Torque3D/Engine/source/math/mPoint3.h

//-----------------------------------------------------------------------------
// Copyright (c) 2012 GarageGames, LLC
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
//-----------------------------------------------------------------------------

#ifndef _MPOINT3_H_
#define _MPOINT3_H_

#ifndef _MMATHFN_H_
#include "math/mMathFn.h"
#endif
#ifndef _MPOINT2_H_
#include "math/mPoint2.h"
#endif

//------------------------------------------------------------------------------
/// 3D integer point
///
/// Uses S32 internally.
class Point3I
{
   //-------------------------------------- Public data
  public:
   S32 x;                                                   ///< X co-ordinate
   S32 y;                                                   ///< Y co-ordinate
   S32 z;                                                   ///< Z co-ordinate

   //-------------------------------------- Public interface
  public:
   Point3I();               ///< Create an uninitialized point.
   Point3I(const Point3I&); ///< Copy constructor.
   explicit Point3I(S32 xyz);        ///< Initializes all elements to the same value.
   Point3I(S32 in_x, S32 in_y, S32 in_z); ///< Create a point from co-ordinates.

   //-------------------------------------- Non-math mutators and misc functions
   void set(S32 xyz);           ///< Initializes all elements to the same value.
   void set(S32 in_x, S32 in_y, S32 in_z); ///< Set co-ordinates.
   void setMin(const Point3I&); ///< Store lesser co-ordinates in this point.
   void setMax(const Point3I&); ///< Store greater co-ordinates in this point.
   void zero();                 ///< Zero all values

   //-------------------------------------- Math mutators
   void neg();                      ///< Invert co-ordinate's signs.
   void convolve(const Point3I&);   ///< Convolve by parameter.

   //-------------------------------------- Queries
   bool isZero() const;             ///< Check for point at origin. (No epsilon.)
   F32  len() const;                ///< Get length.

   //-------------------------------------- Overloaded operators
  public:
   operator S32*() { return &x; }
   operator const S32*() const { return &x; }

   // Comparison operators
   bool operator==(const Point3I&) const;
   bool operator!=(const Point3I&) const;

   // Arithmetic w/ other points
   Point3I  operator+(const Point3I&) const;
   Point3I  operator-(const Point3I&) const;
   Point3I& operator+=(const Point3I&);
   Point3I& operator-=(const Point3I&);

   // Arithmetic w/ scalars
   Point3I  operator*(S32) const;
   Point3I& operator*=(S32);
   Point3I  operator/(S32) const;
   Point3I& operator/=(S32);

   // Unary operators
   Point3I operator-() const;

   //-------------------------------------- Public static constants
public:
   const static Point3I One;
   const static Point3I Zero;
};

class Point3D;

//------------------------------------------------------------------------------
class Point3F
{
   //-------------------------------------- Public data
  public:
   F32 x;
   F32 y;
   F32 z;

  public:
   Point3F();
   Point3F(const Point3F&);
   Point3F(F32 _x, F32 _y, F32 _z);
   explicit Point3F(F32 xyz);

   //-------------------------------------- Non-math mutators and misc functions
  public:
   void set(F32 xyz);
   void set(F32 _x, F32 _y, F32 _z);
   void set(const Point3F&);

   void setMin(const Point3F&);
   void setMax(const Point3F&);

   void interpolate(const Point3F&, const Point3F&, F32);
   void zero();

   /// Returns the smallest absolute value.
   F32 least() const;

   /// Returns the greatest absolute value.
   F32 most() const;

   operator F32*() { return &x; }
   operator const F32*() const { return &x; }

   /// Returns the x and y coords as a Point2F.
   Point2F asPoint2F() const { return Point2F( x, y ); }

   //-------------------------------------- Queries
  public:
   bool  isZero() const;
   bool  isUnitLength() const;
   F32   len()    const;
   F32   lenSquared() const;
   F32   magnitudeSafe() const;
   bool  equal( const Point3F &compare, F32 epsilon = POINT_EPSILON ) const;
   U32   getLeastComponentIndex() const;
   U32   getGreatestComponentIndex() const;

   //-------------------------------------- Mathematical mutators
  public:
   void neg();
   void normalize();
   void normalizeSafe();
   void normalize(F32 val);
   void convolve(const Point3F&);
   void convolveInverse(const Point3F&);

   //-------------------------------------- Overloaded operators
  public:
   // Comparison operators
   bool operator==(const Point3F&) const;
   bool operator!=(const Point3F&) const;

   // Arithmetic w/ other points
   Point3F  operator+(const Point3F&) const;
   Point3F  operator-(const Point3F&) const;
   Point3F& operator+=(const Point3F&);
   Point3F& operator-=(const Point3F&);

   // Arithmetic w/ scalars
   Point3F  operator*(F32) const;
   Point3F  operator/(F32) const;
   Point3F& operator*=(F32);
   Point3F& operator/=(F32);

   Point3F  operator*(const Point3F&) const;
   Point3F& operator*=(const Point3F&);
   Point3F  operator/(const Point3F&) const;
   Point3F& operator/=(const Point3F&);

   // Unary operators
   Point3F operator-() const;

   Point3F& operator=(const Point3D&);

   //-------------------------------------- Public static constants
public:
   const static Point3F One;
   const static Point3F Zero;
   const static Point3F Max;
   const static Point3F Min;
   const static Point3F UnitX;
   const static Point3F UnitY;
   const static Point3F UnitZ;
};

typedef Point3F VectorF;
typedef Point3F EulerF;


//------------------------------------------------------------------------------
class Point3D
{
   //-------------------------------------- Public data
  public:
   F64 x;
   F64 y;
   F64 z;

  public:
   Point3D();
   Point3D(const Point3D&);
   Point3D(const Point3F&);
   explicit Point3D(F64 xyz);
   Point3D(F64 _x, F64 _y, F64 _z);

   //-------------------------------------- Non-math mutators and misc functions
  public:
   void set(F64 xyz);
   void set(F64 _x, F64 _y, F64 _z);

   void setMin(const Point3D&);
   void setMax(const Point3D&);

   void interpolate(const Point3D&, const Point3D&, F64);
   void zero();

   operator F64*() { return (&x); }
   operator const F64*() const { return &x; }

   //-------------------------------------- Queries
  public:
   bool  isZero() const;
   F64 len()    const;
   F64 lenSquared() const;

   //-------------------------------------- Mathematical mutators
  public:
   void neg();
   void normalize();
   void normalize(F64 val);
   void convolve(const Point3D&);
   void convolveInverse(const Point3D&);

   //-------------------------------------- Overloaded operators
  public:
   Point3F toPoint3F() const;
   // Comparison operators
   bool operator==(const Point3D&) const;
   bool operator!=(const Point3D&) const;

   // Arithmetic w/ other points
   Point3D  operator+(const Point3D&) const;
   Point3D  operator-(const Point3D&) const;
   Point3D& operator+=(const Point3D&);
   Point3D& operator-=(const Point3D&);

   // Arithmetic w/ scalars
   Point3D  operator*(F64) const;
   Point3D  operator/(F64) const;
   Point3D& operator*=(F64);
   Point3D& operator/=(F64);

   // Unary operators
   Point3D operator-() const;

   //-------------------------------------- Public static constants
public:
   const static Point3D One;
   const static Point3D Zero;
};

//------------------------------------------------------------------------------
//-------------------------------------- Point3I
//
inline Point3I::Point3I()
{
   //
}

inline Point3I::Point3I(const Point3I& _copy)
 : x(_copy.x), y(_copy.y), z(_copy.z)
{
   //
}

inline Point3I::Point3I(S32 xyz)
 : x(xyz), y(xyz), z(xyz)
{
   //
}

inline Point3I::Point3I(S32 _x, S32 _y, S32 _z)
 : x(_x), y(_y), z(_z)
{
   //
}

inline void Point3I::set(S32 xyz)
{
   x = y = z = xyz;
}

inline void Point3I::set(S32 _x, S32 _y, S32 _z)
{
   x = _x;
   y = _y;
   z = _z;
}

inline void Point3I::setMin(const Point3I& _test)
{
   x = (_test.x < x) ? _test.x : x;
   y = (_test.y < y) ? _test.y : y;
   z = (_test.z < z) ? _test.z : z;
}

inline void Point3I::setMax(const Point3I& _test)
{
   x = (_test.x > x) ? _test.x : x;
   y = (_test.y > y) ? _test.y : y;
   z = (_test.z > z) ? _test.z : z;
}

inline void Point3I::zero()
{
   x = y = z = 0;
}

inline void Point3I::neg()
{
   x = -x;
   y = -y;
   z = -z;
}

inline F32 Point3I::len() const
{
   return mSqrt(F32(x*x + y*y + z*z));
}

inline void Point3I::convolve(const Point3I& c)
{
   x *= c.x;
   y *= c.y;
   z *= c.z;
}

inline bool Point3I::isZero() const
{
   return ((x == 0) && (y == 0) && (z == 0));
}

inline bool Point3I::operator==(const Point3I& _test) const
{
   return ((x == _test.x) && (y == _test.y) && (z == _test.z));
}

inline bool Point3I::operator!=(const Point3I& _test) const
{
   return (operator==(_test) == false);
}

inline Point3I Point3I::operator+(const Point3I& _add) const
{
   return Point3I(x + _add.x, y + _add.y, z + _add.z);
}

inline Point3I Point3I::operator-(const Point3I& _rSub) const
{
   return Point3I(x - _rSub.x, y - _rSub.y, z - _rSub.z);
}

inline Point3I& Point3I::operator+=(const Point3I& _add)
{
   x += _add.x;
   y += _add.y;
   z += _add.z;

   return *this;
}

inline Point3I& Point3I::operator-=(const Point3I& _rSub)
{
   x -= _rSub.x;
   y -= _rSub.y;
   z -= _rSub.z;

   return *this;
}

inline Point3I Point3I::operator-() const
{
   return Point3I(-x, -y, -z);
}

inline Point3I Point3I::operator*(S32 mul) const
{
   return Point3I(x * mul, y * mul, z * mul);
}

inline Point3I Point3I::operator/(S32 div) const
{
   AssertFatal(div != 0, "Error, div by zero attempted");
   return Point3I(x/div, y/div, z/div);
}

inline Point3I& Point3I::operator*=(S32 mul)
{
   x *= mul;
   y *= mul;
   z *= mul;

   return *this;
}

inline Point3I& Point3I::operator/=(S32 div)
{
   AssertFatal(div != 0, "Error, div by zero attempted");

   x /= div;
   y /= div;
   z /= div;

   return *this;
}

//------------------------------------------------------------------------------
//-------------------------------------- Point3F
//
inline Point3F::Point3F()
#if defined(TORQUE_OS_LINUX)
 : x(0.f), y(0.f), z(0.f)
#endif
{
// Uninitialized points are definitely a problem.
// Enable the following code to see how often they crop up.
#ifdef DEBUG_MATH
   *(U32 *)&x = 0x7FFFFFFA;
   *(U32 *)&y = 0x7FFFFFFB;
   *(U32 *)&z = 0x7FFFFFFC;
#endif
}


inline Point3F::Point3F(const Point3F& _copy)
 : x(_copy.x), y(_copy.y), z(_copy.z)
{
   //
}

inline Point3F::Point3F(F32 _x, F32 _y, F32 _z)
 : x(_x), y(_y), z(_z)
{
   //
}

inline Point3F::Point3F(F32 xyz)
 : x(xyz), y(xyz), z(xyz)
{
   //
}

inline void Point3F::set(F32 xyz)
{
   x = y = z = xyz;
}

inline void Point3F::set(F32 _x, F32 _y, F32 _z)
{
   x = _x;
   y = _y;
   z = _z;
}

inline void Point3F::set(const Point3F& copy)
{
   x = copy.x;
   y = copy.y;
   z = copy.z;
}

inline void Point3F::setMin(const Point3F& _test)
{
   x = (_test.x < x) ? _test.x : x;
   y = (_test.y < y) ? _test.y : y;
   z = (_test.z < z) ? _test.z : z;
}

inline void Point3F::setMax(const Point3F& _test)
{
   x = (_test.x > x) ? _test.x : x;
   y = (_test.y > y) ? _test.y : y;
   z = (_test.z > z) ? _test.z : z;
}

inline void Point3F::interpolate(const Point3F& _from, const Point3F& _to, F32 _factor)
{
   AssertFatal(_factor >= 0.0f && _factor <= 1.0f, "Out of bound interpolation factor");
   m_point3F_interpolate( _from, _to, _factor, *this);
}

inline void Point3F::zero()
{
   x = y = z = 0.0f;
}

inline bool Point3F::isZero() const
{
   return ((x*x) <= POINT_EPSILON) && ((y*y) <= POINT_EPSILON) && ((z*z) <= POINT_EPSILON );
}

inline bool Point3F::isUnitLength() const
{
   return ( mFabs( 1.0f - ( x*x + y*y + z*z ) ) < POINT_EPSILON );
}

inline bool Point3F::equal( const Point3F &compare, F32 epsilon ) const
{
   return( ( mFabs( x - compare.x ) < epsilon ) &&
           ( mFabs( y - compare.y ) < epsilon ) &&
           ( mFabs( z - compare.z ) < epsilon ) );
}

inline U32 Point3F::getLeastComponentIndex() const
{
   U32 idx;

   if ( mFabs( x ) < mFabs( y ) )
   {
      if ( mFabs( x ) < mFabs( z ) )
         idx = 0;
      else
         idx = 2;
   }
   else
   {
      if ( mFabs( y ) < mFabs( z ) )
         idx = 1;  
      else
         idx = 2;
   }

   return idx;
}

inline U32 Point3F::getGreatestComponentIndex() const
{
   U32 idx;

   if ( mFabs( x ) > mFabs( y ) )
   {
      if ( mFabs( x ) > mFabs( z ) )
         idx = 0;
      else
         idx = 2;
   }
   else
   {
      if ( mFabs( y ) > mFabs( z ) )
         idx = 1;  
      else
         idx = 2;
   }

   return idx;
}

inline F32 Point3F::least() const
{
   return getMin( mFabs( x ), getMin( mFabs( y ), mFabs( z ) ) );
}

inline F32 Point3F::most() const
{
   return getMax( mFabs( x ), getMax( mFabs( y ), mFabs( z ) ) );
}

inline void Point3F::neg()
{
   x = -x;
   y = -y;
   z = -z;
}

inline void Point3F::convolve(const Point3F& c)
{
   x *= c.x;
   y *= c.y;
   z *= c.z;
}

inline void Point3F::convolveInverse(const Point3F& c)
{
   x /= c.x;
   y /= c.y;
   z /= c.z;
}

inline F32 Point3F::lenSquared() const
{
   return (x * x) + (y * y) + (z * z);
}

inline F32 Point3F::len() const
{
   return mSqrt(x*x + y*y + z*z);
}

inline void Point3F::normalize()
{
   m_point3F_normalize(*this);
}

inline F32 Point3F::magnitudeSafe() const
{
   if( isZero() )
   {
      return 0.0f;
   }
   else
   {
      return len();
   }
}

inline void Point3F::normalizeSafe()
{
   F32 vmag = magnitudeSafe();

   if( vmag > POINT_EPSILON )
   {
      *this *= F32(1.0 / vmag);
   }
}


inline void Point3F::normalize(F32 val)
{
   m_point3F_normalize_f(*this, val);
}

inline bool Point3F::operator==(const Point3F& _test) const
{
   return (x == _test.x) && (y == _test.y) && (z == _test.z);
}

inline bool Point3F::operator!=(const Point3F& _test) const
{
   return operator==(_test) == false;
}

inline Point3F Point3F::operator+(const Point3F& _add) const
{
   return Point3F(x + _add.x, y + _add.y,  z + _add.z);
}

inline Point3F Point3F::operator-(const Point3F& _rSub) const
{
   return Point3F(x - _rSub.x, y - _rSub.y, z - _rSub.z);
}

inline Point3F& Point3F::operator+=(const Point3F& _add)
{
   x += _add.x;
   y += _add.y;
   z += _add.z;

   return *this;
}

inline Point3F& Point3F::operator-=(const Point3F& _rSub)
{
   x -= _rSub.x;
   y -= _rSub.y;
   z -= _rSub.z;

   return *this;
}

inline Point3F Point3F::operator*(F32 _mul) const
{
   return Point3F(x * _mul, y * _mul, z * _mul);
}

inline Point3F Point3F::operator/(F32 _div) const
{
   AssertFatal(_div != 0.0f, "Error, div by zero attempted");

   F32 inv = 1.0f / _div;

   return Point3F(x * inv, y * inv, z * inv);
}

inline Point3F& Point3F::operator*=(F32 _mul)
{
   x *= _mul;
   y *= _mul;
   z *= _mul;

   return *this;
}

inline Point3F& Point3F::operator/=(F32 _div)
{
   AssertFatal(_div != 0.0f, "Error, div by zero attempted");

   F32 inv = 1.0f / _div;
   x *= inv;
   y *= inv;
   z *= inv;

   return *this;
}

inline Point3F Point3F::operator*(const Point3F &_vec) const
{
   return Point3F(x * _vec.x, y * _vec.y, z * _vec.z);
}

inline Point3F& Point3F::operator*=(const Point3F &_vec)
{
   x *= _vec.x;
   y *= _vec.y;
   z *= _vec.z;
   return *this;
}

inline Point3F Point3F::operator/(const Point3F &_vec) const
{
   return Point3F(x / _vec.x, y / _vec.y, z / _vec.z);
}

inline Point3F& Point3F::operator/=(const Point3F &_vec)
{
   x /= _vec.x;
   y /= _vec.y;
   z /= _vec.z;
   return *this;
}

inline Point3F Point3F::operator-() const
{
   return Point3F(-x, -y, -z);
}


inline Point3F& Point3F::operator=(const Point3D &_vec)
{
   x = (F32)_vec.x;
   y = (F32)_vec.y;
   z = (F32)_vec.z;
   return *this;
}

//------------------------------------------------------------------------------
//-------------------------------------- Point3D
//
inline Point3D::Point3D()
{
   //
}

inline Point3D::Point3D(const Point3D& _copy)
 : x(_copy.x), y(_copy.y), z(_copy.z)
{
   //
}

inline Point3D::Point3D(const Point3F& _copy)
 : x(_copy.x), y(_copy.y), z(_copy.z)
{
   //
}

inline Point3D::Point3D(F64 xyz)
 : x(xyz), y(xyz), z(xyz)
{
   //
}

inline Point3D::Point3D(F64 _x, F64 _y, F64 _z)
 : x(_x), y(_y), z(_z)
{
   //
}

inline void Point3D::set( F64 xyz )
{
   x = y = z = xyz;
}

inline void Point3D::set(F64 _x, F64 _y, F64 _z)
{
   x = _x;
   y = _y;
   z = _z;
}

inline void Point3D::setMin(const Point3D& _test)
{
   x = (_test.x < x) ? _test.x : x;
   y = (_test.y < y) ? _test.y : y;
   z = (_test.z < z) ? _test.z : z;
}

inline void Point3D::setMax(const Point3D& _test)
{
   x = (_test.x > x) ? _test.x : x;
   y = (_test.y > y) ? _test.y : y;
   z = (_test.z > z) ? _test.z : z;
}

inline void Point3D::interpolate(const Point3D& _from, const Point3D& _to, F64 _factor)
{
   AssertFatal(_factor >= 0.0f && _factor <= 1.0f, "Out of bound interpolation factor");
   m_point3D_interpolate( _from, _to, _factor, *this);
}

inline void Point3D::zero()
{
   x = y = z = 0.0;
}

inline bool Point3D::isZero() const
{
   return (x == 0.0f) && (y == 0.0f) && (z == 0.0f);
}

inline void Point3D::neg()
{
   x = -x;
   y = -y;
   z = -z;
}

inline void Point3D::convolve(const Point3D& c)
{
   x *= c.x;
   y *= c.y;
   z *= c.z;
}

inline void Point3D::convolveInverse(const Point3D& c)
{
   x /= c.x;
   y /= c.y;
   z /= c.z;
}

inline F64 Point3D::lenSquared() const
{
   return (x * x) + (y * y) + (z * z);
}

inline F64 Point3D::len() const
{
   return mSqrtD(x*x + y*y + z*z);
}

inline void Point3D::normalize()
{
   m_point3D_normalize(*this);
}

inline void Point3D::normalize(F64 val)
{
   m_point3D_normalize_f(*this, val);
}

inline bool Point3D::operator==(const Point3D& _test) const
{
   return (x == _test.x) && (y == _test.y) && (z == _test.z);
}

inline bool Point3D::operator!=(const Point3D& _test) const
{
   return operator==(_test) == false;
}

inline Point3D Point3D::operator+(const Point3D& _add) const
{
   return Point3D(x + _add.x, y + _add.y,  z + _add.z);
}


inline Point3D Point3D::operator-(const Point3D& _rSub) const
{
   return Point3D(x - _rSub.x, y - _rSub.y, z - _rSub.z);
}

inline Point3D& Point3D::operator+=(const Point3D& _add)
{
   x += _add.x;
   y += _add.y;
   z += _add.z;

   return *this;
}

inline Point3D& Point3D::operator-=(const Point3D& _rSub)
{
   x -= _rSub.x;
   y -= _rSub.y;
   z -= _rSub.z;

   return *this;
}

inline Point3D Point3D::operator*(F64 _mul) const
{
   return Point3D(x * _mul, y * _mul, z * _mul);
}

inline Point3D Point3D::operator/(F64 _div) const
{
   AssertFatal(_div != 0.0f, "Error, div by zero attempted");

   F64 inv = 1.0f / _div;

   return Point3D(x * inv, y * inv, z * inv);
}

inline Point3D& Point3D::operator*=(F64 _mul)
{
   x *= _mul;
   y *= _mul;
   z *= _mul;

   return *this;
}

inline Point3D& Point3D::operator/=(F64 _div)
{
   AssertFatal(_div != 0.0f, "Error, div by zero attempted");

   F64 inv = 1.0f / _div;
   x *= inv;
   y *= inv;
   z *= inv;

   return *this;
}

inline Point3D Point3D::operator-() const
{
   return Point3D(-x, -y, -z);
}

inline Point3F Point3D::toPoint3F() const
{
   return Point3F((F32)x,(F32)y,(F32)z);
}

//-------------------------------------------------------------------
// Non-Member Operators
//-------------------------------------------------------------------

inline Point3I operator*(S32 mul, const Point3I& multiplicand)
{
   return multiplicand * mul;
}

inline Point3F operator*(F32 mul, const Point3F& multiplicand)
{
   return multiplicand * mul;
}

inline Point3D operator*(F64 mul, const Point3D& multiplicand)
{
   return multiplicand * mul;
}

inline F32 mDot(const Point3F &p1, const Point3F &p2)
{
   return (p1.x*p2.x + p1.y*p2.y + p1.z*p2.z);
}

inline F64 mDot(const Point3D &p1, const Point3D &p2)
{
   return (p1.x*p2.x + p1.y*p2.y + p1.z*p2.z);
}

inline void mCross(const Point3F &a, const Point3F &b, Point3F *res)
{
   res->x = (a.y * b.z) - (a.z * b.y);
   res->y = (a.z * b.x) - (a.x * b.z);
   res->z = (a.x * b.y) - (a.y * b.x);
}

inline void mCross(const Point3D &a, const Point3D &b, Point3D *res)
{
   res->x = (a.y * b.z) - (a.z * b.y);
   res->y = (a.z * b.x) - (a.x * b.z);
   res->z = (a.x * b.y) - (a.y * b.x);
}

inline Point3F mCross(const Point3F &a, const Point3F &b)
{
   Point3F r;
   mCross( a, b, &r );
   return r;
}

inline Point3D mCross(const Point3D &a, const Point3D &b)
{
   Point3D r;
   mCross( a, b, &r );
   return r;
}

/// Returns the vector normalized.
inline Point3F mNormalize( const Point3F &vec )
{
   Point3F out( vec );
   out.normalize();
   return out;
}

/// Returns true if the point is NaN.
inline bool mIsNaN( const Point3F &p )
{
   return mIsNaN_F( p.x ) || mIsNaN_F( p.y ) || mIsNaN_F( p.z );
}

/// Returns a copy of the vector reflected by a normal
inline Point3F mReflect( const Point3F &v, const Point3F &n )
{
   return v - 2 * n * mDot( v, n );
}

/// Returns a perpendicular vector to the unit length input vector.
extern Point3F mPerp( const Point3F &normal );

#endif // _MPOINT3_H_