text: /****************************************************************************
  
   Copyright (C) 2002-2014 Gilles Debunne. All rights reserved.
  
   This file is part of the QGLViewer library version 2.6.2.
  
   http://www.libqglviewer.com - contact@libqglviewer.com
  
   This file may be used under the terms of the GNU General Public License 
   versions 2.0 or 3.0 as published by the Free Software Foundation and
   appearing in the LICENSE file included in the packaging of this file.
   In addition, as a special exception, Gilles Debunne gives you certain 
   additional rights, described in the file GPL_EXCEPTION in this package.
  
   libQGLViewer uses dual licensing. Commercial/proprietary software must
   purchase a libQGLViewer Commercial License.
  
   This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
   WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
  
  *****************************************************************************/
  
  #ifndef QGLVIEWER_VEC_H
  #define QGLVIEWER_VEC_H
  
  #include <math.h>
  #include <iostream>
  
  # include <QDomElement>
  
  // Included by all files as vec.h is at the end of the include hierarchy
  #include "config.h" // Specific configuration options.
  
  namespace qglviewer {
  
  /*! \brief The Vec class represents 3D positions and 3D vectors.
    \class Vec vec.h QGLViewer/vec.h
  
    Vec is used as a parameter and return type by many methods of the library. It provides classical
    algebraic computational methods and is compatible with OpenGL:
  
    \code
    // Draws a point located at 3.0 OpenGL units in front of the camera
    Vec pos = camera()->position() + 3.0 * camera()->viewDirection();
    glBegin(GL_POINTS);
    glVertex3fv(pos);
    glEnd();
    \endcode
  
    This makes of Vec a good candidate for representing positions and vectors in your programs. Since
    it is part of the \c qglviewer namespace, specify \c qglviewer::Vec or use the qglviewer
    namespace:
    \code
    using namespace qglviewer;
    \endcode
  
    <h3>Interface with other vector classes</h3>
  
    Vec implements a universal explicit converter, based on the \c [] \c operator.
    Everywhere a \c const \c Vec& argument is expected, you can use your own vector type
    instead, as long as it implements this operator (see the Vec(const C& c) documentation).
  
    See also the Quaternion and the Frame documentations.
    \nosubgrouping */
  class QGLVIEWER_EXPORT Vec
  {
  
  	// If your compiler complains the "The class "qglviewer::Vec" has no member "x"."
  	// Add your architecture Q_OS_XXXX flag (see qglobal.h) in this list.
  #if defined (Q_OS_IRIX) || defined (Q_OS_AIX) || defined (Q_OS_HPUX)
  # define QGLVIEWER_UNION_NOT_SUPPORTED
  #endif
  
  public:
  	/*! The internal data representation is public. One can use v.x, v.y, v.z. See also operator[](). */
  #if defined (DOXYGEN) || defined (QGLVIEWER_UNION_NOT_SUPPORTED)
  	qreal x, y, z;
  #else
  	union
  	{
  		struct { qreal x, y, z; };
  		qreal v_[3];
  	};
  #endif
  
  	/*! @name Setting the value */
  	//@{
  	/*! Default constructor. Value is set to (0,0,0). */
  	Vec() : x(0.0), y(0.0), z(0.0) {}
  
  	/*! Standard constructor with the x, y and z values. */
  	Vec(qreal X, qreal Y, qreal Z) : x(X), y(Y), z(Z) {}
  
  	/*! Universal explicit converter from any class to Vec. You can use your own vector class everywhere
    a \c const \c Vec& parameter is required, as long as it implements the \c operator[ ]:
  
    \code
    class MyVec
    {
  	// ...
  	qreal operator[](int i) const { returns x, y or z when i=0, 1 or 2; }
    }
  
    MyVec v(...);
    camera()->setPosition(v);
    \endcode
  
    Note that standard vector types (STL, \c qreal[3], ...) implement this operator and can hence
    be used in place of Vec. See also operator const qreal*() .*/
  	template <class C>
  	explicit Vec(const C& c) : x(c[0]), y(c[1]), z(c[2]) {}
  	// Should NOT be explicit to prevent conflicts with operator<<.
  
  	// ! Copy constructor
  	// Vec(const Vec& v) : x(v.x), y(v.y), z(v.z) {}
  
  	/*! Equal operator. */
  	Vec& operator=(const Vec& v)
  	{
  		x = v.x;   y = v.y;   z = v.z;
  		return *this;
  	}
  
  	/*! Set the current value. May be faster than using operator=() with a temporary Vec(x,y,z). */
  	void setValue(qreal X, qreal Y, qreal Z)
  	{ x=X; y=Y; z=Z; }
  
  	// Universal equal operator which allows the use of any type in place of Vec,
  	// as long as the [] operator is implemented (v[0]=v.x, v[1]=v.y, v[2]=v.z).
  	// template <class C>
  	// Vec& operator=(const C& c)
  	// {
  	// x=c[0]; y=c[1]; z=c[2];
  	// return *this;
  	// }
  	//@}
  
  	/*! @name Accessing the value */
  	//@{
  	/*! Bracket operator, with a constant return value. \p i must range in [0..2]. */
  	qreal operator[](int i) const {
  #ifdef QGLVIEWER_UNION_NOT_SUPPORTED
  		return (&x)[i];
  #else
  		return v_[i];
  #endif
  	}
  
  	/*! Bracket operator returning an l-value. \p i must range in [0..2]. */
  	qreal& operator[](int i) {
  #ifdef QGLVIEWER_UNION_NOT_SUPPORTED
  		return (&x)[i];
  #else
  		return v_[i];
  #endif
  	}
  
  #ifndef DOXYGEN
  	/*! This method is deprecated since version 2.0. Use operator const double* instead. */
  	const double* address() const { qWarning("Vec::address() is deprecated, use operator const double* instead."); return operator const double*(); }
  #endif
  
  	/*! Conversion operator returning the memory address of the vector.
  
    Very convenient to pass a Vec pointer as a parameter to \c GLdouble OpenGL functions:
    \code
    Vec pos, normal;
    glNormal3dv(normal);
    glVertex3dv(pos);
    \endcode */
  	operator const double*() const {
  #ifdef QGLVIEWER_UNION_NOT_SUPPORTED
  		return &x;
  #else
  		return v_;
  #endif
  	}
  
  	/*! Non const conversion operator returning the memory address of the vector.
  
    Useful to pass a Vec to a method that requires and fills a \c double*, as provided by certain libraries. */
  	operator double*() {
  #ifdef QGLVIEWER_UNION_NOT_SUPPORTED
  		return &x;
  #else
  		return v_;
  #endif
  	}
  
  	/*! Conversion operator returning the memory address of the vector.
  
    Very convenient to pass a Vec pointer as a \c float parameter to OpenGL functions:
    \code
    Vec pos, normal;
    glNormal3fv(normal);
    glVertex3fv(pos);
    \endcode
    \note The returned float array is a static shared by all \c Vec instances. */
  	operator const float*() const {
  		static float* const result = new float[3];
  		result[0] = (float)x;
  		result[1] = (float)y;
  		result[2] = (float)z;
  		return result;
  	}
  	//@}
  
  	/*! @name Algebraic computations */
  	//@{
  	/*! Returns the sum of the two vectors. */
  	friend Vec operator+(const Vec &a, const Vec &b)
  	{
  		return Vec(a.x+b.x, a.y+b.y, a.z+b.z);
  	}
  
  	/*! Returns the difference of the two vectors. */
  	friend Vec operator-(const Vec &a, const Vec &b)
  	{
  		return Vec(a.x-b.x, a.y-b.y, a.z-b.z);
  	}
  
  	/*! Unary minus operator. */
  	friend Vec operator-(const Vec &a)
  	{
  		return Vec(-a.x, -a.y, -a.z);
  	}
  
  	/*! Returns the product of the vector with a scalar. */
  	friend Vec operator*(const Vec &a, qreal k)
  	{
  		return Vec(a.x*k, a.y*k, a.z*k);
  	}
  
  	/*! Returns the product of a scalar with the vector. */
  	friend Vec operator*(qreal k, const Vec &a)
  	{
  		return a*k;
  	}
  
  	/*! Returns the division of the vector with a scalar.
  
    Too small \p k values are \e not tested (unless the library was compiled with the "debug" Qt \c
    CONFIG flag) and may result in \c NaN values. */
  	friend Vec operator/(const Vec &a, qreal k)
  	{
  #ifndef QT_NO_DEBUG
  		if (fabs(k) < 1.0E-10)
  			qWarning("Vec::operator / : dividing by a null value (%f)", k);
  #endif
  		return Vec(a.x/k, a.y/k, a.z/k);
  	}
  
  	/*! Returns \c true only when the two vector are not equal (see operator==()). */
  	friend bool operator!=(const Vec &a, const Vec &b)
  	{
  		return !(a==b);
  	}
  
  	/*! Returns \c true when the squaredNorm() of the difference vector is lower than 1E-10. */
  	friend bool operator==(const Vec &a, const Vec &b)
  	{
  		const qreal epsilon = 1.0E-10;
  		return (a-b).squaredNorm() < epsilon;
  	}
  
  	/*! Adds \p a to the vector. */
  	Vec& operator+=(const Vec &a)
  	{
  		x += a.x; y += a.y; z += a.z;
  		return *this;
  	}
  
  	/*! Subtracts \p a to the vector. */
  	Vec& operator-=(const Vec &a)
  	{
  		x -= a.x; y -= a.y; z -= a.z;
  		return *this;
  	}
  
  	/*! Multiply the vector by a scalar \p k. */
  	Vec& operator*=(qreal k)
  	{
  		x *= k; y *= k; z *= k;
  		return *this;
  	}
  
  	/*! Divides the vector by a scalar \p k.
  
    An absolute \p k value lower than 1E-10 will print a warning if the library was compiled with the
    "debug" Qt \c CONFIG flag. Otherwise, no test is performed for efficiency reasons. */
  	Vec& operator/=(qreal k)
  	{
  #ifndef QT_NO_DEBUG
  		if (fabs(k)<1.0E-10)
  			qWarning("Vec::operator /= : dividing by a null value (%f)", k);
  #endif
  		x /= k; y /= k; z /= k;
  		return *this;
  	}
  
  	/*! Dot product of the two Vec. */
  	friend qreal operator*(const Vec &a, const Vec &b)
  	{
  		return a.x*b.x + a.y*b.y + a.z*b.z;
  	}
  
  	/*! Cross product of the two vectors. Same as cross(). */
  	friend Vec operator^(const Vec &a, const Vec &b)
  	{
  		return cross(a,b);
  	}
  
  	/*! Cross product of the two Vec. Mind the order ! */
  	friend Vec cross(const Vec &a, const Vec &b)
  	{
  		return Vec(a.y*b.z - a.z*b.y,
  				   a.z*b.x - a.x*b.z,
  				   a.x*b.y - a.y*b.x);
  	}
  
  	Vec orthogonalVec() const;
  	//@}
  
  	/*! @name Norm of the vector */
  	//@{
  #ifndef DOXYGEN
  	/*! This method is deprecated since version 2.0. Use squaredNorm() instead. */
  	qreal sqNorm() const { return x*x + y*y + z*z; }
  #endif
  
  	/*! Returns the \e squared norm of the Vec. */
  	qreal squaredNorm() const { return x*x + y*y + z*z; }
  
  	/*! Returns the norm of the vector. */
  	qreal norm() const { return sqrt(x*x + y*y + z*z); }
  
  	/*! Normalizes the Vec and returns its original norm.
  
    Normalizing a null vector will result in \c NaN values. */
  	qreal normalize()
  	{
  		const qreal n = norm();
  #ifndef QT_NO_DEBUG
  		if (n < 1.0E-10)
  			qWarning("Vec::normalize: normalizing a null vector (norm=%f)", n);
  #endif
  		*this /= n;
  		return n;
  	}
  
  	/*! Returns a unitary (normalized) \e representation of the vector. The original Vec is not modified. */
  	Vec unit() const
  	{
  		Vec v = *this;
  		v.normalize();
  		return v;
  	}
  	//@}
  
  	/*! @name Projection */
  	//@{
  	void projectOnAxis(const Vec& direction);
  	void projectOnPlane(const Vec& normal);
  	//@}
  
  	/*! @name XML representation */
  	//@{
  	explicit Vec(const QDomElement& element);
  	QDomElement domElement(const QString& name, QDomDocument& document) const;
  	void initFromDOMElement(const QDomElement& element);
  	//@}
  
  #ifdef DOXYGEN
  	/*! @name Output stream */
  	//@{
  	/*! Output stream operator. Enables debugging code like:
    \code
    Vec pos(...);
    cout << "Position=" << pos << endl;
    \endcode */
  	std::ostream& operator<<(std::ostream& o, const qglviewer::Vec&);
  	//@}
  #endif
  };
  
  } // namespace
  
  std::ostream& operator<<(std::ostream& o, const qglviewer::Vec&);
  
  #endif // QGLVIEWER_VEC_H
  