Wm4Vector2.h

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// Wild Magic Source Code
// David Eberly
// http://www.geometrictools.com
// Copyright (c) 1998-2007
//
// This library 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 2.1 of the License, or (at
// your option) any later version.  The license is available for reading at
// either of the locations:
//     http://www.gnu.org/copyleft/lgpl.html
//     http://www.geometrictools.com/License/WildMagicLicense.pdf
// The license applies to versions 0 through 4 of Wild Magic.
//
// Version: 4.0.2 (2006/07/25)

#ifndef WM4VECTOR2_H
#define WM4VECTOR2_H

#include "Wm4FoundationLIB.h"
#include "Wm4Math.h"

namespace Wm4
{
template <class Real>
class Vector2
{
public:
    // construction
    Vector2 ();  // uninitialized
    Vector2 (Real fX, Real fY);
    Vector2 (const Real* afTuple);
    Vector2 (const Vector2& rkV);

    // coordinate access
    operator const Real* () const;
    operator Real* ();
    Real operator[] (int i) const;
    Real& operator[] (int i);
    Real X () const;
    Real& X ();
    Real Y () const;
    Real& Y ();

    // assignment
    Vector2& operator= (const Vector2& rkV);

    // comparison
    bool operator== (const Vector2& rkV) const;
    bool operator!= (const Vector2& rkV) const;
    bool operator<  (const Vector2& rkV) const;
    bool operator<= (const Vector2& rkV) const;
    bool operator>  (const Vector2& rkV) const;
    bool operator>= (const Vector2& rkV) const;

    // arithmetic operations
    Vector2 operator+ (const Vector2& rkV) const;
    Vector2 operator- (const Vector2& rkV) const;
    Vector2 operator* (Real fScalar) const;
    Vector2 operator/ (Real fScalar) const;
    Vector2 operator- () const;

    // arithmetic updates
    Vector2& operator+= (const Vector2& rkV);
    Vector2& operator-= (const Vector2& rkV);
    Vector2& operator*= (Real fScalar);
    Vector2& operator/= (Real fScalar);

    // vector operations
    Real Length () const;
    Real SquaredLength () const;
    Real Dot (const Vector2& rkV) const;
    Real Normalize ();

    // returns (y,-x)
    Vector2 Perp () const;

    // returns (y,-x)/sqrt(x*x+y*y)
    Vector2 UnitPerp () const;

    // returns DotPerp((x,y),(V.x,V.y)) = x*V.y - y*V.x
    Real DotPerp (const Vector2& rkV) const;

    // Compute the barycentric coordinates of the point with respect to the
    // triangle <V0,V1,V2>, P = b0*V0 + b1*V1 + b2*V2, where b0 + b1 + b2 = 1.
    void GetBarycentrics (const Vector2& rkV0, const Vector2& rkV1,
        const Vector2& rkV2, Real afBary[3]) const;

    // Gram-Schmidt orthonormalization.  Take linearly independent vectors U
    // and V and compute an orthonormal set (unit length, mutually
    // perpendicular).
    static void Orthonormalize (Vector2& rkU, Vector2& rkV);

    // Input V must be a nonzero vector.  The output is an orthonormal basis
    // {U,V}.  The input V is normalized by this function.  If you know V is
    // already unit length, use U = V.Perp().
    static void GenerateOrthonormalBasis (Vector2& rkU, Vector2& rkV);

    // Compute the extreme values.
    static void ComputeExtremes (int iVQuantity, const Vector2* akPoint,
        Vector2& rkMin, Vector2& rkMax);

    // special vectors
    WM4_FOUNDATION_ITEM static const Vector2 ZERO;    // (0,0)
    WM4_FOUNDATION_ITEM static const Vector2 UNIT_X;  // (1,0)
    WM4_FOUNDATION_ITEM static const Vector2 UNIT_Y;  // (0,1)
    WM4_FOUNDATION_ITEM static const Vector2 ONE;     // (1,1)

private:
    // support for comparisons
    int CompareArrays (const Vector2& rkV) const;

    Real m_afTuple[2];
};

// arithmetic operations
template <class Real>
Vector2<Real> operator* (Real fScalar, const Vector2<Real>& rkV);

// debugging output
template <class Real>
std::ostream& operator<< (std::ostream& rkOStr, const Vector2<Real>& rkV);

}

#include "Wm4Vector2.inl"

namespace Wm4
{
typedef Vector2<float> Vector2f;
typedef Vector2<double> Vector2d;

}

#endif