OgreVector2.h

/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2014 Torus Knot Software Ltd

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
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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 __Vector2_H__
#define __Vector2_H__


#include "Prerequisites.h"
#include "OgreMath.h"

    /** \addtogroup Core
    *  @{
    */
    /** \addtogroup Math
    *  @{
    */
    /** Standard 2-dimensional vector.
        @remarks
            A direction in 2D space represented as distances along the 2
            orthogonal axes (x, y). Note that positions, directions and
            scaling factors can be represented by a vector, depending on how
            you interpret the values.
    */
    class  Vector2
    {
    public:
        Real x, y;

    public:
        /** Default constructor.
            @note
                It does <b>NOT</b> initialize the vector for efficiency.
        */
        inline Vector2()
        {
        }

        inline Vector2(const Real fX, const Real fY )
            : x( fX ), y( fY )
        {
        }

        inline explicit Vector2( const Real scaler )
            : x( scaler), y( scaler )
        {
        }

        inline explicit Vector2( const Real afCoordinate[2] )
            : x( afCoordinate[0] ),
              y( afCoordinate[1] )
        {
        }

        inline explicit Vector2( const int afCoordinate[2] )
        {
            x = (Real)afCoordinate[0];
            y = (Real)afCoordinate[1];
        }

        inline explicit Vector2( Real* const r )
            : x( r[0] ), y( r[1] )
        {
        }

        /** Exchange the contents of this vector with another. 
        */
        inline void swap(Vector2& other)
        {
            std::swap(x, other.x);
            std::swap(y, other.y);
        }

        inline Real operator [] ( const size_t i ) const
        {
            assert( i < 2 );

            return *(&x+i);
        }

        inline Real& operator [] ( const size_t i )
        {
            assert( i < 2 );

            return *(&x+i);
        }

        /// Pointer accessor for direct copying
        inline Real* ptr()
        {
            return &x;
        }
        /// Pointer accessor for direct copying
        inline const Real* ptr() const
        {
            return &x;
        }

        /** Assigns the value of the other vector.
            @param
                rkVector The other vector
        */
        inline Vector2& operator = ( const Vector2& rkVector )
        {
            x = rkVector.x;
            y = rkVector.y;

            return *this;
        }

        inline Vector2& operator = ( const Real fScalar)
        {
            x = fScalar;
            y = fScalar;

            return *this;
        }

        inline bool operator == ( const Vector2& rkVector ) const
        {
            return ( x == rkVector.x && y == rkVector.y );
        }

        inline bool operator != ( const Vector2& rkVector ) const
        {
            return ( x != rkVector.x || y != rkVector.y  );
        }

        // arithmetic operations
        inline Vector2 operator + ( const Vector2& rkVector ) const
        {
            return Vector2(
                x + rkVector.x,
                y + rkVector.y);
        }

        inline Vector2 operator - ( const Vector2& rkVector ) const
        {
            return Vector2(
                x - rkVector.x,
                y - rkVector.y);
        }

        inline Vector2 operator * ( const Real fScalar ) const
        {
            return Vector2(
                x * fScalar,
                y * fScalar);
        }

        inline Vector2 operator * ( const Vector2& rhs) const
        {
            return Vector2(
                x * rhs.x,
                y * rhs.y);
        }

        inline Vector2 operator / ( const Real fScalar ) const
        {
            assert( fScalar != 0.0 );

            Real fInv = 1.0f / fScalar;

            return Vector2(
                x * fInv,
                y * fInv);
        }

        inline Vector2 operator / ( const Vector2& rhs) const
        {
            return Vector2(
                x / rhs.x,
                y / rhs.y);
        }

        inline const Vector2& operator + () const
        {
            return *this;
        }

        inline Vector2 operator - () const
        {
            return Vector2(-x, -y);
        }

        // overloaded operators to help Vector2
        inline friend Vector2 operator * ( const Real fScalar, const Vector2& rkVector )
        {
            return Vector2(
                fScalar * rkVector.x,
                fScalar * rkVector.y);
        }

        inline friend Vector2 operator / ( const Real fScalar, const Vector2& rkVector )
        {
            return Vector2(
                fScalar / rkVector.x,
                fScalar / rkVector.y);
        }

        inline friend Vector2 operator + (const Vector2& lhs, const Real rhs)
        {
            return Vector2(
                lhs.x + rhs,
                lhs.y + rhs);
        }

        inline friend Vector2 operator + (const Real lhs, const Vector2& rhs)
        {
            return Vector2(
                lhs + rhs.x,
                lhs + rhs.y);
        }

        inline friend Vector2 operator - (const Vector2& lhs, const Real rhs)
        {
            return Vector2(
                lhs.x - rhs,
                lhs.y - rhs);
        }

        inline friend Vector2 operator - (const Real lhs, const Vector2& rhs)
        {
            return Vector2(
                lhs - rhs.x,
                lhs - rhs.y);
        }

        // arithmetic updates
        inline Vector2& operator += ( const Vector2& rkVector )
        {
            x += rkVector.x;
            y += rkVector.y;

            return *this;
        }

        inline Vector2& operator += ( const Real fScaler )
        {
            x += fScaler;
            y += fScaler;

            return *this;
        }

        inline Vector2& operator -= ( const Vector2& rkVector )
        {
            x -= rkVector.x;
            y -= rkVector.y;

            return *this;
        }

        inline Vector2& operator -= ( const Real fScaler )
        {
            x -= fScaler;
            y -= fScaler;

            return *this;
        }

        inline Vector2& operator *= ( const Real fScalar )
        {
            x *= fScalar;
            y *= fScalar;

            return *this;
        }

        inline Vector2& operator *= ( const Vector2& rkVector )
        {
            x *= rkVector.x;
            y *= rkVector.y;

            return *this;
        }

        inline Vector2& operator /= ( const Real fScalar )
        {
            assert( fScalar != 0.0 );

            Real fInv = 1.0f / fScalar;

            x *= fInv;
            y *= fInv;

            return *this;
        }

        inline Vector2& operator /= ( const Vector2& rkVector )
        {
            x /= rkVector.x;
            y /= rkVector.y;

            return *this;
        }

        /// @copydoc Vector3::length
        inline Real length () const
        {
            return Math::Sqrt( x * x + y * y );
        }

        /// @copydoc Vector3::squaredLength
        inline Real squaredLength () const
        {
            return x * x + y * y;
        }

        /// @copydoc Vector3::distance
        inline Real distance(const Vector2& rhs) const
        {
            return (*this - rhs).length();
        }

        /// @copydoc Vector3::squaredDistance
        inline Real squaredDistance(const Vector2& rhs) const
        {
            return (*this - rhs).squaredLength();
        }

        /// @copydoc Vector3::dotProduct
        inline Real dotProduct(const Vector2& vec) const
        {
            return x * vec.x + y * vec.y;
        }

        /// @copydoc Vector3::normalise
        inline Real normalise()
        {
            Real fLength = Math::Sqrt( x * x + y * y);

            // Will also work for zero-sized vectors, but will change nothing
            // We're not using epsilons because we don't need to.
            // Read http://www.ogre3d.org/forums/viewtopic.php?f=4&t=61259
            if ( fLength > Real(0.0f) )
            {
                Real fInvLength = 1.0f / fLength;
                x *= fInvLength;
                y *= fInvLength;
            }

            return fLength;
        }

        /** Returns a vector at a point half way between this and the passed
            in vector.
        */
        inline Vector2 midPoint( const Vector2& vec ) const
        {
            return Vector2(
                ( x + vec.x ) * 0.5f,
                ( y + vec.y ) * 0.5f );
        }

        /** 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 Vector2& rhs ) const
        {
            if( x < rhs.x && y < rhs.y )
                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 Vector2& rhs ) const
        {
            if( x > rhs.x && y > rhs.y )
                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 Vector2& cmp )
        {
            if( cmp.x < x ) x = cmp.x;
            if( cmp.y < y ) y = cmp.y;
        }

        /** 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 Vector2& cmp )
        {
            if( cmp.x > x ) x = cmp.x;
            if( cmp.y > y ) y = cmp.y;
        }

        /** 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 Vector2 perpendicular(void) const
        {
            return Vector2 (-y, x);
        }

        /** Calculates the 2 dimensional cross-product of 2 vectors, which results
            in a single floating point value which is 2 times the area of the triangle.
        */
        inline Real crossProduct( const Vector2& rkVector ) const
        {
            return x * rkVector.y - y * rkVector.x;
        }

        /** Generates a new random vector which deviates from this vector by a
            given angle in a random direction.
            @remarks
                This method assumes that the random number generator has already
                been seeded appropriately.
            @param angle
                The angle at which to deviate in radians
            @return
                A random vector which deviates from this vector by angle. This
                vector will not be normalised, normalise it if you wish
                afterwards.
        */
        inline Vector2 randomDeviant(Radian angle) const
        {
            angle *= Math::RangeRandom(-1, 1);
            Real cosa = Math::Cos(angle);
            Real sina = Math::Sin(angle);
            return Vector2(cosa * x - sina * y,
                           sina * x + cosa * y);
        }

        /** Returns true if this vector is zero length. */
        inline bool isZeroLength(void) const
        {
            Real sqlen = (x * x) + (y * y);
            return (sqlen < (1e-06 * 1e-06));

        }

        /** As normalise, except that this vector is unaffected and the
            normalised vector is returned as a copy. */
        inline Vector2 normalisedCopy(void) const
        {
            Vector2 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 Vector2 reflect(const Vector2& normal) const
        {
            return Vector2( *this - ( 2 * this->dotProduct(normal) * normal ) );
        }

        /// Check whether this vector contains valid values
        inline bool isNaN() const
        {
            return Math::isNaN(x) || Math::isNaN(y);
        }

        /**  Gets the angle between 2 vectors.
        @remarks
            Vectors do not have to be unit-length but must represent directions.
        */
        inline Radian angleBetween(const Vector2& other) const
        {       
            Real lenProduct = length() * other.length();
            // Divide by zero check
            if(lenProduct < 1e-6f)
                lenProduct = 1e-6f;
        
            Real f = dotProduct(other) / lenProduct;
    
            f = Math::Clamp(f, (Real)-1.0, (Real)1.0);
            return Math::ACos(f);
        }

        /**  Gets the oriented angle between 2 vectors.
        @remarks
            Vectors do not have to be unit-length but must represent directions.
            The angle is comprised between 0 and 2 PI.
        */
        inline Radian angleTo(const Vector2& other) const
        {
            Radian angle = angleBetween(other);
        
            if (crossProduct(other)<0)          
                angle = (Radian)Math::TWO_PI - angle;       

            return angle;
        }

        // special points
        static const Vector2 ZERO;
        static const Vector2 UNIT_X;
        static const Vector2 UNIT_Y;
        static const Vector2 NEGATIVE_UNIT_X;
        static const Vector2 NEGATIVE_UNIT_Y;
        static const Vector2 UNIT_SCALE;

        /** Function for writing to a stream.
        */
        inline  friend std::ostream& operator <<
            ( std::ostream& o, const Vector2& v )
        {
            o << "Vector2(" << v.x << ", " << v.y <<  ")";
            return o;
        }
    };
#endif