Untested first draft.

vcg/space/plane3.h

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+/****************************************************************************
+* VCGLib                                                            o o     *
+* Visual and Computer Graphics Library                            o     o   *
+*                                                                _   O  _   *
+* Copyright(C) 2004                                                \/)\/    *
+* Visual Computing Lab                                            /\/|      *
+* ISTI - Italian National Research Council                           |      *
+*                                                                    \      *
+* All rights reserved.                                                      *
+*                                                                           *
+* This program is free software; 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.                                       *
+*                                                                           *
+* This program 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 General Public License (http://www.gnu.org/licenses/gpl.txt)          *
+* for more details.                                                         *
+*                                                                           *
+****************************************************************************/
+/****************************************************************************
+  History
+
+$Log: not supported by cvs2svn $
+
+****************************************************************************/
+
+
+
+#ifndef VCG_PLANE3_H
+#define VCG_PLANE3_H
+
+#include <vcg/space/point3.h>
+
+namespace vcg {
+
+/** \addtogroup space */
+/*@{*/
+/** 
+Templated class for 2D planes in 3D spaces.
+  This is the class for infinite planes in 3D space. A Plane is stored just as a Point3 and a scalar:
+	a direction (not necessarily normalized), and a distance from the origin
+	@param T (template parameter) Specifies the type of scalar used to represent coords.
+	@param NORM: if on, the direction is always Normalized
+*/
+template <class T, bool NORM=true> class Plane3 {
+public: 
+  typedef T ScalarType;
+	typedef Point3<T> PointType;
+
+private:
+  /// Distance
+  ScalarType _offset;
+  ///Direction (not necessarily normalized unless NORM is true)
+  PointType _dir;
+
+public:
+  //@{
+	 /** @name Constructors 
+	**/
+	/// The empty constructor
+  Plane3() {}
+  /// The (distance, direction) constructor
+  Plane3(const ScalarType &dist, const PointType &dir) { Set(dist, dir); }
+
+//@{
+	 /** @name Members to access the distance or direction
+	   Direction() cannot be assigned directly.
+		 Use SetDirection() or Set() instead.
+	**/		
+  const ScalarType &Offset() const { return _offset; } 
+  ScalarType &Offset() { return _offset; } 
+  	/// sets the origin
+	void SetOffset( const ScalarType &o ) {	_offset=o; }
+	
+  const PointType &Direction() const { return _dir; } 
+		/// sets the direction
+	void SetDirection( const PointType & dir)	{	
+    _dir=dir; 
+    if (NORM) _dir.Normalize();  
+  }
+		/// sets origin and direction.
+	void Set( const ScalarType & off, const PointType & dir ) {
+    SetOrigin(off); 
+    SetDirection(dir); 
+  }
+
+    /// Operator to compare two lines
+	bool operator==(Plane3 const &p) const	{	
+    return _offset == p._offset && _dir == p._dir; 
+  }
+	  /// Operator to dispare two lines
+	bool operator!=(Plane3 const &p) const	{	
+    return _offset != p._offset || _dir != p._dir; 
+  }
+	
+  ///Project a point on the plane
+  PointType Projection(PointType &p) const	{
+		ScalarType k = p * _dir - _offset;
+		return p - _dir * k;
+	}
+		
+  /// Function to normalize direction
+  void Normalize() {
+	  _dir.Normalize();
+  }
+
+	/// Calculates the plane passing through three points (Rename this method)
+  void Init(const PointType &p0, const PointType &p1, const PointType &p2) {
+	  _dir = (p2 - p0) ^ (p1 - p0);
+	  _offset = p0 * _dist;
+    if(NORM) Normalize();
+  }
+
+  /// Calculates the plane passing through a point and the normal (Rename this method
+  inline void Init(const PointType &p0, const PointType &norm) {
+	  _dir = norm;
+	  _dist = p0 * _dir;
+  }
+};	// end class Plane3
+
+typedef Plane3<float>  Plane3f;
+typedef Plane3<double> Plane3d;
+
+///Distance plane - point (Move this function to somewhere else)
+template<class T> T Distance(const Plane3<T> &plane, const Point3<T> &point) {
+  return plane.Direction() * point - plane.Offset;      
+}
+
+	///Distance point-plane (Move this function to somewhere else)
+template<class T> T Distance(const Point3<T> &po, const Plane3<T> &plane) {
+  return plane.Direction() * point - plane.Offset;      
+}
+
+} // end namespace
+
+
+#endif