some hyperplane changes:

- the coefficients are stored in a single vector
- added transformation methods
- removed Line* typedef since in 2D this is really an hyperplane
  and not really a line...
- HyperPlane => Hyperplane

1 files changed, 179 insertions, 0 deletions

diff --git a/Eigen/src/Geometry/Hyperplane.h b/Eigen/src/Geometry/Hyperplane.h
new file mode 100644
index 000000000..f7049883e
--- /dev/null
+++ b/Eigen/src/Geometry/Hyperplane.h
@@ -0,0 +1,179 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_Hyperplane_H
+#define EIGEN_Hyperplane_H
+
+/** \geometry_module \ingroup GeometryModule
+  *
+  * \class Hyperplane
+  *
+  * \brief Represents an hyper plane in any dimensions
+  *
+  * \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
+  *
+  * This class represents an hyper-plane as the zero set of the implicit equation
+  * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is the normal of the plane (linear part)
+  * and \f$ d \f$ is the distance (offset) to the origin.
+  *
+  */
+
+template <typename _Scalar, int _Dim>
+class Hyperplane
+{
+
+  public:
+
+    enum { DimAtCompileTime = _Dim };
+    typedef _Scalar Scalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+    typedef Matrix<Scalar,DimAtCompileTime,1> VectorType;
+    typedef Matrix<Scalar,DimAtCompileTime==Dynamic
+                          ? Dynamic
+                          : DimAtCompileTime+1,1> Coefficients;
+    typedef Block<Coefficients,DimAtCompileTime,1> NormalReturnType;
+
+    /** Default constructor without initialization */
+    inline Hyperplane(int _dim = DimAtCompileTime) : 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.dot(n);
+    }
+    
+    /** Constructs a plane from its normal \a n and distance to the origin \a d.
+      * \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;
+    }
+    
+    ~Hyperplane() {}
+
+    /** \returns the dimension in which the plane holds */
+    inline int dim() const { return DimAtCompileTime==Dynamic ? m_coeffs.size()-1 : DimAtCompileTime; }
+
+    void normalize(void);
+    
+    /** \returns the signed distance between the plane \c *this and a point \a p.
+      */
+    inline Scalar distanceTo(const VectorType& p) const { return p.dot(normal()) + offset(); }
+    
+    /** \returns the projection of a point \a p onto the plane \c *this.
+      */
+    inline VectorType project(const VectorType& p) const { return p - distanceTo(p) * normal(); }
+
+    /**  \returns the normal of the plane, which corresponds to the linear part of the implicit equation. */
+    inline const NormalReturnType normal() const { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+    /** \returns the distance to the origin, which is also the constant part
+      * of the implicit equation */
+    inline Scalar offset() const { return m_coeffs(dim()); }
+    
+    /** Set the normal of the plane.
+      * \warning the vector normal is assumed to be normalized. */
+    inline void setNormal(const VectorType& normal) { _normal() = normal; }
+
+    /** Set the distance to origin */
+    inline void setOffset(Scalar d) { _offset() = d; }
+
+    /** \returns the coefficients c_i of the plane equation:
+      * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+      */
+    // FIXME name: equation vs coeffs vs coefficients ???
+    inline Coefficients equation(void) const { return m_coeffs; }
+    
+    /** \brief Plane/ray intersection.
+        Returns the parameter value of the intersection between the plane \a *this
+        and the parametric ray of origin \a rayOrigin and axis \a rayDir
+    */
+    inline Scalar rayIntersection(const VectorType& rayOrigin, const VectorType& rayDir)
+    {
+      return -(_offset()+rayOrigin.dot(_normal()))/(rayDir.dot(_normal()));
+    }
+
+    template<typename XprType>
+    inline Hyperplane operator* (const MatrixBase<XprType>& mat) const
+    { return Hyperplane(mat.inverse().transpose() * _normal(), _offset()); }
+
+    template<typename XprType>
+    inline Hyperplane& operator*= (const MatrixBase<XprType>& mat) const
+    { _normal() = mat.inverse().transpose() * _normal(); return *this; }
+
+    // TODO some convenient functions to fit a 3D plane on 3 points etc...
+//     void makePassBy(const VectorType& p0, const VectorType& p1, const VectorType& p2)
+//     {
+//       EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(3);
+//       m_normal = (p2 - p0).cross(p1 - p0).normalized();
+//       m_offset = -m_normal.dot(p0);
+//     }
+// 
+//     void makePassBy(const VectorType& p0, const VectorType& p1)
+//     {
+//       EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(2);
+//       m_normal = (p2 - p0).cross(p1 - p0).normalized();
+//       m_offset = -m_normal.dot(p0);
+//     }
+
+protected:
+
+    inline NormalReturnType _normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+    inline Scalar& _offset() { return m_coeffs(dim()); }
+
+    Coefficients m_coeffs;
+};
+
+/** \addtogroup GeometryModule */
+//@{
+typedef Hyperplane<float, 2> Hyperplane2f;
+typedef Hyperplane<double,2> Hyperplane2d;
+typedef Hyperplane<float, 3> Hyperplane3f;
+typedef Hyperplane<double,3> Hyperplane3d;
+
+typedef Hyperplane<float, 3> Planef;
+typedef Hyperplane<double,3> Planed;
+
+typedef Hyperplane<float, Dynamic> HyperplaneXf;
+typedef Hyperplane<double,Dynamic> HyperplaneXd;
+//@}
+
+/** normalizes \c *this */
+template <typename _Scalar, int _Dim>
+void Hyperplane<_Scalar,_Dim>::normalize(void)
+{
+  RealScalar l = Scalar(1)/_normal().norm();
+  _normal() *= l;
+  _offset() *= l;
+}
+
+#endif // EIGEN_Hyperplane_H