axis, radians);
return simplify(affineMap);
}
MapBase::Ptr postTranslate(const Vec3d& t) const
{
return MapBase::Ptr( new ScaleTranslateMap(mScaleValues, mTranslation + t));
}
MapBase::Ptr postScale(const Vec3d& v) const;
MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
private:
Vec3d mTranslation, mScaleValues, mVoxelSize, mScaleValuesInverse,
mInvScaleSqr, mInvTwiceScale;
}; // class ScaleTanslateMap
inline MapBase::Ptr
ScaleMap::postTranslate(const Vec3d& t) const
{
return MapBase::Ptr(new ScaleTranslateMap(mScaleValues, t));
}
inline MapBase::Ptr
ScaleMap::preTranslate(const Vec3d& t) const
{
const Vec3d& s = mScaleValues;
const Vec3d scaled_trans( t.x() * s.x(),
t.y() * s.y(),
t.z() * s.z() );
return MapBase::Ptr(new ScaleTranslateMap(mScaleValues, scaled_trans));
}
/// @brief A specialized Affine transform that uniformaly scales along the principal axis
/// and then translates the result.
class OPENVDB_API UniformScaleTranslateMap: public ScaleTranslateMap
{
public:
typedef boost::shared_ptr<UniformScaleTranslateMap> Ptr;
typedef boost::shared_ptr<const UniformScaleTranslateMap> ConstPtr;
UniformScaleTranslateMap():ScaleTranslateMap(Vec3d(1,1,1), Vec3d(0,0,0)) {}
UniformScaleTranslateMap(double scale, const Vec3d& translate):
ScaleTranslateMap(Vec3d(scale,scale,scale), translate) {}
UniformScaleTranslateMap(const UniformScaleMap& scale, const TranslationMap& translate):
ScaleTranslateMap(scale.getScale(), translate.getTranslation()) {}
UniformScaleTranslateMap(const UniformScaleTranslateMap& other):ScaleTranslateMap(other) {}
~UniformScaleTranslateMap() {}
/// Return a MapBase::Ptr to a new UniformScaleTranslateMap
static MapBase::Ptr create() { return MapBase::Ptr(new UniformScaleTranslateMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new UniformScaleTranslateMap(*this)); }
MapBase::Ptr inverseMap() const
{
const Vec3d& scaleInv = getInvScale();
const Vec3d& trans = getTranslation();
return MapBase::Ptr(new UniformScaleTranslateMap(scaleInv[0], -scaleInv[0] * trans));
}
static bool isRegistered()
{
return MapRegistry::isRegistered(UniformScaleTranslateMap::mapType());
}
static void registerMap()
{
MapRegistry::registerMap(
UniformScaleTranslateMap::mapType(),
UniformScaleTranslateMap::create);
}
Name type() const { return mapType(); }
static Name mapType() { return Name("UniformScaleTranslateMap"); }
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const UniformScaleTranslateMap& other) const
{
return ScaleTranslateMap::operator==(other);
}
bool operator!=(const UniformScaleTranslateMap& other) const { return !(*this == other); }
/// @brief Return a MapBase::Ptr to a UniformScaleTranslateMap that is
/// the result of prepending translation on this map.
MapBase::Ptr preTranslate(const Vec3d& t) const
{
const double scale = this->getScale().x();
const Vec3d new_trans = this->getTranslation() + scale * t;
return MapBase::Ptr( new UniformScaleTranslateMap(scale, new_trans));
}
/// @brief Return a MapBase::Ptr to a UniformScaleTranslateMap that is
/// the result of postfixing translation on this map.
MapBase::Ptr postTranslate(const Vec3d& t) const
{
const double scale = this->getScale().x();
return MapBase::Ptr( new UniformScaleTranslateMap(scale, this->getTranslation() + t));
}
}; // class UniformScaleTanslateMap
inline MapBase::Ptr
UniformScaleMap::postTranslate(const Vec3d& t) const
{
const double scale = this->getScale().x();
return MapBase::Ptr(new UniformScaleTranslateMap(scale, t));
}
inline MapBase::Ptr
UniformScaleMap::preTranslate(const Vec3d& t) const
{
const double scale = this->getScale().x();
return MapBase::Ptr(new UniformScaleTranslateMap(scale, scale*t));
}
inline MapBase::Ptr
TranslationMap::preScale(const Vec3d& v) const
{
if (isApproxEqual(v[0],v[1]) && isApproxEqual(v[0],v[2])) {
return MapBase::Ptr(new UniformScaleTranslateMap(v[0], mTranslation));
} else {
return MapBase::Ptr(new ScaleTranslateMap(v, mTranslation));
}
}
inline MapBase::Ptr
TranslationMap::postScale(const Vec3d& v) const
{
if (isApproxEqual(v[0],v[1]) && isApproxEqual(v[0],v[2])) {
return MapBase::Ptr(new UniformScaleTranslateMap(v[0], v[0]*mTranslation));
} else {
const Vec3d trans(mTranslation.x()*v.x(),
mTranslation.y()*v.y(),
mTranslation.z()*v.z());
return MapBase::Ptr(new ScaleTranslateMap(v, trans));
}
}
inline MapBase::Ptr
ScaleTranslateMap::preScale(const Vec3d& v) const
{
const Vec3d new_scale( v * mScaleValues );
if (isApproxEqual(new_scale[0],new_scale[1]) && isApproxEqual(new_scale[0],new_scale[2])) {
return MapBase::Ptr( new UniformScaleTranslateMap(new_scale[0], mTranslation));
} else {
return MapBase::Ptr( new ScaleTranslateMap(new_scale, mTranslation));
}
}
inline MapBase::Ptr
ScaleTranslateMap::postScale(const Vec3d& v) const
{
const Vec3d new_scale( v * mScaleValues );
const Vec3d new_trans( mTranslation.x()*v.x(),
mTranslation.y()*v.y(),
mTranslation.z()*v.z() );
if (isApproxEqual(new_scale[0],new_scale[1]) && isApproxEqual(new_scale[0],new_scale[2])) {
return MapBase::Ptr( new UniformScaleTranslateMap(new_scale[0], new_trans));
} else {
return MapBase::Ptr( new ScaleTranslateMap(new_scale, new_trans));
}
}
////////////////////////////////////////
/// @brief A specialized linear transform that performs a unitary maping
/// i.e. rotation and or reflection.
class OPENVDB_API UnitaryMap: public MapBase
{
public:
typedef boost::shared_ptr<UnitaryMap> Ptr;
typedef boost::shared_ptr<const UnitaryMap> ConstPtr;
/// default constructor makes an Idenity.
UnitaryMap(): mAffineMap(Mat4d::identity())
{
}
UnitaryMap(const Vec3d& axis, double radians)
{
Mat3d matrix;
matrix.setToRotation(axis, radians);
mAffineMap = AffineMap(matrix);
}
UnitaryMap(Axis axis, double radians)
{
Mat4d matrix;
matrix.setToRotation(axis, radians);
mAffineMap = AffineMap(matrix);
}
UnitaryMap(const Mat3d& m)
{
// test that the mat3 is a rotation || reflection
if (!isUnitary(m)) {
OPENVDB_THROW(ArithmeticError, "Matrix initializing unitary map was not unitary");
}
Mat4d matrix(Mat4d::identity());
matrix.setMat3(m);
mAffineMap = AffineMap(matrix);
}
UnitaryMap(const Mat4d& m)
{
if (!isInvertible(m)) {
OPENVDB_THROW(ArithmeticError,
"4x4 Matrix initializing unitary map was not unitary: not invertible");
}
if (!isAffine(m)) {
OPENVDB_THROW(ArithmeticError,
"4x4 Matrix initializing unitary map was not unitary: not affine");
}
if (hasTranslation(m)) {
OPENVDB_THROW(ArithmeticError,
"4x4 Matrix initializing unitary map was not unitary: had translation");
}
if (!isUnitary(m.getMat3())) {
OPENVDB_THROW(ArithmeticError,
"4x4 Matrix initializing unitary map was not unitary");
}
mAffineMap = AffineMap(m);
}
UnitaryMap(const UnitaryMap& other):
MapBase(other),
mAffineMap(other.mAffineMap)
{
}
UnitaryMap(const UnitaryMap& first, const UnitaryMap& second):
mAffineMap(*(first.getAffineMap()), *(second.getAffineMap()))
{
}
~UnitaryMap() {}
/// Return a MapBase::Ptr to a new UnitaryMap
static MapBase::Ptr create() { return MapBase::Ptr(new UnitaryMap()); }
/// Returns a MapBase::Ptr to a deep copy of *this
MapBase::Ptr copy() const { return MapBase::Ptr(new UnitaryMap(*this)); }
MapBase::Ptr inverseMap() const
{
return MapBase::Ptr(new UnitaryMap(mAffineMap.getMat4().inverse()));
}
static bool isRegistered() { return MapRegistry::isRegistered(UnitaryMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
UnitaryMap::mapType(),
UnitaryMap::create);
}
/// Return @c UnitaryMap
Name type() const { return mapType(); }
/// Return @c UnitaryMap
static Name mapType() { return Name("UnitaryMap"); }
/// Return @c true (a UnitaryMap is always linear).
bool isLinear() const { return true; }
/// Return @c false (by convention true)
bool hasUniformScale() const { return true; }
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const UnitaryMap& other) const
{
// compare underlying linear map.
if (mAffineMap!=other.mAffineMap) return false;
return true;
}
bool operator!=(const UnitaryMap& other) const { return !(*this == other); }
/// Return the image of @c in under the map
Vec3d applyMap(const Vec3d& in) const { return mAffineMap.applyMap(in); }
/// Return the pre-image of @c in under the map
Vec3d applyInverseMap(const Vec3d& in) const { return mAffineMap.applyInverseMap(in); }
Vec3d applyJacobian(const Vec3d& in, const Vec3d&) const { return applyJacobian(in); }
/// Return the Jacobian of the map applied to @a in.
Vec3d applyJacobian(const Vec3d& in) const { return mAffineMap.applyJacobian(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d&) const { return applyInverseJacobian(in); }
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in) const { return mAffineMap.applyInverseJacobian(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
/// This tranforms range-space gradients to domain-space gradients
Vec3d applyJT(const Vec3d& in, const Vec3d&) const { return applyJT(in); }
/// Return the Jacobian Transpose of the map applied to @a in.
Vec3d applyJT(const Vec3d& in) const {
// The transpose of the unitary map is its inverse
return applyInverseMap(in);
}
/// @brief Return the transpose of the inverse Jacobian of the map applied to @a in
/// @details Ignores second argument
Vec3d applyIJT(const Vec3d& in, const Vec3d& ) const { return applyIJT(in);}
/// Return the transpose of the inverse Jacobian of the map applied to @c in
Vec3d applyIJT(const Vec3d& in) const { return mAffineMap.applyIJT(in); }
/// Return the Jacobian Curvature: zero for a linear map
Mat3d applyIJC(const Mat3d& in) const { return mAffineMap.applyIJC(in); }
Mat3d applyIJC(const Mat3d& in, const Vec3d&, const Vec3d& ) const { return applyIJC(in); }
/// Return the determinant of the Jacobian, ignores argument
double determinant(const Vec3d& ) const { return determinant(); }
/// Return the determinant of the Jacobian
double determinant() const { return mAffineMap.determinant(); }
/// @brief Returns the lengths of the images
/// of the segments
/// \f$(0,0,0)-(1,0,0)\f$, \f$(0,0,0)-(0,1,0)\f$,
/// \f$(0,0,0)-(0,0,1)\f$
Vec3d voxelSize() const { return mAffineMap.voxelSize();}
Vec3d voxelSize(const Vec3d&) const { return voxelSize();}
/// read serialization
void read(std::istream& is)
{
mAffineMap.read(is);
}
/// write serialization
void write(std::ostream& os) const
{
mAffineMap.write(os);
}
/// string serialization, useful for debuging
std::string str() const
{
std::ostringstream buffer;
buffer << mAffineMap.str();
return buffer.str();
}
/// Return AffineMap::Ptr to an AffineMap equivalent to *this
AffineMap::Ptr getAffineMap() const { return AffineMap::Ptr(new AffineMap(mAffineMap)); }
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropraite operation.
MapBase::Ptr preRotate(double radians, Axis axis) const
{
UnitaryMap first(axis, radians);
UnitaryMap::Ptr unitaryMap(new UnitaryMap(first, *this));
return boost::static_pointer_cast<MapBase, UnitaryMap>(unitaryMap);
}
MapBase::Ptr preTranslate(const Vec3d& t) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreTranslation(t);
return simplify(affineMap);
}
MapBase::Ptr preScale(const Vec3d& v) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreScale(v);
return simplify(affineMap);
}
MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPreShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of postfixing the appropraite operation.
MapBase::Ptr postRotate(double radians, Axis axis) const
{
UnitaryMap second(axis, radians);
UnitaryMap::Ptr unitaryMap(new UnitaryMap(*this, second));
return boost::static_pointer_cast<MapBase, UnitaryMap>(unitaryMap);
}
MapBase::Ptr postTranslate(const Vec3d& t) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostTranslation(t);
return simplify(affineMap);
}
MapBase::Ptr postScale(const Vec3d& v) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostScale(v);
return simplify(affineMap);
}
MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const
{
AffineMap::Ptr affineMap = getAffineMap();
affineMap->accumPostShear(axis0, axis1, shear);
return simplify(affineMap);
}
//@}
private:
AffineMap mAffineMap;
}; // class UnitaryMap
////////////////////////////////////////
/// @brief This map is composed of three steps.
/// First it will take a box of size (Lx X Ly X Lz) defined by a member data bounding box
/// and map it into a frustum with near plane (1 X Ly/Lx) and prescribed depth
/// Then this frustum is transformed by an internal second map: most often a uniform scale,
/// but other effects can be achieved by accumulating translation, shear and rotation: these
/// are all applied to the second map
class OPENVDB_API NonlinearFrustumMap: public MapBase
{
public:
typedef boost::shared_ptr<NonlinearFrustumMap> Ptr;
typedef boost::shared_ptr<const NonlinearFrustumMap> ConstPtr;
NonlinearFrustumMap():
MapBase(),
mBBox(Vec3d(0), Vec3d(1)),
mTaper(1),
mDepth(1)
{
init();
}
/// @brief Constructor that takes an index-space bounding box
/// to be mapped into a frustum with a given @a depth and @a taper
/// (defined as ratio of nearplane/farplane).
NonlinearFrustumMap(const BBoxd& bb, double taper, double depth):
MapBase(),mBBox(bb), mTaper(taper), mDepth(depth)
{
init();
}
/// @brief Constructor that takes an index-space bounding box
/// to be mapped into a frustum with a given @a depth and @a taper
/// (defined as ratio of nearplane/farplane).
/// @details This frustum is further modifed by the @a secondMap,
/// intended to be a simple translation and rotation and uniform scale
NonlinearFrustumMap(const BBoxd& bb, double taper, double depth,
const MapBase::Ptr& secondMap):
mBBox(bb), mTaper(taper), mDepth(depth)
{
if (!secondMap->isLinear() ) {
OPENVDB_THROW(ArithmeticError,
"The second map in the Frustum transfrom must be linear");
}
mSecondMap = *( secondMap->getAffineMap() );
init();
}
NonlinearFrustumMap(const NonlinearFrustumMap& other):
MapBase(),
mBBox(other.mBBox),
mTaper(other.mTaper),
mDepth(other.mDepth),
mSecondMap(other.mSecondMap),
mHasSimpleAffine(other.mHasSimpleAffine)
{
init();
}
/// @brief Constructor from a camera frustum
///
/// @param position the tip of the frustum (i.e., the camera's position).
/// @param direction a vector pointing from @a position toward the near plane.
/// @param up a non-unit vector describing the direction and extent of
/// the frustum's intersection on the near plane. Together,
/// @a up must be orthogonal to @a direction.
/// @param aspect the aspect ratio of the frustum intersection with near plane
/// defined as width / height
/// @param z_near,depth the distance from @a position along @a direction to the
/// near and far planes of the frustum.
/// @param x_count the number of voxels, aligned with @a left,
/// across the face of the frustum
/// @param z_count the number of voxels, aligned with @a direction,
/// between the near and far planes
NonlinearFrustumMap(const Vec3d& position,
const Vec3d& direction,
const Vec3d& up,
double aspect /* width / height */,
double z_near, double depth,
Coord::ValueType x_count, Coord::ValueType z_count) {
/// @todo check that depth > 0
/// @todo check up.length > 0
/// @todo check that direction dot up = 0
if (!(depth > 0)) {
OPENVDB_THROW(ArithmeticError,
"The frustum depth must be non-zero and positive");
}
if (!(up.length() > 0)) {
OPENVDB_THROW(ArithmeticError,
"The frustum height must be non-zero and positive");
}
if (!(aspect > 0)) {
OPENVDB_THROW(ArithmeticError,
"The frustum aspect ratio must be non-zero and positive");
}
if (!(isApproxEqual(up.dot(direction), 0.))) {
OPENVDB_THROW(ArithmeticError,
"The frustum up orientation must be perpendicular to into-frustum direction");
}
double near_plane_height = 2 * up.length();
double near_plane_width = aspect * near_plane_height;
Coord::ValueType y_count = static_cast<int>(Round(x_count / aspect));
mBBox = BBoxd(Vec3d(0,0,0), Vec3d(x_count, y_count, z_count));
mDepth = depth / near_plane_width; // depth non-dimensionalized on width
double gamma = near_plane_width / z_near;
mTaper = 1./(mDepth*gamma + 1.);
Vec3d direction_unit = direction;
direction_unit.normalize();
Mat4d r1(Mat4d::identity());
r1.setToRotation(/*from*/Vec3d(0,0,1), /*to */direction_unit);
Mat4d r2(Mat4d::identity());
Vec3d temp = r1.inverse().transform(up);
r2.setToRotation(/*from*/Vec3d(0,1,0), /*to*/temp );
Mat4d scale = math::scale<Mat4d>(
Vec3d(near_plane_width, near_plane_width, near_plane_width));
// move the near plane to origin, rotate to align with axis, and scale down
// T_inv * R1_inv * R2_inv * scale_inv
Mat4d mat = scale * r2 * r1;
mat.setTranslation(position + z_near*direction_unit);
mSecondMap = AffineMap(mat);
init();
}
~NonlinearFrustumMap(){}
/// Return a MapBase::Ptr to a new NonlinearFrustumMap
static MapBase::Ptr create() { return MapBase::Ptr(new NonlinearFrustumMap()); }
/// Return a MapBase::Ptr to a deep copy of this map
MapBase::Ptr copy() const { return MapBase::Ptr(new NonlinearFrustumMap(*this)); }
/// @brief Not implemented, since there is currently no map type that can
/// represent the inverse of a frustum
/// @throw NotImplementedError
MapBase::Ptr inverseMap() const
{
OPENVDB_THROW(NotImplementedError,
"inverseMap() is not implemented for NonlinearFrustumMap");
}
static bool isRegistered() { return MapRegistry::isRegistered(NonlinearFrustumMap::mapType()); }
static void registerMap()
{
MapRegistry::registerMap(
NonlinearFrustumMap::mapType(),
NonlinearFrustumMap::create);
}
/// Return @c NonlinearFrustumMap
Name type() const { return mapType(); }
/// Return @c NonlinearFrustumMap
static Name mapType() { return Name("NonlinearFrustumMap"); }
/// Return @c false (a NonlinearFrustumMap is never linear).
bool isLinear() const { return false; }
/// Return @c false (by convention false)
bool hasUniformScale() const { return false; }
/// Return @c true if the map is equivalent to an identity
bool isIdentity() const
{
// The frustum can only be consistent with a linear map if the taper value is 1
if (!isApproxEqual(mTaper, double(1)) ) return false;
// There are various ways an identity can decomposed between the two parts of the
// map. Best to just check that the principle vectors are stationary.
const Vec3d e1(1,0,0);
if (!applyMap(e1).eq(e1)) return false;
const Vec3d e2(0,1,0);
if (!applyMap(e2).eq(e2)) return false;
const Vec3d e3(0,0,1);
if (!applyMap(e3).eq(e3)) return false;
return true;
}
virtual bool isEqual(const MapBase& other) const { return isEqualBase(*this, other); }
bool operator==(const NonlinearFrustumMap& other) const
{
if (mBBox!=other.mBBox) return false;
if (!isApproxEqual(mTaper, other.mTaper)) return false;
if (!isApproxEqual(mDepth, other.mDepth)) return false;
// Two linear transforms are equivalent iff they have the same translation
// and have the same affects on orthongal spanning basis check translation
Vec3d e(0,0,0);
if (!mSecondMap.applyMap(e).eq(other.mSecondMap.applyMap(e))) return false;
/// check spanning vectors
e(0) = 1;
if (!mSecondMap.applyMap(e).eq(other.mSecondMap.applyMap(e))) return false;
e(0) = 0;
e(1) = 1;
if (!mSecondMap.applyMap(e).eq(other.mSecondMap.applyMap(e))) return false;
e(1) = 0;
e(2) = 1;
if (!mSecondMap.applyMap(e).eq(other.mSecondMap.applyMap(e))) return false;
return true;
}
bool operator!=(const NonlinearFrustumMap& other) const { return !(*this == other); }
/// Return the image of @c in under the map
Vec3d applyMap(const Vec3d& in) const
{
return mSecondMap.applyMap(applyFrustumMap(in));
}
/// Return the pre-image of @c in under the map
Vec3d applyInverseMap(const Vec3d& in) const
{
return applyFrustumInverseMap(mSecondMap.applyInverseMap(in));
}
/// Return the Jacobian of the linear second map applied to @c in
Vec3d applyJacobian(const Vec3d& in) const { return mSecondMap.applyJacobian(in); }
/// Return the Jacobian defined at @c isloc applied to @c in
Vec3d applyJacobian(const Vec3d& in, const Vec3d& isloc) const
{
// Move the center of the x-face of the bbox
// to the origin in index space.
Vec3d centered(isloc);
centered = centered - mBBox.min();
centered.x() -= mXo;
centered.y() -= mYo;
// scale the z-direction on depth / K count
const double zprime = centered.z()*mDepthOnLz;
const double scale = (mGamma * zprime + 1.) / mLx;
const double scale2 = mGamma * mDepthOnLz / mLx;
const Vec3d tmp(scale * in.x() + scale2 * centered.x()* in.z(),
scale * in.y() + scale2 * centered.y()* in.z(),
mDepthOnLz * in.z());
return mSecondMap.applyJacobian(tmp);
}
/// Return the Inverse Jacobian of the map applied to @a in. (i.e. inverse map with out translation)
Vec3d applyInverseJacobian(const Vec3d& in) const { return mSecondMap.applyInverseJacobian(in); }
/// Return the Inverse Jacobian defined at @c isloc of the map applied to @a in.
Vec3d applyInverseJacobian(const Vec3d& in, const Vec3d& isloc) const {
// Move the center of the x-face of the bbox
// to the origin in index space.
Vec3d centered(isloc);
centered = centered - mBBox.min();
centered.x() -= mXo;
centered.y() -= mYo;
// scale the z-direction on depth / K count
const double zprime = centered.z()*mDepthOnLz;
const double scale = (mGamma * zprime + 1.) / mLx;
const double scale2 = mGamma * mDepthOnLz / mLx;
Vec3d out = mSecondMap.applyInverseJacobian(in);
out.x() = (out.x() - scale2 * centered.x() * out.z() / mDepthOnLz) / scale;
out.y() = (out.y() - scale2 * centered.y() * out.z() / mDepthOnLz) / scale;
out.z() = out.z() / mDepthOnLz;
return out;
}
/// Return the Jacobian Transpose of the map applied to vector @c in at @c indexloc.
/// This tranforms range-space gradients to domain-space gradients.
///
Vec3d applyJT(const Vec3d& in, const Vec3d& isloc) const {
const Vec3d tmp = mSecondMap.applyJT(in);
// Move the center of the x-face of the bbox
// to the origin in index space.
Vec3d centered(isloc);
centered = centered - mBBox.min();
centered.x() -= mXo;
centered.y() -= mYo;
// scale the z-direction on depth / K count
const double zprime = centered.z()*mDepthOnLz;
const double scale = (mGamma * zprime + 1.) / mLx;
const double scale2 = mGamma * mDepthOnLz / mLx;
return Vec3d(scale * tmp.x(),
scale * tmp.y(),
scale2 * centered.x()* tmp.x() +
scale2 * centered.y()* tmp.y() +
mDepthOnLz * tmp.z());
}
/// Return the Jacobian Transpose of the second map applied to @c in.
Vec3d applyJT(const Vec3d& in) const {
return mSecondMap.applyJT(in);
}
/// Return the transpose of the inverse Jacobian of the linear second map applied to @c in
Vec3d applyIJT(const Vec3d& in) const { return mSecondMap.applyIJT(in); }
// the Jacobian of the nonlinear part of the transform is a sparse matrix
// Jacobian^(-T) =
//
// (Lx)( 1/s 0 0 )
// ( 0 1/s 0 )
// ( -(x-xo)g/(sLx) -(y-yo)g/(sLx) Lz/(Depth Lx) )
/// Return the transpose of the inverse Jacobain (at @c locW applied to @c in.
/// @c ijk is the location in the pre-image space (e.g. index space)
Vec3d applyIJT(const Vec3d& d1_is, const Vec3d& ijk) const
{
const Vec3d loc = applyFrustumMap(ijk);
const double s = mGamma * loc.z() + 1.;
// verify that we aren't at the singularity
if (isApproxEqual(s, 0.)) {
OPENVDB_THROW(ArithmeticError, "Tried to evaluate the frustum transform"
" at the singular focal point (e.g. camera)");
}
const double sinv = 1.0/s; // 1/(z*gamma + 1)
const double pt0 = mLx * sinv; // Lx / (z*gamma +1)
const double pt1 = mGamma * pt0; // gamma * Lx / ( z*gamma +1)
const double pt2 = pt1 * sinv; // gamma * Lx / ( z*gamma +1)**2
const Mat3d& jacinv = mSecondMap.getConstJacobianInv();
// compute \frac{\partial E_i}{\partial x_j}
Mat3d gradE(Mat3d::zero());
for (int j = 0; j < 3; ++j ) {
gradE(0,j) = pt0 * jacinv(0,j) - pt2 * loc.x()*jacinv(2,j);
gradE(1,j) = pt0 * jacinv(1,j) - pt2 * loc.y()*jacinv(2,j);
gradE(2,j) = (1./mDepthOnLz) * jacinv(2,j);
}
Vec3d result;
for (int i = 0; i < 3; ++i) {
result(i) = d1_is(0) * gradE(0,i) + d1_is(1) * gradE(1,i) + d1_is(2) * gradE(2,i);
}
return result;
}
/// Return the Jacobian Curvature for the linear second map
Mat3d applyIJC(const Mat3d& in) const { return mSecondMap.applyIJC(in); }
/// Return the Jacobian Curvature: all the second derivatives in range space
/// @param d2_is second derivative matrix computed in index space
/// @param d1_is gradient computed in index space
/// @param ijk the index space location where the result is computed
Mat3d applyIJC(const Mat3d& d2_is, const Vec3d& d1_is, const Vec3d& ijk) const
{
const Vec3d loc = applyFrustumMap(ijk);
const double s = mGamma * loc.z() + 1.;
// verify that we aren't at the singularity
if (isApproxEqual(s, 0.)) {
OPENVDB_THROW(ArithmeticError, "Tried to evaluate the frustum transform"
" at the singular focal point (e.g. camera)");
}
// precompute
const double sinv = 1.0/s; // 1/(z*gamma + 1)
const double pt0 = mLx * sinv; // Lx / (z*gamma +1)
const double pt1 = mGamma * pt0; // gamma * Lx / ( z*gamma +1)
const double pt2 = pt1 * sinv; // gamma * Lx / ( z*gamma +1)**2
const double pt3 = pt2 * sinv; // gamma * Lx / ( z*gamma +1)**3
const Mat3d& jacinv = mSecondMap.getConstJacobianInv();
// compute \frac{\partial^2 E_i}{\partial x_j \partial x_k}
Mat3d matE0(Mat3d::zero());
Mat3d matE1(Mat3d::zero()); // matE2 = 0
for(int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++) {
const double pt4 = 2. * jacinv(2,j) * jacinv(2,k) * pt3;
matE0(j,k) = -(jacinv(0,j) * jacinv(2,k) + jacinv(2,j) * jacinv(0,k)) * pt2 +
pt4 * loc.x();
matE1(j,k) = -(jacinv(1,j) * jacinv(2,k) + jacinv(2,j) * jacinv(1,k)) * pt2 +
pt4 * loc.y();
}
}
// compute \frac{\partial E_i}{\partial x_j}
Mat3d gradE(Mat3d::zero());
for (int j = 0; j < 3; ++j ) {
gradE(0,j) = pt0 * jacinv(0,j) - pt2 * loc.x()*jacinv(2,j);
gradE(1,j) = pt0 * jacinv(1,j) - pt2 * loc.y()*jacinv(2,j);
gradE(2,j) = (1./mDepthOnLz) * jacinv(2,j);
}
Mat3d result(Mat3d::zero());
// compute \fac{\partial E_j}{\partial x_m} \fac{\partial E_i}{\partial x_n}
// \frac{\partial^2 input}{\partial E_i \partial E_j}
for (int m = 0; m < 3; ++m ) {
for ( int n = 0; n < 3; ++n) {
for (int i = 0; i < 3; ++i ) {
for (int j = 0; j < 3; ++j) {
result(m, n) += gradE(j, m) * gradE(i, n) * d2_is(i, j);
}
}
}
}
for (int m = 0; m < 3; ++m ) {
for ( int n = 0; n < 3; ++n) {
result(m, n) +=
matE0(m, n) * d1_is(0) + matE1(m, n) * d1_is(1);// + matE2(m, n) * d1_is(2);
}
}
return result;
}
/// Return the determinant of the Jacobian of linear second map
double determinant() const {return mSecondMap.determinant();} // no implementation
/// Return the determinate of the Jacobian evaluated at @c loc
/// @c loc is a location in the pre-image space (e.g., index space)
double determinant(const Vec3d& loc) const
{
double s = mGamma * loc.z() + 1.0;
double frustum_determinant = s * s * mDepthOnLzLxLx;
return mSecondMap.determinant() * frustum_determinant;
}
/// Return the size of a voxel at the center of the near plane
Vec3d voxelSize() const
{
const Vec3d loc( 0.5*(mBBox.min().x() + mBBox.max().x()),
0.5*(mBBox.min().y() + mBBox.max().y()),
mBBox.min().z());
return voxelSize(loc);
}
/// @brief Returns the lengths of the images of the three segments
/// from @a loc to @a loc + (1,0,0), from @a loc to @a loc + (0,1,0)
/// and from @a loc to @a loc + (0,0,1)
/// @param loc a location in the pre-image space (e.g., index space)
Vec3d voxelSize(const Vec3d& loc) const
{
Vec3d out, pos = applyMap(loc);
out(0) = (applyMap(loc + Vec3d(1,0,0)) - pos).length();
out(1) = (applyMap(loc + Vec3d(0,1,0)) - pos).length();
out(2) = (applyMap(loc + Vec3d(0,0,1)) - pos).length();
return out;
}
AffineMap::Ptr getAffineMap() const { return mSecondMap.getAffineMap(); }
/// set the taper value, the ratio of nearplane width / far plane width
void setTaper(double t) { mTaper = t; init();}
/// Return the taper value.
double getTaper() const { return mTaper; }
/// set the frustum depth: distance between near and far plane = frustm depth * frustm x-width
void setDepth(double d) { mDepth = d; init();}
/// Return the unscaled frustm depth
double getDepth() const { return mDepth; }
// gamma a non-dimensional number: nearplane x-width / camera to near plane distance
double getGamma() const { return mGamma; }
/// Return the bounding box that defines the frustum in pre-image space
const BBoxd& getBBox() const { return mBBox; }
/// Return MapBase::Ptr& to the second map
const AffineMap& secondMap() const { return mSecondMap; }
/// Return @c true if the the bounding box in index space that defines the region that
/// is maped into the frustum is non-zero, otherwise @c false
bool isValid() const { return !mBBox.empty();}
/// Return @c true if the second map is a uniform scale, Rotation and translation
bool hasSimpleAffine() const { return mHasSimpleAffine; }
/// read serialization
void read(std::istream& is)
{
// for backward compatibility with earlier version
if (io::getFormatVersion(is) < OPENVDB_FILE_VERSION_FLOAT_FRUSTUM_BBOX ) {
CoordBBox bb;
bb.read(is);
mBBox = BBoxd(bb.min().asVec3d(), bb.max().asVec3d());
} else {
mBBox.read(is);
}
is.read(reinterpret_cast<char*>(&mTaper), sizeof(double));
is.read(reinterpret_cast<char*>(&mDepth), sizeof(double));
// Read the second maps type.
Name type = readString(is);
// Check if the map has been registered.
if(!MapRegistry::isRegistered(type)) {
OPENVDB_THROW(KeyError, "Map " << type << " is not registered");
}
// Create the second map of the type and then read it in.
MapBase::Ptr proxy = math::MapRegistry::createMap(type);
proxy->read(is);
mSecondMap = *(proxy->getAffineMap());
init();
}
/// write serialization
void write(std::ostream& os) const
{
mBBox.write(os);
os.write(reinterpret_cast<const char*>(&mTaper), sizeof(double));
os.write(reinterpret_cast<const char*>(&mDepth), sizeof(double));
writeString(os, mSecondMap.type());
mSecondMap.write(os);
}
/// string serialization, useful for debuging
std::string str() const
{
std::ostringstream buffer;
buffer << " - taper: " << mTaper << std::endl;
buffer << " - depth: " << mDepth << std::endl;
buffer << " SecondMap: "<< mSecondMap.type() << std::endl;
buffer << mSecondMap.str() << std::endl;
return buffer.str();
}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of prepending the appropriate operation to the linear part of this map
MapBase::Ptr preRotate(double radians, Axis axis = X_AXIS) const
{
return MapBase::Ptr(
new NonlinearFrustumMap(mBBox, mTaper, mDepth, mSecondMap.preRotate(radians, axis)));
}
MapBase::Ptr preTranslate(const Vec3d& t) const
{
return MapBase::Ptr(
new NonlinearFrustumMap(mBBox, mTaper, mDepth, mSecondMap.preTranslate(t)));
}
MapBase::Ptr preScale(const Vec3d& s) const
{
return MapBase::Ptr(
new NonlinearFrustumMap(mBBox, mTaper, mDepth, mSecondMap.preScale(s)));
}
MapBase::Ptr preShear(double shear, Axis axis0, Axis axis1) const
{
return MapBase::Ptr(new NonlinearFrustumMap(
mBBox, mTaper, mDepth, mSecondMap.preShear(shear, axis0, axis1)));
}
//@}
//@{
/// @brief Return a MapBase::Ptr to a new map that is the result
/// of postfixing the appropiate operation to the linear part of this map.
MapBase::Ptr postRotate(double radians, Axis axis = X_AXIS) const
{
return MapBase::Ptr(
new NonlinearFrustumMap(mBBox, mTaper, mDepth, mSecondMap.postRotate(radians, axis)));
}
MapBase::Ptr postTranslate(const Vec3d& t) const
{
return MapBase::Ptr(
new NonlinearFrustumMap(mBBox, mTaper, mDepth, mSecondMap.postTranslate(t)));
}
MapBase::Ptr postScale(const Vec3d& s) const
{
return MapBase::Ptr(
new NonlinearFrustumMap(mBBox, mTaper, mDepth, mSecondMap.postScale(s)));
}
MapBase::Ptr postShear(double shear, Axis axis0, Axis axis1) const
{
return MapBase::Ptr(new NonlinearFrustumMap(
mBBox, mTaper, mDepth, mSecondMap.postShear(shear, axis0, axis1)));
}
//@}
private:
void init()
{
// set up as a frustum
mLx = mBBox.extents().x();
mLy = mBBox.extents().y();
mLz = mBBox.extents().z();
if (isApproxEqual(mLx,0.) || isApproxEqual(mLy,0.) || isApproxEqual(mLz,0.) ) {
OPENVDB_THROW(ArithmeticError, "The index space bounding box"
" must have at least two index points in each direction.");
}
mXo = 0.5* mLx;
mYo = 0.5* mLy;
// mDepth is non-dimensionalized on near
mGamma = (1./mTaper - 1) / mDepth;
mDepthOnLz = mDepth/mLz;
mDepthOnLzLxLx = mDepthOnLz/(mLx * mLx);
/// test for shear and non-uniform scale
mHasSimpleAffine = true;
Vec3d tmp = mSecondMap.voxelSize();
/// false if there is non-uniform scale
if (!isApproxEqual(tmp(0), tmp(1))) { mHasSimpleAffine = false; return; }
if (!isApproxEqual(tmp(0), tmp(2))) { mHasSimpleAffine = false; return; }
Vec3d trans = mSecondMap.applyMap(Vec3d(0,0,0));
/// look for shear
Vec3d tmp1 = mSecondMap.applyMap(Vec3d(1,0,0)) - trans;
Vec3d tmp2 = mSecondMap.applyMap(Vec3d(0,1,0)) - trans;
Vec3d tmp3 = mSecondMap.applyMap(Vec3d(0,0,1)) - trans;
/// false if there is shear
if (!isApproxEqual(tmp1.dot(tmp2), 0., 1.e-7)) { mHasSimpleAffine = false; return; }
if (!isApproxEqual(tmp2.dot(tmp3), 0., 1.e-7)) { mHasSimpleAffine = false; return; }
if (!isApproxEqual(tmp3.dot(tmp1), 0., 1.e-7)) { mHasSimpleAffine = false; return; }
}
Vec3d applyFrustumMap(const Vec3d& in) const
{
// Move the center of the x-face of the bbox
// to the origin in index space.
Vec3d out(in);
out = out - mBBox.min();
out.x() -= mXo;
out.y() -= mYo;
// scale the z-direction on depth / K count
out.z() *= mDepthOnLz;
double scale = (mGamma * out.z() + 1.)/ mLx;
// scale the x-y on the length I count and apply tapper
out.x() *= scale ;
out.y() *= scale ;
return out;
}
Vec3d applyFrustumInverseMap(const Vec3d& in) const
{
// invert taper and resize: scale = 1/( (z+1)/2 (mt-1) + 1)
Vec3d out(in);
double invScale = mLx / (mGamma * out.z() + 1.);
out.x() *= invScale;
out.y() *= invScale;
out.x() += mXo;
out.y() += mYo;
out.z() /= mDepthOnLz;
// move back
out = out + mBBox.min();
return out;
}
// bounding box in index space used in Frustum transforms.
BBoxd mBBox;
// taper value used in constructing Frustums.
double mTaper;
double mDepth;
// defines the second map
AffineMap mSecondMap;
// these are derived from the above.
double mLx, mLy, mLz;
double mXo, mYo, mGamma, mDepthOnLz, mDepthOnLzLxLx;
// true: if the mSecondMap is linear and has no shear, and has no non-uniform scale
bool mHasSimpleAffine;
}; // class NonlinearFrustumMap
////////////////////////////////////////
/// @brief Creates the composition of two maps, each of which could be a composition.
/// In the case that each component of the composition classified as linear an
/// acceleration AffineMap is stored.
template<typename FirstMapType, typename SecondMapType>
class CompoundMap
{
public:
typedef CompoundMap<FirstMapType, SecondMapType> MyType;
typedef boost::shared_ptr<MyType> Ptr;
typedef boost::shared_ptr<const MyType> ConstPtr;
CompoundMap() { updateAffineMatrix(); }
CompoundMap(const FirstMapType& f, const SecondMapType& s): mFirstMap(f), mSecondMap(s)
{
updateAffineMatrix();
}
CompoundMap(const MyType& other):
mFirstMap(other.mFirstMap),
mSecondMap(other.mSecondMap),
mAffineMap(other.mAffineMap)
{}
Name type() const { return mapType(); }
static Name mapType()
{
return (FirstMapType::mapType() + Name(":") + SecondMapType::mapType());
}
bool operator==(const MyType& other) const
{
if (mFirstMap != other.mFirstMap) return false;
if (mSecondMap != other.mSecondMap) return false;
if (mAffineMap != other.mAffineMap) return false;
return true;
}
bool operator!=(const MyType& other) const { return !(*this == other); }
MyType& operator=(const MyType& other)
{
mFirstMap = other.mFirstMap;
mSecondMap = other.mSecondMap;
mAffineMap = other.mAffineMap;
return *this;
}
bool isIdentity() const
{
if (is_linear<MyType>::value) {
return mAffineMap.isIdentity();
} else {
return mFirstMap.isIdentity()&&mSecondMap.isIdentity();
}
}
bool isDiagonal() const {
if (is_linear<MyType>::value) {
return mAffineMap.isDiagonal();
} else {
return mFirstMap.isDiagonal()&&mSecondMap.isDiagonal();
}
}
AffineMap::Ptr getAffineMap() const
{
if (is_linear<MyType>::value) {
AffineMap::Ptr affine(new AffineMap(mAffineMap));
return affine;
} else {
OPENVDB_THROW(ArithmeticError,
"Constant affine matrix representation not possible for this nonlinear map");
}
}
// direct decompotion
const FirstMapType& firstMap() const { return mFirstMap; }
const SecondMapType& secondMap() const {return mSecondMap; }
void setFirstMap(const FirstMapType& first) { mFirstMap = first; updateAffineMatrix(); }
void setSecondMap(const SecondMapType& second) { mSecondMap = second; updateAffineMatrix(); }
void read(std::istream& is)
{
mAffineMap.read(is);
mFirstMap.read(is);
mSecondMap.read(is);
}
void write(std::ostream& os) const
{
mAffineMap.write(os);
mFirstMap.write(os);
mSecondMap.write(os);
}
private:
void updateAffineMatrix()
{
if (is_linear<MyType>::value) {
// both maps need to be linear, these methods are only defined for linear maps
AffineMap::Ptr first = mFirstMap.getAffineMap();
AffineMap::Ptr second= mSecondMap.getAffineMap();
mAffineMap = AffineMap(*first, *second);
}
}
FirstMapType mFirstMap;
SecondMapType mSecondMap;
// used for acceleration
AffineMap mAffineMap;
}; // class CompoundMap
} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb
#endif // OPENVDB_MATH_MAPS_HAS_BEEN_INCLUDED
// Copyright (c) 2012-2016 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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