text: /*
      Copyright (c) 2008-2009 NetAllied Systems GmbH
  
      This file is part of COLLADABaseUtils.
  
      Licensed under the MIT Open Source License, 
      for details please see LICENSE file or the website
      http://www.opensource.org/licenses/mit-license.php
  */
  
  #ifndef __COLLADABU_MATH_VECTOR3_H__
  #define __COLLADABU_MATH_VECTOR3_H__
  
  #include "COLLADABUPlatform.h"
  #include "COLLADABUMathPrerequisites.h"
  #include "COLLADABUMathQuaternion.h"
  
  #include <math.h>
  
  namespace COLLADABU
  {
      namespace Math
      {
          /** Standard 3-dimensional vector.
              @remarks
                  A direction in 3D space represented as distances along the 3
                  orthogonal axes (x, y, z). Note that positions, directions and
                  scaling factors can be represented by a vector, depending on how
                  you interpret the values.
          */
  
          class Vector3
          {
  
          public:
              union {
  
                  struct
                  {
                      Real x, y, z;
                  };
  
                  Real val[ 3 ];
              };
  
          public:
              inline Vector3() : x(0), y(0), z(0)
              {}
  
              inline Vector3( Real fX, Real fY, Real fZ )
                      : x( fX ), y( fY ), z( fZ )
              {}
  
              inline Vector3( Real afCoordinate[ 3 ] )
                      : x( afCoordinate[ 0 ] ),
                      y( afCoordinate[ 1 ] ),
                      z( afCoordinate[ 2 ] )
              {}
  
              inline Vector3( int afCoordinate[ 3 ] )
              {
                  x = ( Real ) afCoordinate[ 0 ];
                  y = ( Real ) afCoordinate[ 1 ];
                  z = ( Real ) afCoordinate[ 2 ];
              }
  
              inline Vector3( const Real* const r )
                      : x( r[ 0 ] ), y( r[ 1 ] ), z( r[ 2 ] )
              {}
  
              inline Vector3( const Vector3& rkVector )
                      : x( rkVector.x ), y( rkVector.y ), z( rkVector.z )
              {}
  
  			inline void set( Real fX, Real fY, Real fZ )
  			{
  				x = fX;
  				y = fY;
  				z = fZ;
  			}
  
              inline Real operator [] ( size_t i ) const
              {
  				COLLADABU_ASSERT( i < 3 );
  
                  return *( &x + i );
              }
  
              inline Real& operator [] ( size_t i )
              {
                  COLLADABU_ASSERT( i < 3 );
  
                  return *( &x + i );
              }
  
              /** Assigns the value of the other vector.
                  @param
                      rkVector The other vector
              */
              inline Vector3& operator = ( const Vector3& rkVector )
              {
                  x = rkVector.x;
                  y = rkVector.y;
                  z = rkVector.z;
  
                  return *this;
              }
  
              inline bool operator == ( const Vector3& rkVector ) const
              {
                  return ( x == rkVector.x && y == rkVector.y && z == rkVector.z );
              }
  
              inline bool operator != ( const Vector3& rkVector ) const
              {
                  return ( x != rkVector.x || y != rkVector.y || z != rkVector.z );
              }
  
              // arithmetic operations
              inline Vector3 operator + ( const Vector3& rkVector ) const
              {
                  Vector3 kSum;
  
                  kSum.x = x + rkVector.x;
                  kSum.y = y + rkVector.y;
                  kSum.z = z + rkVector.z;
  
                  return kSum;
              }
  
              inline Vector3 operator - ( const Vector3& rkVector ) const
              {
                  Vector3 kDiff;
  
                  kDiff.x = x - rkVector.x;
                  kDiff.y = y - rkVector.y;
                  kDiff.z = z - rkVector.z;
  
                  return kDiff;
              }
  
              inline Vector3 operator * ( Real fScalar ) const
              {
                  Vector3 kProd;
  
                  kProd.x = fScalar * x;
                  kProd.y = fScalar * y;
                  kProd.z = fScalar * z;
  
                  return kProd;
              }
  
              inline Vector3 operator * ( const Vector3& rhs ) const
              {
                  Vector3 kProd;
  
                  kProd.x = rhs.x * x;
                  kProd.y = rhs.y * y;
                  kProd.z = rhs.z * z;
  
                  return kProd;
              }
  
              inline Vector3 operator / ( Real fScalar ) const
              {
                  COLLADABU_ASSERT( fScalar != 0.0 );
  
                  Vector3 kDiv;
  
                  Real fInv = 1.0 / fScalar;
                  kDiv.x = x * fInv;
                  kDiv.y = y * fInv;
                  kDiv.z = z * fInv;
  
                  return kDiv;
              }
  
              inline Vector3 operator / ( const Vector3& rhs ) const
              {
                  Vector3 kDiv;
  
                  kDiv.x = x / rhs.x;
                  kDiv.y = y / rhs.y;
                  kDiv.z = z / rhs.z;
  
                  return kDiv;
              }
  
  
              inline Vector3 operator - () const
              {
                  Vector3 kNeg;
  
                  kNeg.x = -x;
                  kNeg.y = -y;
                  kNeg.z = -z;
  
                  return kNeg;
              }
  
              inline friend Vector3 operator * ( Real fScalar, const Vector3& rkVector )
              {
                  Vector3 kProd;
  
                  kProd.x = fScalar * rkVector.x;
                  kProd.y = fScalar * rkVector.y;
                  kProd.z = fScalar * rkVector.z;
  
                  return kProd;
              }
  
              // arithmetic updates
              inline Vector3& operator += ( const Vector3& rkVector )
              {
                  x += rkVector.x;
                  y += rkVector.y;
                  z += rkVector.z;
  
                  return *this;
              }
  
              inline Vector3& operator -= ( const Vector3& rkVector )
              {
                  x -= rkVector.x;
                  y -= rkVector.y;
                  z -= rkVector.z;
  
                  return *this;
              }
  
              inline Vector3& operator *= ( Real fScalar )
              {
                  x *= fScalar;
                  y *= fScalar;
                  z *= fScalar;
                  return *this;
              }
  
              inline Vector3& operator *= ( const Vector3& rkVector )
              {
                  x *= rkVector.x;
                  y *= rkVector.y;
                  z *= rkVector.z;
  
                  return *this;
              }
  
              inline Vector3& operator /= ( Real fScalar )
              {
                  COLLADABU_ASSERT( fScalar != 0.0 );
  
                  Real fInv = 1.0 / fScalar;
  
                  x *= fInv;
                  y *= fInv;
                  z *= fInv;
  
                  return *this;
              }
  
              inline Vector3& operator /= ( const Vector3& rkVector )
              {
                  x /= rkVector.x;
                  y /= rkVector.y;
                  z /= rkVector.z;
  
                  return *this;
              }
  
  
              /** Returns the length (magnitude) of the vector.
                  @warning
                      This operation requires a square root and is expensive in
                      terms of CPU operations. If you don't need to know the exact
                      length (e.g. for just comparing lengths) use squaredLength()
                      instead.
              */
              inline Real length () const
              {
                  return sqrt( x * x + y * y + z * z );
              }
  
              /** Returns the square of the length(magnitude) of the vector.
                  @remarks
                      This  method is for efficiency - calculating the actual
                      length of a vector requires a square root, which is expensive
                      in terms of the operations required. This method returns the
                      square of the length of the vector, i.e. the same as the
                      length but before the square root is taken. Use this if you
                      want to find the longest / shortest vector without incurring
                      the square root.
              */
              inline Real squaredLength () const
              {
                  return x * x + y * y + z * z;
              }
  
              /** Calculates the dot (scalar) product of this vector with another.
                  @remarks
                      The dot product can be used to calculate the angle between 2
                      vectors. If both are unit vectors, the dot product is the
                      cosine of the angle; otherwise the dot product must be
                      divided by the product of the lengths of both vectors to get
                      the cosine of the angle. This result can further be used to
                      calculate the distance of a point from a plane.
                  @param
                      vec Vector with which to calculate the dot product (together
                      with this one).
                  @returns
                      A float representing the dot product value.
              */
              inline Real dotProduct( const Vector3& vec ) const
              {
                  return x * vec.x + y * vec.y + z * vec.z;
              }
  
              /** Normalises the vector.
                  @remarks
                      This method normalises the vector such that it's
                      length / magnitude is 1. The result is called a unit vector.
                  @note
                      This function will not crash for zero-sized vectors, but there
                      will be no changes made to their components.
                  @returns The previous length of the vector.
              */
              inline Real normalise()
              {
                  Real fLength = sqrt( x * x + y * y + z * z );
  
                  // Will also work for zero-sized vectors, but will change nothing
  
                  if ( fLength > 1e-08 )
                  {
                      Real fInvLength = 1.0 / fLength;
                      x *= fInvLength;
                      y *= fInvLength;
                      z *= fInvLength;
                  }
  
                  return fLength;
              }
  
              /** Calculates the cross-product of 2 vectors, i.e. the vector that
                  lies perpendicular to them both.
                  @remarks
                      The cross-product is normally used to calculate the normal
                      vector of a plane, by calculating the cross-product of 2
                      non-equivalent vectors which lie on the plane (e.g. 2 edges
                      of a triangle).
                  @param
                      rkVector Vector which, together with this one, will be used to
                      calculate the cross-product.
                  @returns
                      A vector which is the result of the cross-product. This
                      vector will <b>NOT</b> be normalised, to maximise efficiency
                      - call Vector3::normalise on the result if you wish this to
                      be done. As for which side the resultant vector will be on, the
                      returned vector will be on the side from which the arc from 'this'
                      to rkVector is anticlockwise, e.g. UNIT_Y.crossProduct(UNIT_Z) 
                      = UNIT_X, whilst UNIT_Z.crossProduct(UNIT_Y) = -UNIT_X.
                  @par
                      For a clearer explanation, look a the left and the bottom edges
                      of your monitor's screen. Assume that the first vector is the
                      left edge and the second vector is the bottom edge, both of
                      them starting from the lower-left corner of the screen. The
                      resulting vector is going to be perpendicular to both of them
                      and will go <i>inside</i> the screen, towards the cathode tube
                      (assuming you're using a CRT monitor, of course).
              */
              inline Vector3 crossProduct( const Vector3& rkVector ) const
              {
                  Vector3 kCross;
  
                  kCross.x = y * rkVector.z - z * rkVector.y;
                  kCross.y = z * rkVector.x - x * rkVector.z;
                  kCross.z = x * rkVector.y - y * rkVector.x;
  
                  return kCross;
              }
  
              /** Returns a vector at a point half way between this and the passed
                  in vector.
              */
              inline Vector3 midPoint( const Vector3& vec ) const
              {
                  return Vector3(
                             ( x + vec.x ) * 0.5,
                             ( y + vec.y ) * 0.5,
                             ( z + vec.z ) * 0.5 );
              }
  
              /** Returns true if the vector's scalar components are all greater
                  that the ones of the vector it is compared against.
              */
              inline bool operator < ( const Vector3& rhs ) const
              {
                  if ( x < rhs.x && y < rhs.y && z < rhs.z )
                      return true;
  
                  return false;
              }
  
              /** Returns true if the vector's scalar components are all smaller
                  that the ones of the vector it is compared against.
              */
              inline bool operator > ( const Vector3& rhs ) const
              {
                  if ( x > rhs.x && y > rhs.y && z > rhs.z )
                      return true;
  
                  return false;
              }
  
              /** Sets this vector's components to the minimum of its own and the
                  ones of the passed in vector.
                  @remarks
                      'Minimum' in this case means the combination of the lowest
                      value of x, y and z from both vectors. Lowest is taken just
                      numerically, not magnitude, so -1 < 0.
              */
              inline void makeFloor( const Vector3& cmp )
              {
                  if ( cmp.x < x )
                      x = cmp.x;
  
                  if ( cmp.y < y )
                      y = cmp.y;
  
                  if ( cmp.z < z )
                      z = cmp.z;
              }
  
              /** Sets this vector's components to the maximum of its own and the
                  ones of the passed in vector.
                  @remarks
                      'Maximum' in this case means the combination of the highest
                      value of x, y and z from both vectors. Highest is taken just
                      numerically, not magnitude, so 1 > -3.
              */
              inline void makeCeil( const Vector3& cmp )
              {
                  if ( cmp.x > x )
                      x = cmp.x;
  
                  if ( cmp.y > y )
                      y = cmp.y;
  
                  if ( cmp.z > z )
                      z = cmp.z;
              }
  
              /** Generates a vector perpendicular to this vector (eg an 'up' vector).
                  @remarks
                      This method will return a vector which is perpendicular to this
                      vector. There are an infinite number of possibilities but this 
                      method will guarantee to generate one of them. If you need more 
                      control you should use the Quaternion class.
              */
              inline Vector3 perpendicular( void ) const
              {
                  static const Real fSquareZero = 1e-06 * 1e-06;
  
                  Vector3 perp = this->crossProduct( Vector3::UNIT_X );
  
                  // Check length
  
                  if ( perp.squaredLength() < fSquareZero )
                  {
                      /* This vector is the Y axis multiplied by a scalar, so we have
                         to use another axis.
                      */
                      perp = this->crossProduct( Vector3::UNIT_Y );
                  }
  
                  return perp;
              }
  
  
  
              /** Returns true if this vector is zero length. */
              inline bool isZeroLength( void ) const
              {
                  Real sqlen = ( x * x ) + ( y * y ) + ( z * z );
                  return ( sqlen < ( 1e-06 * 1e-06 ) );
  
              }
  
              /** As normalise, except that this vector is unaffected and the
                  normalised vector is returned as a copy. */
              inline Vector3 normalisedCopy( void ) const
              {
                  Vector3 ret = *this;
                  ret.normalise();
                  return ret;
              }
  
              /** Calculates a reflection vector to the plane with the given normal .
              @remarks NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not.
              */
              inline Vector3 reflect( const Vector3& normal ) const
              {
                  return Vector3( *this - ( 2 * this->dotProduct( normal ) * normal ) );
              }
  
  
              /** Returns whether this vector is within a directional tolerance
               of another vector.
              @param rhs The vector to compare with
              @param tolerance_radian The maximum angle by which the vectors may vary and
               still be considered equal
              */
              inline bool directionEquals( const Vector3& rhs,
                                           const Real& tolerance_radian ) const
              {
                  Real dot = dotProduct( rhs );
                  Real angle_radian = acos( dot );
  
                  return fabs( angle_radian ) <= tolerance_radian;
  
              }
  
              // special points
              static const Vector3 ZERO;
              static const Vector3 UNIT_X;
              static const Vector3 UNIT_Y;
              static const Vector3 UNIT_Z;
              static const Vector3 NEGATIVE_UNIT_X;
              static const Vector3 NEGATIVE_UNIT_Y;
              static const Vector3 NEGATIVE_UNIT_Z;
              static const Vector3 UNIT_SCALE;
  
          };
  		
      }	        
  }
  
  #endif //__COLLADABU_MATH_VECTOR3_H__
  