/* ----------------------------------------------------------------------------- This source file is part of OGRE (Object-oriented Graphics Rendering Engine) For the latest info, see http://www.ogre3d.org/ Copyright (c) 2000-2009 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 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 __Vector2_H__ #define __Vector2_H__ #include "OgrePrerequisites.h" #include "OgreMath.h" namespace Ogre { /** \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 _OgreExport Vector2 { public: Real x, y; public: 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; } /** 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 Math::Sqrt( x * x + y * y ); } /** 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; } /** Returns the distance to another 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 distance (e.g. for just comparing distances) use squaredDistance() instead. */ inline Real distance(const Vector2& rhs) const { return (*this - rhs).length(); } /** Returns the square of the distance to another vector. @remarks This method is for efficiency - calculating the actual distance to another vector requires a square root, which is expensive in terms of the operations required. This method returns the square of the distance to another vector, i.e. the same as the distance but before the square root is taken. Use this if you want to find the longest / shortest distance without incurring the square root. */ inline Real squaredDistance(const Vector2& rhs) const { return (*this - rhs).squaredLength(); } /** 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 Vector2& vec) const { return x * vec.x + y * vec.y; } /** 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 = 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 @param up Any vector perpendicular to this one (which could generated by cross-product of this vector and any other non-colinear vector). If you choose not to provide this the function will derive one on it's own, however if you provide one yourself the function will be faster (this allows you to reuse up vectors if you call this method more than once) @returns 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( Real angle) const { angle *= Math::UnitRandom() * Math::TWO_PI; Real cosa = cos(angle); Real sina = 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 Ogre::Radian angleBetween(const Ogre::Vector2& other) { Ogre::Real lenProduct = length() * other.length(); // Divide by zero check if(lenProduct < 1e-6f) lenProduct = 1e-6f; Ogre::Real f = dotProduct(other) / lenProduct; f = Ogre::Math::Clamp(f, (Ogre::Real)-1.0, (Ogre::Real)1.0); return Ogre::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 Ogre::Radian angleTo(const Ogre::Vector2& other) { Ogre::Radian angle = angleBetween(other); if (crossProduct(other)<0) angle = (Ogre::Radian)Ogre::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 _OgreExport friend std::ostream& operator << ( std::ostream& o, const Vector2& v ) { o << "Vector2(" << v.x << ", " << v.y << ")"; return o; } }; /** @} */ /** @} */ } #endif