Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/Eigen/src/Eigen2Support/Geometry/AlignedBox.h b/Eigen/src/Eigen2Support/Geometry/AlignedBox.h
new file mode 100644
index 0000000..2e4309d
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/AlignedBox.h
@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ * \nonstableyet
+ *
+ * \class AlignedBox
+ *
+ * \brief An axis aligned box
+ *
+ * \param _Scalar the type of the scalar coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ *
+ * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+ */
+template <typename _Scalar, int _AmbientDim>
+class AlignedBox
+{
+public:
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+ /** Default constructor initializing a null box. */
+ inline AlignedBox()
+ { if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
+
+ /** Constructs a null box with \a _dim the dimension of the ambient space. */
+ inline explicit AlignedBox(int _dim) : m_min(_dim), m_max(_dim)
+ { setNull(); }
+
+ /** Constructs a box with extremities \a _min and \a _max. */
+ inline AlignedBox(const VectorType& _min, const VectorType& _max) : m_min(_min), m_max(_max) {}
+
+ /** Constructs a box containing a single point \a p. */
+ inline explicit AlignedBox(const VectorType& p) : m_min(p), m_max(p) {}
+
+ ~AlignedBox() {}
+
+ /** \returns the dimension in which the box holds */
+ inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; }
+
+ /** \returns true if the box is null, i.e, empty. */
+ inline bool isNull() const { return (m_min.cwise() > m_max).any(); }
+
+ /** Makes \c *this a null/empty box. */
+ inline void setNull()
+ {
+ m_min.setConstant( (std::numeric_limits<Scalar>::max)());
+ m_max.setConstant(-(std::numeric_limits<Scalar>::max)());
+ }
+
+ /** \returns the minimal corner */
+ inline const VectorType& (min)() const { return m_min; }
+ /** \returns a non const reference to the minimal corner */
+ inline VectorType& (min)() { return m_min; }
+ /** \returns the maximal corner */
+ inline const VectorType& (max)() const { return m_max; }
+ /** \returns a non const reference to the maximal corner */
+ inline VectorType& (max)() { return m_max; }
+
+ /** \returns true if the point \a p is inside the box \c *this. */
+ inline bool contains(const VectorType& p) const
+ { return (m_min.cwise()<=p).all() && (p.cwise()<=m_max).all(); }
+
+ /** \returns true if the box \a b is entirely inside the box \c *this. */
+ inline bool contains(const AlignedBox& b) const
+ { return (m_min.cwise()<=(b.min)()).all() && ((b.max)().cwise()<=m_max).all(); }
+
+ /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
+ inline AlignedBox& extend(const VectorType& p)
+ { m_min = (m_min.cwise().min)(p); m_max = (m_max.cwise().max)(p); return *this; }
+
+ /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
+ inline AlignedBox& extend(const AlignedBox& b)
+ { m_min = (m_min.cwise().min)(b.m_min); m_max = (m_max.cwise().max)(b.m_max); return *this; }
+
+ /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
+ inline AlignedBox& clamp(const AlignedBox& b)
+ { m_min = (m_min.cwise().max)(b.m_min); m_max = (m_max.cwise().min)(b.m_max); return *this; }
+
+ /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
+ inline AlignedBox& translate(const VectorType& t)
+ { m_min += t; m_max += t; return *this; }
+
+ /** \returns the squared distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa exteriorDistance()
+ */
+ inline Scalar squaredExteriorDistance(const VectorType& p) const;
+
+ /** \returns the distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa squaredExteriorDistance()
+ */
+ inline Scalar exteriorDistance(const VectorType& p) const
+ { return ei_sqrt(squaredExteriorDistance(p)); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
+ {
+ m_min = (other.min)().template cast<Scalar>();
+ m_max = (other.max)().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
+
+protected:
+
+ VectorType m_min, m_max;
+};
+
+template<typename Scalar,int AmbiantDim>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const
+{
+ Scalar dist2(0);
+ Scalar aux;
+ for (int k=0; k<dim(); ++k)
+ {
+ if ((aux = (p[k]-m_min[k]))<Scalar(0))
+ dist2 += aux*aux;
+ else if ( (aux = (m_max[k]-p[k]))<Scalar(0))
+ dist2 += aux*aux;
+ }
+ return dist2;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/All.h b/Eigen/src/Eigen2Support/Geometry/All.h
new file mode 100644
index 0000000..e0b00fc
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/All.h
@@ -0,0 +1,115 @@
+#ifndef EIGEN2_GEOMETRY_MODULE_H
+#define EIGEN2_GEOMETRY_MODULE_H
+
+#include <limits>
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+#include "RotationBase.h"
+#include "Rotation2D.h"
+#include "Quaternion.h"
+#include "AngleAxis.h"
+#include "Transform.h"
+#include "Translation.h"
+#include "Scaling.h"
+#include "AlignedBox.h"
+#include "Hyperplane.h"
+#include "ParametrizedLine.h"
+#endif
+
+
+#define RotationBase eigen2_RotationBase
+#define Rotation2D eigen2_Rotation2D
+#define Rotation2Df eigen2_Rotation2Df
+#define Rotation2Dd eigen2_Rotation2Dd
+
+#define Quaternion eigen2_Quaternion
+#define Quaternionf eigen2_Quaternionf
+#define Quaterniond eigen2_Quaterniond
+
+#define AngleAxis eigen2_AngleAxis
+#define AngleAxisf eigen2_AngleAxisf
+#define AngleAxisd eigen2_AngleAxisd
+
+#define Transform eigen2_Transform
+#define Transform2f eigen2_Transform2f
+#define Transform2d eigen2_Transform2d
+#define Transform3f eigen2_Transform3f
+#define Transform3d eigen2_Transform3d
+
+#define Translation eigen2_Translation
+#define Translation2f eigen2_Translation2f
+#define Translation2d eigen2_Translation2d
+#define Translation3f eigen2_Translation3f
+#define Translation3d eigen2_Translation3d
+
+#define Scaling eigen2_Scaling
+#define Scaling2f eigen2_Scaling2f
+#define Scaling2d eigen2_Scaling2d
+#define Scaling3f eigen2_Scaling3f
+#define Scaling3d eigen2_Scaling3d
+
+#define AlignedBox eigen2_AlignedBox
+
+#define Hyperplane eigen2_Hyperplane
+#define ParametrizedLine eigen2_ParametrizedLine
+
+#define ei_toRotationMatrix eigen2_ei_toRotationMatrix
+#define ei_quaternion_assign_impl eigen2_ei_quaternion_assign_impl
+#define ei_transform_product_impl eigen2_ei_transform_product_impl
+
+#include "RotationBase.h"
+#include "Rotation2D.h"
+#include "Quaternion.h"
+#include "AngleAxis.h"
+#include "Transform.h"
+#include "Translation.h"
+#include "Scaling.h"
+#include "AlignedBox.h"
+#include "Hyperplane.h"
+#include "ParametrizedLine.h"
+
+#undef ei_toRotationMatrix
+#undef ei_quaternion_assign_impl
+#undef ei_transform_product_impl
+
+#undef RotationBase
+#undef Rotation2D
+#undef Rotation2Df
+#undef Rotation2Dd
+
+#undef Quaternion
+#undef Quaternionf
+#undef Quaterniond
+
+#undef AngleAxis
+#undef AngleAxisf
+#undef AngleAxisd
+
+#undef Transform
+#undef Transform2f
+#undef Transform2d
+#undef Transform3f
+#undef Transform3d
+
+#undef Translation
+#undef Translation2f
+#undef Translation2d
+#undef Translation3f
+#undef Translation3d
+
+#undef Scaling
+#undef Scaling2f
+#undef Scaling2d
+#undef Scaling3f
+#undef Scaling3d
+
+#undef AlignedBox
+
+#undef Hyperplane
+#undef ParametrizedLine
+
+#endif // EIGEN2_GEOMETRY_MODULE_H
diff --git a/Eigen/src/Eigen2Support/Geometry/AngleAxis.h b/Eigen/src/Eigen2Support/Geometry/AngleAxis.h
new file mode 100644
index 0000000..af598a4
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/AngleAxis.h
@@ -0,0 +1,214 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class AngleAxis
+ *
+ * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c AngleAxisf for \c float
+ * \li \c AngleAxisd for \c double
+ *
+ * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles
+ *
+ * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
+ * mimic Euler-angles. Here is an example:
+ * \include AngleAxis_mimic_euler.cpp
+ * Output: \verbinclude AngleAxis_mimic_euler.out
+ *
+ * \note This class is not aimed to be used to store a rotation transformation,
+ * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
+ * and transformation objects.
+ *
+ * \sa class Quaternion, class Transform, MatrixBase::UnitX()
+ */
+
+template<typename _Scalar> struct ei_traits<AngleAxis<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
+{
+ typedef RotationBase<AngleAxis<_Scalar>,3> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 3 };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> QuaternionType;
+
+protected:
+
+ Vector3 m_axis;
+ Scalar m_angle;
+
+public:
+
+ /** Default constructor without initialization. */
+ AngleAxis() {}
+ /** Constructs and initialize the angle-axis rotation from an \a angle in radian
+ * and an \a axis which must be normalized. */
+ template<typename Derived>
+ inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
+ /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
+ inline AngleAxis(const QuaternionType& q) { *this = q; }
+ /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
+ template<typename Derived>
+ inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
+
+ Scalar angle() const { return m_angle; }
+ Scalar& angle() { return m_angle; }
+
+ const Vector3& axis() const { return m_axis; }
+ Vector3& axis() { return m_axis; }
+
+ /** Concatenates two rotations */
+ inline QuaternionType operator* (const AngleAxis& other) const
+ { return QuaternionType(*this) * QuaternionType(other); }
+
+ /** Concatenates two rotations */
+ inline QuaternionType operator* (const QuaternionType& other) const
+ { return QuaternionType(*this) * other; }
+
+ /** Concatenates two rotations */
+ friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
+ { return a * QuaternionType(b); }
+
+ /** Concatenates two rotations */
+ inline Matrix3 operator* (const Matrix3& other) const
+ { return toRotationMatrix() * other; }
+
+ /** Concatenates two rotations */
+ inline friend Matrix3 operator* (const Matrix3& a, const AngleAxis& b)
+ { return a * b.toRotationMatrix(); }
+
+ /** Applies rotation to vector */
+ inline Vector3 operator* (const Vector3& other) const
+ { return toRotationMatrix() * other; }
+
+ /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
+ AngleAxis inverse() const
+ { return AngleAxis(-m_angle, m_axis); }
+
+ AngleAxis& operator=(const QuaternionType& q);
+ template<typename Derived>
+ AngleAxis& operator=(const MatrixBase<Derived>& m);
+
+ template<typename Derived>
+ AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
+ Matrix3 toRotationMatrix(void) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
+ {
+ m_axis = other.axis().template cast<Scalar>();
+ m_angle = Scalar(other.angle());
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision angle-axis type */
+typedef AngleAxis<float> AngleAxisf;
+/** \ingroup Geometry_Module
+ * double precision angle-axis type */
+typedef AngleAxis<double> AngleAxisd;
+
+/** Set \c *this from a quaternion.
+ * The axis is normalized.
+ */
+template<typename Scalar>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionType& q)
+{
+ Scalar n2 = q.vec().squaredNorm();
+ if (n2 < precision<Scalar>()*precision<Scalar>())
+ {
+ m_angle = 0;
+ m_axis << 1, 0, 0;
+ }
+ else
+ {
+ m_angle = 2*std::acos(q.w());
+ m_axis = q.vec() / ei_sqrt(n2);
+ }
+ return *this;
+}
+
+/** Set \c *this from a 3x3 rotation matrix \a mat.
+ */
+template<typename Scalar>
+template<typename Derived>
+AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
+{
+ // Since a direct conversion would not be really faster,
+ // let's use the robust Quaternion implementation:
+ return *this = QuaternionType(mat);
+}
+
+/** Constructs and \returns an equivalent 3x3 rotation matrix.
+ */
+template<typename Scalar>
+typename AngleAxis<Scalar>::Matrix3
+AngleAxis<Scalar>::toRotationMatrix(void) const
+{
+ Matrix3 res;
+ Vector3 sin_axis = ei_sin(m_angle) * m_axis;
+ Scalar c = ei_cos(m_angle);
+ Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
+
+ Scalar tmp;
+ tmp = cos1_axis.x() * m_axis.y();
+ res.coeffRef(0,1) = tmp - sin_axis.z();
+ res.coeffRef(1,0) = tmp + sin_axis.z();
+
+ tmp = cos1_axis.x() * m_axis.z();
+ res.coeffRef(0,2) = tmp + sin_axis.y();
+ res.coeffRef(2,0) = tmp - sin_axis.y();
+
+ tmp = cos1_axis.y() * m_axis.z();
+ res.coeffRef(1,2) = tmp - sin_axis.x();
+ res.coeffRef(2,1) = tmp + sin_axis.x();
+
+ res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c;
+
+ return res;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt b/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt
new file mode 100644
index 0000000..c347a8f
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Eigen2Support_Geometry_SRCS "*.h")
+
+INSTALL(FILES
+ ${Eigen_Eigen2Support_Geometry_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Eigen2Support/Geometry
+ )
diff --git a/Eigen/src/Eigen2Support/Geometry/Hyperplane.h b/Eigen/src/Eigen2Support/Geometry/Hyperplane.h
new file mode 100644
index 0000000..b95bf00
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Hyperplane.h
@@ -0,0 +1,254 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Hyperplane
+ *
+ * \brief A hyperplane
+ *
+ * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
+ * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ * Notice that the dimension of the hyperplane is _AmbientDim-1.
+ *
+ * This class represents an hyperplane as the zero set of the implicit equation
+ * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
+ * and \f$ d \f$ is the distance (offset) to the origin.
+ */
+template <typename _Scalar, int _AmbientDim>
+class Hyperplane
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+ typedef Matrix<Scalar,int(AmbientDimAtCompileTime)==Dynamic
+ ? Dynamic
+ : int(AmbientDimAtCompileTime)+1,1> Coefficients;
+ typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
+
+ /** Default constructor without initialization */
+ inline Hyperplane() {}
+
+ /** Constructs a dynamic-size hyperplane with \a _dim the dimension
+ * of the ambient space */
+ inline explicit Hyperplane(int _dim) : m_coeffs(_dim+1) {}
+
+ /** Construct a plane from its normal \a n and a point \a e onto the plane.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline Hyperplane(const VectorType& n, const VectorType& e)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = -e.eigen2_dot(n);
+ }
+
+ /** Constructs a plane from its normal \a n and distance to the origin \a d
+ * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline Hyperplane(const VectorType& n, Scalar d)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = d;
+ }
+
+ /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
+ * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
+ */
+ static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
+ {
+ Hyperplane result(p0.size());
+ result.normal() = (p1 - p0).unitOrthogonal();
+ result.offset() = -result.normal().eigen2_dot(p0);
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
+ * is required to be exactly 3.
+ */
+ static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
+ Hyperplane result(p0.size());
+ result.normal() = (p2 - p0).cross(p1 - p0).normalized();
+ result.offset() = -result.normal().eigen2_dot(p0);
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the parametrized line \a parametrized.
+ * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
+ * so an arbitrary choice is made.
+ */
+ // FIXME to be consitent with the rest this could be implemented as a static Through function ??
+ explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
+ {
+ normal() = parametrized.direction().unitOrthogonal();
+ offset() = -normal().eigen2_dot(parametrized.origin());
+ }
+
+ ~Hyperplane() {}
+
+ /** \returns the dimension in which the plane holds */
+ inline int dim() const { return int(AmbientDimAtCompileTime)==Dynamic ? m_coeffs.size()-1 : int(AmbientDimAtCompileTime); }
+
+ /** normalizes \c *this */
+ void normalize(void)
+ {
+ m_coeffs /= normal().norm();
+ }
+
+ /** \returns the signed distance between the plane \c *this and a point \a p.
+ * \sa absDistance()
+ */
+ inline Scalar signedDistance(const VectorType& p) const { return p.eigen2_dot(normal()) + offset(); }
+
+ /** \returns the absolute distance between the plane \c *this and a point \a p.
+ * \sa signedDistance()
+ */
+ inline Scalar absDistance(const VectorType& p) const { return ei_abs(signedDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the plane \c *this.
+ */
+ inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
+
+ /** \returns a constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ inline const NormalReturnType normal() const { return NormalReturnType(*const_cast<Coefficients*>(&m_coeffs),0,0,dim(),1); }
+
+ /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+ /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
+ * \warning the vector normal is assumed to be normalized.
+ */
+ inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
+
+ /** \returns a non-constant reference to the distance to the origin, which is also the constant part
+ * of the implicit equation */
+ inline Scalar& offset() { return m_coeffs(dim()); }
+
+ /** \returns a constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ /** \returns a non-constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ inline Coefficients& coeffs() { return m_coeffs; }
+
+ /** \returns the intersection of *this with \a other.
+ *
+ * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
+ *
+ * \note If \a other is approximately parallel to *this, this method will return any point on *this.
+ */
+ VectorType intersection(const Hyperplane& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
+ // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
+ // whether the two lines are approximately parallel.
+ if(ei_isMuchSmallerThan(det, Scalar(1)))
+ { // special case where the two lines are approximately parallel. Pick any point on the first line.
+ if(ei_abs(coeffs().coeff(1))>ei_abs(coeffs().coeff(0)))
+ return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
+ else
+ return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
+ }
+ else
+ { // general case
+ Scalar invdet = Scalar(1) / det;
+ return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
+ invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
+ }
+ }
+
+ /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
+ *
+ * \param mat the Dim x Dim transformation matrix
+ * \param traits specifies whether the matrix \a mat represents an Isometry
+ * or a more generic Affine transformation. The default is Affine.
+ */
+ template<typename XprType>
+ inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
+ {
+ if (traits==Affine)
+ normal() = mat.inverse().transpose() * normal();
+ else if (traits==Isometry)
+ normal() = mat * normal();
+ else
+ {
+ ei_assert("invalid traits value in Hyperplane::transform()");
+ }
+ return *this;
+ }
+
+ /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
+ *
+ * \param t the transformation of dimension Dim
+ * \param traits specifies whether the transformation \a t represents an Isometry
+ * or a more generic Affine transformation. The default is Affine.
+ * Other kind of transformations are not supported.
+ */
+ inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime>& t,
+ TransformTraits traits = Affine)
+ {
+ transform(t.linear(), traits);
+ offset() -= t.translation().eigen2_dot(normal());
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+
+ Coefficients m_coeffs;
+};
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h b/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h
new file mode 100644
index 0000000..9b57b7e
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h
@@ -0,0 +1,141 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class ParametrizedLine
+ *
+ * \brief A parametrized line
+ *
+ * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
+ * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
+ * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ l \in \mathbf{R} \f$.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+ */
+template <typename _Scalar, int _AmbientDim>
+class ParametrizedLine
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
+ enum { AmbientDimAtCompileTime = _AmbientDim };
+ typedef _Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+ /** Default constructor without initialization */
+ inline ParametrizedLine() {}
+
+ /** Constructs a dynamic-size line with \a _dim the dimension
+ * of the ambient space */
+ inline explicit ParametrizedLine(int _dim) : m_origin(_dim), m_direction(_dim) {}
+
+ /** Initializes a parametrized line of direction \a direction and origin \a origin.
+ * \warning the vector direction is assumed to be normalized.
+ */
+ ParametrizedLine(const VectorType& origin, const VectorType& direction)
+ : m_origin(origin), m_direction(direction) {}
+
+ explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
+
+ /** Constructs a parametrized line going from \a p0 to \a p1. */
+ static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
+ { return ParametrizedLine(p0, (p1-p0).normalized()); }
+
+ ~ParametrizedLine() {}
+
+ /** \returns the dimension in which the line holds */
+ inline int dim() const { return m_direction.size(); }
+
+ const VectorType& origin() const { return m_origin; }
+ VectorType& origin() { return m_origin; }
+
+ const VectorType& direction() const { return m_direction; }
+ VectorType& direction() { return m_direction; }
+
+ /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
+ * \sa distance()
+ */
+ RealScalar squaredDistance(const VectorType& p) const
+ {
+ VectorType diff = p-origin();
+ return (diff - diff.eigen2_dot(direction())* direction()).squaredNorm();
+ }
+ /** \returns the distance of a point \a p to its projection onto the line \c *this.
+ * \sa squaredDistance()
+ */
+ RealScalar distance(const VectorType& p) const { return ei_sqrt(squaredDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the line \c *this. */
+ VectorType projection(const VectorType& p) const
+ { return origin() + (p-origin()).eigen2_dot(direction()) * direction(); }
+
+ Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime>& other)
+ {
+ m_origin = other.origin().template cast<Scalar>();
+ m_direction = other.direction().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
+
+protected:
+
+ VectorType m_origin, m_direction;
+};
+
+/** Constructs a parametrized line from a 2D hyperplane
+ *
+ * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
+ */
+template <typename _Scalar, int _AmbientDim>
+inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ direction() = hyperplane.normal().unitOrthogonal();
+ origin() = -hyperplane.normal()*hyperplane.offset();
+}
+
+/** \returns the parameter value of the intersection between \c *this and the given hyperplane
+ */
+template <typename _Scalar, int _AmbientDim>
+inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
+{
+ return -(hyperplane.offset()+origin().eigen2_dot(hyperplane.normal()))
+ /(direction().eigen2_dot(hyperplane.normal()));
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Quaternion.h b/Eigen/src/Eigen2Support/Geometry/Quaternion.h
new file mode 100644
index 0000000..4b6390c
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Quaternion.h
@@ -0,0 +1,495 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+template<typename Other,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct ei_quaternion_assign_impl;
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Quaternion
+ *
+ * \brief The quaternion class used to represent 3D orientations and rotations
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ *
+ * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
+ * orientations and rotations of objects in three dimensions. Compared to other representations
+ * like Euler angles or 3x3 matrices, quatertions offer the following advantages:
+ * \li \b compact storage (4 scalars)
+ * \li \b efficient to compose (28 flops),
+ * \li \b stable spherical interpolation
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c Quaternionf for \c float
+ * \li \c Quaterniond for \c double
+ *
+ * \sa class AngleAxis, class Transform
+ */
+
+template<typename _Scalar> struct ei_traits<Quaternion<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class Quaternion : public RotationBase<Quaternion<_Scalar>,3>
+{
+ typedef RotationBase<Quaternion<_Scalar>,3> Base;
+
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4)
+
+ using Base::operator*;
+
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+
+ /** the type of the Coefficients 4-vector */
+ typedef Matrix<Scalar, 4, 1> Coefficients;
+ /** the type of a 3D vector */
+ typedef Matrix<Scalar,3,1> Vector3;
+ /** the equivalent rotation matrix type */
+ typedef Matrix<Scalar,3,3> Matrix3;
+ /** the equivalent angle-axis type */
+ typedef AngleAxis<Scalar> AngleAxisType;
+
+ /** \returns the \c x coefficient */
+ inline Scalar x() const { return m_coeffs.coeff(0); }
+ /** \returns the \c y coefficient */
+ inline Scalar y() const { return m_coeffs.coeff(1); }
+ /** \returns the \c z coefficient */
+ inline Scalar z() const { return m_coeffs.coeff(2); }
+ /** \returns the \c w coefficient */
+ inline Scalar w() const { return m_coeffs.coeff(3); }
+
+ /** \returns a reference to the \c x coefficient */
+ inline Scalar& x() { return m_coeffs.coeffRef(0); }
+ /** \returns a reference to the \c y coefficient */
+ inline Scalar& y() { return m_coeffs.coeffRef(1); }
+ /** \returns a reference to the \c z coefficient */
+ inline Scalar& z() { return m_coeffs.coeffRef(2); }
+ /** \returns a reference to the \c w coefficient */
+ inline Scalar& w() { return m_coeffs.coeffRef(3); }
+
+ /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+ inline const Block<const Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); }
+
+ /** \returns a vector expression of the imaginary part (x,y,z) */
+ inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); }
+
+ /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+ inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ /** \returns a vector expression of the coefficients (x,y,z,w) */
+ inline Coefficients& coeffs() { return m_coeffs; }
+
+ /** Default constructor leaving the quaternion uninitialized. */
+ inline Quaternion() {}
+
+ /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+ * its four coefficients \a w, \a x, \a y and \a z.
+ *
+ * \warning Note the order of the arguments: the real \a w coefficient first,
+ * while internally the coefficients are stored in the following order:
+ * [\c x, \c y, \c z, \c w]
+ */
+ inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z)
+ { m_coeffs << x, y, z, w; }
+
+ /** Copy constructor */
+ inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; }
+
+ /** Constructs and initializes a quaternion from the angle-axis \a aa */
+ explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
+
+ /** Constructs and initializes a quaternion from either:
+ * - a rotation matrix expression,
+ * - a 4D vector expression representing quaternion coefficients.
+ * \sa operator=(MatrixBase<Derived>)
+ */
+ template<typename Derived>
+ explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
+
+ Quaternion& operator=(const Quaternion& other);
+ Quaternion& operator=(const AngleAxisType& aa);
+ template<typename Derived>
+ Quaternion& operator=(const MatrixBase<Derived>& m);
+
+ /** \returns a quaternion representing an identity rotation
+ * \sa MatrixBase::Identity()
+ */
+ static inline Quaternion Identity() { return Quaternion(1, 0, 0, 0); }
+
+ /** \sa Quaternion::Identity(), MatrixBase::setIdentity()
+ */
+ inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; }
+
+ /** \returns the squared norm of the quaternion's coefficients
+ * \sa Quaternion::norm(), MatrixBase::squaredNorm()
+ */
+ inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); }
+
+ /** \returns the norm of the quaternion's coefficients
+ * \sa Quaternion::squaredNorm(), MatrixBase::norm()
+ */
+ inline Scalar norm() const { return m_coeffs.norm(); }
+
+ /** Normalizes the quaternion \c *this
+ * \sa normalized(), MatrixBase::normalize() */
+ inline void normalize() { m_coeffs.normalize(); }
+ /** \returns a normalized version of \c *this
+ * \sa normalize(), MatrixBase::normalized() */
+ inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); }
+
+ /** \returns the dot product of \c *this and \a other
+ * Geometrically speaking, the dot product of two unit quaternions
+ * corresponds to the cosine of half the angle between the two rotations.
+ * \sa angularDistance()
+ */
+ inline Scalar eigen2_dot(const Quaternion& other) const { return m_coeffs.eigen2_dot(other.m_coeffs); }
+
+ inline Scalar angularDistance(const Quaternion& other) const;
+
+ Matrix3 toRotationMatrix(void) const;
+
+ template<typename Derived1, typename Derived2>
+ Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+ inline Quaternion operator* (const Quaternion& q) const;
+ inline Quaternion& operator*= (const Quaternion& q);
+
+ Quaternion inverse(void) const;
+ Quaternion conjugate(void) const;
+
+ Quaternion slerp(Scalar t, const Quaternion& other) const;
+
+ template<typename Derived>
+ Vector3 operator* (const MatrixBase<Derived>& vec) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Quaternion(const Quaternion<OtherScalarType>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+ Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+ * single precision quaternion type */
+typedef Quaternion<float> Quaternionf;
+/** \ingroup Geometry_Module
+ * double precision quaternion type */
+typedef Quaternion<double> Quaterniond;
+
+// Generic Quaternion * Quaternion product
+template<typename Scalar> inline Quaternion<Scalar>
+ei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b)
+{
+ return Quaternion<Scalar>
+ (
+ a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+ a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+ a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+ a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+ );
+}
+
+/** \returns the concatenation of two rotations as a quaternion-quaternion product */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const
+{
+ return ei_quaternion_product(*this,other);
+}
+
+/** \sa operator*(Quaternion) */
+template <typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other)
+{
+ return (*this = *this * other);
+}
+
+/** Rotation of a vector by a quaternion.
+ * \remarks If the quaternion is used to rotate several points (>1)
+ * then it is much more efficient to first convert it to a 3x3 Matrix.
+ * Comparison of the operation cost for n transformations:
+ * - Quaternion: 30n
+ * - Via a Matrix3: 24 + 15n
+ */
+template <typename Scalar>
+template<typename Derived>
+inline typename Quaternion<Scalar>::Vector3
+Quaternion<Scalar>::operator* (const MatrixBase<Derived>& v) const
+{
+ // Note that this algorithm comes from the optimization by hand
+ // of the conversion to a Matrix followed by a Matrix/Vector product.
+ // It appears to be much faster than the common algorithm found
+ // in the litterature (30 versus 39 flops). It also requires two
+ // Vector3 as temporaries.
+ Vector3 uv;
+ uv = 2 * this->vec().cross(v);
+ return v + this->w() * uv + this->vec().cross(uv);
+}
+
+template<typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other)
+{
+ m_coeffs = other.m_coeffs;
+ return *this;
+}
+
+/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
+ */
+template<typename Scalar>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa)
+{
+ Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
+ this->w() = ei_cos(ha);
+ this->vec() = ei_sin(ha) * aa.axis();
+ return *this;
+}
+
+/** Set \c *this from the expression \a xpr:
+ * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
+ * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+ * and \a xpr is converted to a quaternion
+ */
+template<typename Scalar>
+template<typename Derived>
+inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr)
+{
+ ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived());
+ return *this;
+}
+
+/** Convert the quaternion to a 3x3 rotation matrix */
+template<typename Scalar>
+inline typename Quaternion<Scalar>::Matrix3
+Quaternion<Scalar>::toRotationMatrix(void) const
+{
+ // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
+ // if not inlined then the cost of the return by value is huge ~ +35%,
+ // however, not inlining this function is an order of magnitude slower, so
+ // it has to be inlined, and so the return by value is not an issue
+ Matrix3 res;
+
+ const Scalar tx = Scalar(2)*this->x();
+ const Scalar ty = Scalar(2)*this->y();
+ const Scalar tz = Scalar(2)*this->z();
+ const Scalar twx = tx*this->w();
+ const Scalar twy = ty*this->w();
+ const Scalar twz = tz*this->w();
+ const Scalar txx = tx*this->x();
+ const Scalar txy = ty*this->x();
+ const Scalar txz = tz*this->x();
+ const Scalar tyy = ty*this->y();
+ const Scalar tyz = tz*this->y();
+ const Scalar tzz = tz*this->z();
+
+ res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
+ res.coeffRef(0,1) = txy-twz;
+ res.coeffRef(0,2) = txz+twy;
+ res.coeffRef(1,0) = txy+twz;
+ res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
+ res.coeffRef(1,2) = tyz-twx;
+ res.coeffRef(2,0) = txz-twy;
+ res.coeffRef(2,1) = tyz+twx;
+ res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
+
+ return res;
+}
+
+/** Sets *this to be a quaternion representing a rotation sending the vector \a a to the vector \a b.
+ *
+ * \returns a reference to *this.
+ *
+ * Note that the two input vectors do \b not have to be normalized.
+ */
+template<typename Scalar>
+template<typename Derived1, typename Derived2>
+inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+ Vector3 v0 = a.normalized();
+ Vector3 v1 = b.normalized();
+ Scalar c = v0.eigen2_dot(v1);
+
+ // if dot == 1, vectors are the same
+ if (ei_isApprox(c,Scalar(1)))
+ {
+ // set to identity
+ this->w() = 1; this->vec().setZero();
+ return *this;
+ }
+ // if dot == -1, vectors are opposites
+ if (ei_isApprox(c,Scalar(-1)))
+ {
+ this->vec() = v0.unitOrthogonal();
+ this->w() = 0;
+ return *this;
+ }
+
+ Vector3 axis = v0.cross(v1);
+ Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2));
+ Scalar invs = Scalar(1)/s;
+ this->vec() = axis * invs;
+ this->w() = s * Scalar(0.5);
+
+ return *this;
+}
+
+/** \returns the multiplicative inverse of \c *this
+ * Note that in most cases, i.e., if you simply want the opposite rotation,
+ * and/or the quaternion is normalized, then it is enough to use the conjugate.
+ *
+ * \sa Quaternion::conjugate()
+ */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
+{
+ // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
+ Scalar n2 = this->squaredNorm();
+ if (n2 > 0)
+ return Quaternion(conjugate().coeffs() / n2);
+ else
+ {
+ // return an invalid result to flag the error
+ return Quaternion(Coefficients::Zero());
+ }
+}
+
+/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
+ * if the quaternion is normalized.
+ * The conjugate of a quaternion represents the opposite rotation.
+ *
+ * \sa Quaternion::inverse()
+ */
+template <typename Scalar>
+inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const
+{
+ return Quaternion(this->w(),-this->x(),-this->y(),-this->z());
+}
+
+/** \returns the angle (in radian) between two rotations
+ * \sa eigen2_dot()
+ */
+template <typename Scalar>
+inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
+{
+ double d = ei_abs(this->eigen2_dot(other));
+ if (d>=1.0)
+ return 0;
+ return Scalar(2) * std::acos(d);
+}
+
+/** \returns the spherical linear interpolation between the two quaternions
+ * \c *this and \a other at the parameter \a t
+ */
+template <typename Scalar>
+Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const
+{
+ static const Scalar one = Scalar(1) - machine_epsilon<Scalar>();
+ Scalar d = this->eigen2_dot(other);
+ Scalar absD = ei_abs(d);
+
+ Scalar scale0;
+ Scalar scale1;
+
+ if (absD>=one)
+ {
+ scale0 = Scalar(1) - t;
+ scale1 = t;
+ }
+ else
+ {
+ // theta is the angle between the 2 quaternions
+ Scalar theta = std::acos(absD);
+ Scalar sinTheta = ei_sin(theta);
+
+ scale0 = ei_sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ scale1 = ei_sin( ( t * theta) ) / sinTheta;
+ if (d<0)
+ scale1 = -scale1;
+ }
+
+ return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
+}
+
+// set from a rotation matrix
+template<typename Other>
+struct ei_quaternion_assign_impl<Other,3,3>
+{
+ typedef typename Other::Scalar Scalar;
+ static inline void run(Quaternion<Scalar>& q, const Other& mat)
+ {
+ // This algorithm comes from "Quaternion Calculus and Fast Animation",
+ // Ken Shoemake, 1987 SIGGRAPH course notes
+ Scalar t = mat.trace();
+ if (t > 0)
+ {
+ t = ei_sqrt(t + Scalar(1.0));
+ q.w() = Scalar(0.5)*t;
+ t = Scalar(0.5)/t;
+ q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
+ q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
+ q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
+ }
+ else
+ {
+ int i = 0;
+ if (mat.coeff(1,1) > mat.coeff(0,0))
+ i = 1;
+ if (mat.coeff(2,2) > mat.coeff(i,i))
+ i = 2;
+ int j = (i+1)%3;
+ int k = (j+1)%3;
+
+ t = ei_sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
+ q.coeffs().coeffRef(i) = Scalar(0.5) * t;
+ t = Scalar(0.5)/t;
+ q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
+ q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
+ q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
+ }
+ }
+};
+
+// set from a vector of coefficients assumed to be a quaternion
+template<typename Other>
+struct ei_quaternion_assign_impl<Other,4,1>
+{
+ typedef typename Other::Scalar Scalar;
+ static inline void run(Quaternion<Scalar>& q, const Other& vec)
+ {
+ q.coeffs() = vec;
+ }
+};
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Rotation2D.h b/Eigen/src/Eigen2Support/Geometry/Rotation2D.h
new file mode 100644
index 0000000..19b8582
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Rotation2D.h
@@ -0,0 +1,145 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Rotation2D
+ *
+ * \brief Represents a rotation/orientation in a 2 dimensional space.
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ *
+ * This class is equivalent to a single scalar representing a counter clock wise rotation
+ * as a single angle in radian. It provides some additional features such as the automatic
+ * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
+ * interface to Quaternion in order to facilitate the writing of generic algorithms
+ * dealing with rotations.
+ *
+ * \sa class Quaternion, class Transform
+ */
+template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> >
+{
+ typedef _Scalar Scalar;
+};
+
+template<typename _Scalar>
+class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
+{
+ typedef RotationBase<Rotation2D<_Scalar>,2> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 2 };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ typedef Matrix<Scalar,2,1> Vector2;
+ typedef Matrix<Scalar,2,2> Matrix2;
+
+protected:
+
+ Scalar m_angle;
+
+public:
+
+ /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
+ inline Rotation2D(Scalar a) : m_angle(a) {}
+
+ /** \returns the rotation angle */
+ inline Scalar angle() const { return m_angle; }
+
+ /** \returns a read-write reference to the rotation angle */
+ inline Scalar& angle() { return m_angle; }
+
+ /** \returns the inverse rotation */
+ inline Rotation2D inverse() const { return -m_angle; }
+
+ /** Concatenates two rotations */
+ inline Rotation2D operator*(const Rotation2D& other) const
+ { return m_angle + other.m_angle; }
+
+ /** Concatenates two rotations */
+ inline Rotation2D& operator*=(const Rotation2D& other)
+ { return m_angle += other.m_angle; return *this; }
+
+ /** Applies the rotation to a 2D vector */
+ Vector2 operator* (const Vector2& vec) const
+ { return toRotationMatrix() * vec; }
+
+ template<typename Derived>
+ Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
+ Matrix2 toRotationMatrix(void) const;
+
+ /** \returns the spherical interpolation between \c *this and \a other using
+ * parameter \a t. It is in fact equivalent to a linear interpolation.
+ */
+ inline Rotation2D slerp(Scalar t, const Rotation2D& other) const
+ { return m_angle * (1-t) + other.angle() * t; }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
+ {
+ m_angle = Scalar(other.angle());
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return ei_isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision 2D rotation type */
+typedef Rotation2D<float> Rotation2Df;
+/** \ingroup Geometry_Module
+ * double precision 2D rotation type */
+typedef Rotation2D<double> Rotation2Dd;
+
+/** Set \c *this from a 2x2 rotation matrix \a mat.
+ * In other words, this function extract the rotation angle
+ * from the rotation matrix.
+ */
+template<typename Scalar>
+template<typename Derived>
+Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+ EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_angle = ei_atan2(mat.coeff(1,0), mat.coeff(0,0));
+ return *this;
+}
+
+/** Constructs and \returns an equivalent 2x2 rotation matrix.
+ */
+template<typename Scalar>
+typename Rotation2D<Scalar>::Matrix2
+Rotation2D<Scalar>::toRotationMatrix(void) const
+{
+ Scalar sinA = ei_sin(m_angle);
+ Scalar cosA = ei_cos(m_angle);
+ return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/RotationBase.h b/Eigen/src/Eigen2Support/Geometry/RotationBase.h
new file mode 100644
index 0000000..b1c8f38
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/RotationBase.h
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+// this file aims to contains the various representations of rotation/orientation
+// in 2D and 3D space excepted Matrix and Quaternion.
+
+/** \class RotationBase
+ *
+ * \brief Common base class for compact rotation representations
+ *
+ * \param Derived is the derived type, i.e., a rotation type
+ * \param _Dim the dimension of the space
+ */
+template<typename Derived, int _Dim>
+class RotationBase
+{
+ public:
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef typename ei_traits<Derived>::Scalar Scalar;
+
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
+
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ /** \returns an equivalent rotation matrix */
+ inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
+
+ /** \returns the inverse rotation */
+ inline Derived inverse() const { return derived().inverse(); }
+
+ /** \returns the concatenation of the rotation \c *this with a translation \a t */
+ inline Transform<Scalar,Dim> operator*(const Translation<Scalar,Dim>& t) const
+ { return toRotationMatrix() * t; }
+
+ /** \returns the concatenation of the rotation \c *this with a scaling \a s */
+ inline RotationMatrixType operator*(const Scaling<Scalar,Dim>& s) const
+ { return toRotationMatrix() * s; }
+
+ /** \returns the concatenation of the rotation \c *this with an affine transformation \a t */
+ inline Transform<Scalar,Dim> operator*(const Transform<Scalar,Dim>& t) const
+ { return toRotationMatrix() * t; }
+};
+
+/** \geometry_module
+ *
+ * Constructs a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ *this = r.toRotationMatrix();
+}
+
+/** \geometry_module
+ *
+ * Set a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
+template<typename OtherDerived>
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
+Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
+::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ return *this = r.toRotationMatrix();
+}
+
+/** \internal
+ *
+ * Helper function to return an arbitrary rotation object to a rotation matrix.
+ *
+ * \param Scalar the numeric type of the matrix coefficients
+ * \param Dim the dimension of the current space
+ *
+ * It returns a Dim x Dim fixed size matrix.
+ *
+ * Default specializations are provided for:
+ * - any scalar type (2D),
+ * - any matrix expression,
+ * - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
+ *
+ * Currently ei_toRotationMatrix is only used by Transform.
+ *
+ * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
+ */
+template<typename Scalar, int Dim>
+static inline Matrix<Scalar,2,2> ei_toRotationMatrix(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return Rotation2D<Scalar>(s).toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+static inline Matrix<Scalar,Dim,Dim> ei_toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
+{
+ return r.toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+static inline const MatrixBase<OtherDerived>& ei_toRotationMatrix(const MatrixBase<OtherDerived>& mat)
+{
+ EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
+ YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return mat;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Scaling.h b/Eigen/src/Eigen2Support/Geometry/Scaling.h
new file mode 100644
index 0000000..b8fa6cd
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Scaling.h
@@ -0,0 +1,167 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Scaling
+ *
+ * \brief Represents a possibly non uniform scaling transformation
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ * \param _Dim the dimension of the space, can be a compile time value or Dynamic
+ *
+ * \note This class is not aimed to be used to store a scaling transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * \sa class Translation, class Transform
+ */
+template<typename _Scalar, int _Dim>
+class Scaling
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
+ /** dimension of the space */
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** corresponding vector type */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** corresponding translation type */
+ typedef Translation<Scalar,Dim> TranslationType;
+ /** corresponding affine transformation type */
+ typedef Transform<Scalar,Dim> TransformType;
+
+protected:
+
+ VectorType m_coeffs;
+
+public:
+
+ /** Default constructor without initialization. */
+ Scaling() {}
+ /** Constructs and initialize a uniform scaling transformation */
+ explicit inline Scaling(const Scalar& s) { m_coeffs.setConstant(s); }
+ /** 2D only */
+ inline Scaling(const Scalar& sx, const Scalar& sy)
+ {
+ ei_assert(Dim==2);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ }
+ /** 3D only */
+ inline Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+ {
+ ei_assert(Dim==3);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ m_coeffs.z() = sz;
+ }
+ /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
+ explicit inline Scaling(const VectorType& coeffs) : m_coeffs(coeffs) {}
+
+ const VectorType& coeffs() const { return m_coeffs; }
+ VectorType& coeffs() { return m_coeffs; }
+
+ /** Concatenates two scaling */
+ inline Scaling operator* (const Scaling& other) const
+ { return Scaling(coeffs().cwise() * other.coeffs()); }
+
+ /** Concatenates a scaling and a translation */
+ inline TransformType operator* (const TranslationType& t) const;
+
+ /** Concatenates a scaling and an affine transformation */
+ inline TransformType operator* (const TransformType& t) const;
+
+ /** Concatenates a scaling and a linear transformation matrix */
+ // TODO returns an expression
+ inline LinearMatrixType operator* (const LinearMatrixType& other) const
+ { return coeffs().asDiagonal() * other; }
+
+ /** Concatenates a linear transformation matrix and a scaling */
+ // TODO returns an expression
+ friend inline LinearMatrixType operator* (const LinearMatrixType& other, const Scaling& s)
+ { return other * s.coeffs().asDiagonal(); }
+
+ template<typename Derived>
+ inline LinearMatrixType operator*(const RotationBase<Derived,Dim>& r) const
+ { return *this * r.toRotationMatrix(); }
+
+ /** Applies scaling to vector */
+ inline VectorType operator* (const VectorType& other) const
+ { return coeffs().asDiagonal() * other; }
+
+ /** \returns the inverse scaling */
+ inline Scaling inverse() const
+ { return Scaling(coeffs().cwise().inverse()); }
+
+ inline Scaling& operator=(const Scaling& other)
+ {
+ m_coeffs = other.m_coeffs;
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Scaling(const Scaling<OtherScalarType,Dim>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Scaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+typedef Scaling<float, 2> Scaling2f;
+typedef Scaling<double,2> Scaling2d;
+typedef Scaling<float, 3> Scaling3f;
+typedef Scaling<double,3> Scaling3d;
+//@}
+
+template<typename Scalar, int Dim>
+inline typename Scaling<Scalar,Dim>::TransformType
+Scaling<Scalar,Dim>::operator* (const TranslationType& t) const
+{
+ TransformType res;
+ res.matrix().setZero();
+ res.linear().diagonal() = coeffs();
+ res.translation() = m_coeffs.cwise() * t.vector();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Scaling<Scalar,Dim>::TransformType
+Scaling<Scalar,Dim>::operator* (const TransformType& t) const
+{
+ TransformType res = t;
+ res.prescale(m_coeffs);
+ return res;
+}
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Transform.h b/Eigen/src/Eigen2Support/Geometry/Transform.h
new file mode 100644
index 0000000..fab60b2
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Transform.h
@@ -0,0 +1,786 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+// Note that we have to pass Dim and HDim because it is not allowed to use a template
+// parameter to define a template specialization. To be more precise, in the following
+// specializations, it is not allowed to use Dim+1 instead of HDim.
+template< typename Other,
+ int Dim,
+ int HDim,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct ei_transform_product_impl;
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Transform
+ *
+ * \brief Represents an homogeneous transformation in a N dimensional space
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients
+ * \param _Dim the dimension of the space
+ *
+ * The homography is internally represented and stored as a (Dim+1)^2 matrix which
+ * is available through the matrix() method.
+ *
+ * Conversion methods from/to Qt's QMatrix and QTransform are available if the
+ * preprocessor token EIGEN_QT_SUPPORT is defined.
+ *
+ * \sa class Matrix, class Quaternion
+ */
+template<typename _Scalar, int _Dim>
+class Transform
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
+ enum {
+ Dim = _Dim, ///< space dimension in which the transformation holds
+ HDim = _Dim+1 ///< size of a respective homogeneous vector
+ };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** type of the matrix used to represent the transformation */
+ typedef Matrix<Scalar,HDim,HDim> MatrixType;
+ /** type of the matrix used to represent the linear part of the transformation */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** type of read/write reference to the linear part of the transformation */
+ typedef Block<MatrixType,Dim,Dim> LinearPart;
+ /** type of read/write reference to the linear part of the transformation */
+ typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart;
+ /** type of a vector */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** type of a read/write reference to the translation part of the rotation */
+ typedef Block<MatrixType,Dim,1> TranslationPart;
+ /** type of a read/write reference to the translation part of the rotation */
+ typedef const Block<const MatrixType,Dim,1> ConstTranslationPart;
+ /** corresponding translation type */
+ typedef Translation<Scalar,Dim> TranslationType;
+ /** corresponding scaling transformation type */
+ typedef Scaling<Scalar,Dim> ScalingType;
+
+protected:
+
+ MatrixType m_matrix;
+
+public:
+
+ /** Default constructor without initialization of the coefficients. */
+ inline Transform() { }
+
+ inline Transform(const Transform& other)
+ {
+ m_matrix = other.m_matrix;
+ }
+
+ inline explicit Transform(const TranslationType& t) { *this = t; }
+ inline explicit Transform(const ScalingType& s) { *this = s; }
+ template<typename Derived>
+ inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
+
+ inline Transform& operator=(const Transform& other)
+ { m_matrix = other.m_matrix; return *this; }
+
+ template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value
+ struct construct_from_matrix
+ {
+ static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
+ {
+ transform->matrix() = other;
+ }
+ };
+
+ template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true>
+ {
+ static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
+ {
+ transform->linear() = other;
+ transform->translation().setZero();
+ transform->matrix()(Dim,Dim) = Scalar(1);
+ transform->matrix().template block<1,Dim>(Dim,0).setZero();
+ }
+ };
+
+ /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ inline explicit Transform(const MatrixBase<OtherDerived>& other)
+ {
+ construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
+ }
+
+ /** Set \c *this from a (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ inline Transform& operator=(const MatrixBase<OtherDerived>& other)
+ { m_matrix = other; return *this; }
+
+ #ifdef EIGEN_QT_SUPPORT
+ inline Transform(const QMatrix& other);
+ inline Transform& operator=(const QMatrix& other);
+ inline QMatrix toQMatrix(void) const;
+ inline Transform(const QTransform& other);
+ inline Transform& operator=(const QTransform& other);
+ inline QTransform toQTransform(void) const;
+ #endif
+
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operaror(int,int) const */
+ inline Scalar operator() (int row, int col) const { return m_matrix(row,col); }
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operaror(int,int) */
+ inline Scalar& operator() (int row, int col) { return m_matrix(row,col); }
+
+ /** \returns a read-only expression of the transformation matrix */
+ inline const MatrixType& matrix() const { return m_matrix; }
+ /** \returns a writable expression of the transformation matrix */
+ inline MatrixType& matrix() { return m_matrix; }
+
+ /** \returns a read-only expression of the linear (linear) part of the transformation */
+ inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); }
+ /** \returns a writable expression of the linear (linear) part of the transformation */
+ inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); }
+
+ /** \returns a read-only expression of the translation vector of the transformation */
+ inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); }
+ /** \returns a writable expression of the translation vector of the transformation */
+ inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); }
+
+ /** \returns an expression of the product between the transform \c *this and a matrix expression \a other
+ *
+ * The right hand side \a other might be either:
+ * \li a vector of size Dim,
+ * \li an homogeneous vector of size Dim+1,
+ * \li a transformation matrix of size Dim+1 x Dim+1.
+ */
+ // note: this function is defined here because some compilers cannot find the respective declaration
+ template<typename OtherDerived>
+ inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
+ operator * (const MatrixBase<OtherDerived> &other) const
+ { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
+
+ /** \returns the product expression of a transformation matrix \a a times a transform \a b
+ * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */
+ template<typename OtherDerived>
+ friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
+ operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
+ { return a.derived() * b.matrix(); }
+
+ /** Contatenates two transformations */
+ inline const Transform
+ operator * (const Transform& other) const
+ { return Transform(m_matrix * other.matrix()); }
+
+ /** \sa MatrixBase::setIdentity() */
+ void setIdentity() { m_matrix.setIdentity(); }
+ static const typename MatrixType::IdentityReturnType Identity()
+ {
+ return MatrixType::Identity();
+ }
+
+ template<typename OtherDerived>
+ inline Transform& scale(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline Transform& prescale(const MatrixBase<OtherDerived> &other);
+
+ inline Transform& scale(Scalar s);
+ inline Transform& prescale(Scalar s);
+
+ template<typename OtherDerived>
+ inline Transform& translate(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
+
+ template<typename RotationType>
+ inline Transform& rotate(const RotationType& rotation);
+
+ template<typename RotationType>
+ inline Transform& prerotate(const RotationType& rotation);
+
+ Transform& shear(Scalar sx, Scalar sy);
+ Transform& preshear(Scalar sx, Scalar sy);
+
+ inline Transform& operator=(const TranslationType& t);
+ inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
+ inline Transform operator*(const TranslationType& t) const;
+
+ inline Transform& operator=(const ScalingType& t);
+ inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
+ inline Transform operator*(const ScalingType& s) const;
+ friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
+ {
+ Transform res = t;
+ res.matrix().row(Dim) = t.matrix().row(Dim);
+ res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
+ return res;
+ }
+
+ template<typename Derived>
+ inline Transform& operator=(const RotationBase<Derived,Dim>& r);
+ template<typename Derived>
+ inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
+ template<typename Derived>
+ inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
+
+ LinearMatrixType rotation() const;
+ template<typename RotationMatrixType, typename ScalingMatrixType>
+ void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
+ template<typename ScalingMatrixType, typename RotationMatrixType>
+ void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
+
+ template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+ Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
+
+ inline const MatrixType inverse(TransformTraits traits = Affine) const;
+
+ /** \returns a const pointer to the column major internal matrix */
+ const Scalar* data() const { return m_matrix.data(); }
+ /** \returns a non-const pointer to the column major internal matrix */
+ Scalar* data() { return m_matrix.data(); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Transform(const Transform<OtherScalarType,Dim>& other)
+ { m_matrix = other.matrix().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_matrix.isApprox(other.m_matrix, prec); }
+
+ #ifdef EIGEN_TRANSFORM_PLUGIN
+ #include EIGEN_TRANSFORM_PLUGIN
+ #endif
+
+protected:
+
+};
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2> Transform2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3> Transform3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2> Transform2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3> Transform3d;
+
+/**************************
+*** Optional QT support ***
+**************************/
+
+#ifdef EIGEN_QT_SUPPORT
+/** Initialises \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>::Transform(const QMatrix& other)
+{
+ *this = other;
+}
+
+/** Set \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other)
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ 0, 0, 1;
+ return *this;
+}
+
+/** \returns a QMatrix from \c *this assuming the dimension is 2.
+ *
+ * \warning this convertion might loss data if \c *this is not affine
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2));
+}
+
+/** Initialises \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>::Transform(const QTransform& other)
+{
+ *this = other;
+}
+
+/** Set \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other)
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ other.m13(), other.m23(), other.m33();
+ return *this;
+}
+
+/** \returns a QTransform from \c *this assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim>
+QTransform Transform<Scalar,Dim>::toQTransform(void) const
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
+}
+#endif
+
+/*********************
+*** Procedural API ***
+*********************/
+
+/** Applies on the right the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa prescale()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ linear() = (linear() * other.asDiagonal()).lazy();
+ return *this;
+}
+
+/** Applies on the right a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa prescale(Scalar)
+ */
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s)
+{
+ linear() *= s;
+ return *this;
+}
+
+/** Applies on the left the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa scale()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
+ return *this;
+}
+
+/** Applies on the left a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa scale(Scalar)
+ */
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s)
+{
+ m_matrix.template corner<Dim,HDim>(TopLeft) *= s;
+ return *this;
+}
+
+/** Applies on the right the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa pretranslate()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ translation() += linear() * other;
+ return *this;
+}
+
+/** Applies on the left the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa translate()
+ */
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ translation() += other;
+ return *this;
+}
+
+/** Applies on the right the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * The template parameter \a RotationType is the type of the rotation which
+ * must be known by ei_toRotationMatrix<>.
+ *
+ * Natively supported types includes:
+ * - any scalar (2D),
+ * - a Dim x Dim matrix expression,
+ * - a Quaternion (3D),
+ * - a AngleAxis (3D)
+ *
+ * This mechanism is easily extendable to support user types such as Euler angles,
+ * or a pair of Quaternion for 4D rotations.
+ *
+ * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
+ */
+template<typename Scalar, int Dim>
+template<typename RotationType>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::rotate(const RotationType& rotation)
+{
+ linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation);
+ return *this;
+}
+
+/** Applies on the left the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * See rotate() for further details.
+ *
+ * \sa rotate()
+ */
+template<typename Scalar, int Dim>
+template<typename RotationType>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::prerotate(const RotationType& rotation)
+{
+ m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation)
+ * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/** Applies on the right the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa preshear()
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ VectorType tmp = linear().col(0)*sy + linear().col(1);
+ linear() << linear().col(0) + linear().col(1)*sx, tmp;
+ return *this;
+}
+
+/** Applies on the left the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa shear()
+ */
+template<typename Scalar, int Dim>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/******************************************************
+*** Scaling, Translation and Rotation compatibility ***
+******************************************************/
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t)
+{
+ linear().setIdentity();
+ translation() = t.vector();
+ m_matrix.template block<1,Dim>(Dim,0).setZero();
+ m_matrix(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const
+{
+ Transform res = *this;
+ res.translate(t.vector());
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
+{
+ m_matrix.setZero();
+ linear().diagonal() = s.coeffs();
+ m_matrix.coeffRef(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
+{
+ Transform res = *this;
+ res.scale(s.coeffs());
+ return res;
+}
+
+template<typename Scalar, int Dim>
+template<typename Derived>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r)
+{
+ linear() = ei_toRotationMatrix<Scalar,Dim>(r);
+ translation().setZero();
+ m_matrix.template block<1,Dim>(Dim,0).setZero();
+ m_matrix.coeffRef(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+template<typename Scalar, int Dim>
+template<typename Derived>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const
+{
+ Transform res = *this;
+ res.rotate(r.derived());
+ return res;
+}
+
+/************************
+*** Special functions ***
+************************/
+
+/** \returns the rotation part of the transformation
+ * \nonstableyet
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), computeScalingRotation(), class SVD
+ */
+template<typename Scalar, int Dim>
+typename Transform<Scalar,Dim>::LinearMatrixType
+Transform<Scalar,Dim>::rotation() const
+{
+ LinearMatrixType result;
+ computeRotationScaling(&result, (LinearMatrixType*)0);
+ return result;
+}
+
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * \nonstableyet
+ *
+ * \svd_module
+ *
+ * \sa computeScalingRotation(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim>
+template<typename RotationMatrixType, typename ScalingMatrixType>
+void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
+{
+ JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
+ Matrix<Scalar, Dim, 1> sv(svd.singularValues());
+ sv.coeffRef(0) *= x;
+ if(scaling)
+ {
+ scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
+ }
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(0) /= x;
+ rotation->noalias() = m * svd.matrixV().adjoint();
+ }
+}
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ * \nonstableyet
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim>
+template<typename ScalingMatrixType, typename RotationMatrixType>
+void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
+{
+ JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
+ Matrix<Scalar, Dim, 1> sv(svd.singularValues());
+ sv.coeffRef(0) *= x;
+ if(scaling)
+ {
+ scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
+ }
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(0) /= x;
+ rotation->noalias() = m * svd.matrixV().adjoint();
+ }
+}
+
+/** Convenient method to set \c *this from a position, orientation and scale
+ * of a 3D object.
+ */
+template<typename Scalar, int Dim>
+template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
+{
+ linear() = ei_toRotationMatrix<Scalar,Dim>(orientation);
+ linear() *= scale.asDiagonal();
+ translation() = position;
+ m_matrix.template block<1,Dim>(Dim,0).setZero();
+ m_matrix(Dim,Dim) = Scalar(1);
+ return *this;
+}
+
+/** \nonstableyet
+ *
+ * \returns the inverse transformation matrix according to some given knowledge
+ * on \c *this.
+ *
+ * \param traits allows to optimize the inversion process when the transformion
+ * is known to be not a general transformation. The possible values are:
+ * - Projective if the transformation is not necessarily affine, i.e., if the
+ * last row is not guaranteed to be [0 ... 0 1]
+ * - Affine is the default, the last row is assumed to be [0 ... 0 1]
+ * - Isometry if the transformation is only a concatenations of translations
+ * and rotations.
+ *
+ * \warning unless \a traits is always set to NoShear or NoScaling, this function
+ * requires the generic inverse method of MatrixBase defined in the LU module. If
+ * you forget to include this module, then you will get hard to debug linking errors.
+ *
+ * \sa MatrixBase::inverse()
+ */
+template<typename Scalar, int Dim>
+inline const typename Transform<Scalar,Dim>::MatrixType
+Transform<Scalar,Dim>::inverse(TransformTraits traits) const
+{
+ if (traits == Projective)
+ {
+ return m_matrix.inverse();
+ }
+ else
+ {
+ MatrixType res;
+ if (traits == Affine)
+ {
+ res.template corner<Dim,Dim>(TopLeft) = linear().inverse();
+ }
+ else if (traits == Isometry)
+ {
+ res.template corner<Dim,Dim>(TopLeft) = linear().transpose();
+ }
+ else
+ {
+ ei_assert("invalid traits value in Transform::inverse()");
+ }
+ // translation and remaining parts
+ res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation();
+ res.template corner<1,Dim>(BottomLeft).setZero();
+ res.coeffRef(Dim,Dim) = Scalar(1);
+ return res;
+ }
+}
+
+/*****************************************************
+*** Specializations of operator* with a MatrixBase ***
+*****************************************************/
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
+{
+ typedef Transform<typename Other::Scalar,Dim> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ {
+ TransformType res;
+ res.translation() = tr.translation();
+ res.matrix().row(Dim) = tr.matrix().row(Dim);
+ res.linear() = (tr.linear() * other).lazy();
+ return res;
+ }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
+{
+ typedef Transform<typename Other::Scalar,Dim> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
+{
+ typedef typename Other::Scalar Scalar;
+ typedef Transform<Scalar,Dim> TransformType;
+ typedef Matrix<Scalar,Dim,1> ResultType;
+ static ResultType run(const TransformType& tr, const Other& other)
+ { return ((tr.linear() * other) + tr.translation())
+ * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
+};
+
+} // end namespace Eigen
diff --git a/Eigen/src/Eigen2Support/Geometry/Translation.h b/Eigen/src/Eigen2Support/Geometry/Translation.h
new file mode 100644
index 0000000..2b9859f
--- /dev/null
+++ b/Eigen/src/Eigen2Support/Geometry/Translation.h
@@ -0,0 +1,184 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Translation
+ *
+ * \brief Represents a translation transformation
+ *
+ * \param _Scalar the scalar type, i.e., the type of the coefficients.
+ * \param _Dim the dimension of the space, can be a compile time value or Dynamic
+ *
+ * \note This class is not aimed to be used to store a translation transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * \sa class Scaling, class Transform
+ */
+template<typename _Scalar, int _Dim>
+class Translation
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
+ /** dimension of the space */
+ enum { Dim = _Dim };
+ /** the scalar type of the coefficients */
+ typedef _Scalar Scalar;
+ /** corresponding vector type */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** corresponding scaling transformation type */
+ typedef Scaling<Scalar,Dim> ScalingType;
+ /** corresponding affine transformation type */
+ typedef Transform<Scalar,Dim> TransformType;
+
+protected:
+
+ VectorType m_coeffs;
+
+public:
+
+ /** Default constructor without initialization. */
+ Translation() {}
+ /** */
+ inline Translation(const Scalar& sx, const Scalar& sy)
+ {
+ ei_assert(Dim==2);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ }
+ /** */
+ inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+ {
+ ei_assert(Dim==3);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ m_coeffs.z() = sz;
+ }
+ /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
+ explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
+
+ const VectorType& vector() const { return m_coeffs; }
+ VectorType& vector() { return m_coeffs; }
+
+ /** Concatenates two translation */
+ inline Translation operator* (const Translation& other) const
+ { return Translation(m_coeffs + other.m_coeffs); }
+
+ /** Concatenates a translation and a scaling */
+ inline TransformType operator* (const ScalingType& other) const;
+
+ /** Concatenates a translation and a linear transformation */
+ inline TransformType operator* (const LinearMatrixType& linear) const;
+
+ template<typename Derived>
+ inline TransformType operator*(const RotationBase<Derived,Dim>& r) const
+ { return *this * r.toRotationMatrix(); }
+
+ /** Concatenates a linear transformation and a translation */
+ // its a nightmare to define a templated friend function outside its declaration
+ friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t)
+ {
+ TransformType res;
+ res.matrix().setZero();
+ res.linear() = linear;
+ res.translation() = linear * t.m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+ }
+
+ /** Concatenates a translation and an affine transformation */
+ inline TransformType operator* (const TransformType& t) const;
+
+ /** Applies translation to vector */
+ inline VectorType operator* (const VectorType& other) const
+ { return m_coeffs + other; }
+
+ /** \returns the inverse translation (opposite) */
+ Translation inverse() const { return Translation(-m_coeffs); }
+
+ Translation& operator=(const Translation& other)
+ {
+ m_coeffs = other.m_coeffs;
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
+ { m_coeffs = other.vector().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+typedef Translation<float, 2> Translation2f;
+typedef Translation<double,2> Translation2d;
+typedef Translation<float, 3> Translation3f;
+typedef Translation<double,3> Translation3d;
+//@}
+
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const ScalingType& other) const
+{
+ TransformType res;
+ res.matrix().setZero();
+ res.linear().diagonal() = other.coeffs();
+ res.translation() = m_coeffs;
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const
+{
+ TransformType res;
+ res.matrix().setZero();
+ res.linear() = linear;
+ res.translation() = m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const TransformType& t) const
+{
+ TransformType res = t;
+ res.pretranslate(m_coeffs);
+ return res;
+}
+
+} // end namespace Eigen