[7908] | 1 | /* |
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| 2 | ----------------------------------------------------------------------------- |
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| 3 | This source file is part of OGRE |
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| 4 | (Object-oriented Graphics Rendering Engine) |
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| 5 | For the latest info, see http://www.ogre3d.org/ |
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| 6 | |
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| 7 | Copyright (c) 2000-2006 Torus Knot Software Ltd |
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| 8 | Also see acknowledgements in Readme.html |
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| 9 | |
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| 10 | This program is free software; you can redistribute it and/or modify it under |
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| 11 | the terms of the GNU Lesser General Public License as published by the Free Software |
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| 12 | Foundation; either version 2 of the License, or (at your option) any later |
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| 13 | version. |
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| 14 | |
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| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 17 | FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. |
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| 18 | |
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| 19 | You should have received a copy of the GNU Lesser General Public License along with |
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| 20 | this program; if not, write to the Free Software Foundation, Inc., 59 Temple |
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| 21 | Place - Suite 330, Boston, MA 02111-1307, USA, or go to |
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| 22 | http://www.gnu.org/copyleft/lesser.txt. |
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| 23 | |
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| 24 | You may alternatively use this source under the terms of a specific version of |
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| 25 | the OGRE Unrestricted License provided you have obtained such a license from |
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| 26 | Torus Knot Software Ltd. |
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| 27 | ----------------------------------------------------------------------------- |
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| 28 | */ |
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| 29 | #ifndef __Vector2_H__ |
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| 30 | #define __Vector2_H__ |
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| 31 | |
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| 32 | |
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| 33 | #include "OgrePrerequisites.h" |
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| 34 | #include "OgreMath.h" |
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| 35 | #include <ostream> |
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| 36 | |
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| 37 | namespace Ogre |
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| 38 | { |
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| 39 | |
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| 40 | /** Standard 2-dimensional vector. |
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| 41 | @remarks |
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| 42 | A direction in 2D space represented as distances along the 2 |
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| 43 | orthogonal axes (x, y). Note that positions, directions and |
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| 44 | scaling factors can be represented by a vector, depending on how |
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| 45 | you interpret the values. |
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| 46 | */ |
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| 47 | class _OgreExport Vector2 |
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| 48 | { |
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| 49 | public: |
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| 50 | Real x, y; |
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| 51 | |
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| 52 | public: |
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| 53 | inline Vector2() |
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| 54 | { |
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| 55 | } |
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| 56 | |
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| 57 | inline Vector2(const Real fX, const Real fY ) |
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| 58 | : x( fX ), y( fY ) |
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| 59 | { |
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| 60 | } |
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| 61 | |
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| 62 | inline explicit Vector2( const Real scaler ) |
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| 63 | : x( scaler), y( scaler ) |
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| 64 | { |
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| 65 | } |
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| 66 | |
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| 67 | inline explicit Vector2( const Real afCoordinate[2] ) |
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| 68 | : x( afCoordinate[0] ), |
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| 69 | y( afCoordinate[1] ) |
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| 70 | { |
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| 71 | } |
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| 72 | |
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| 73 | inline explicit Vector2( const int afCoordinate[2] ) |
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| 74 | { |
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| 75 | x = (Real)afCoordinate[0]; |
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| 76 | y = (Real)afCoordinate[1]; |
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| 77 | } |
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| 78 | |
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| 79 | inline explicit Vector2( Real* const r ) |
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| 80 | : x( r[0] ), y( r[1] ) |
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| 81 | { |
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| 82 | } |
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| 83 | |
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| 84 | inline Real operator [] ( const size_t i ) const |
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| 85 | { |
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| 86 | assert( i < 2 ); |
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| 87 | |
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| 88 | return *(&x+i); |
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| 89 | } |
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| 90 | |
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| 91 | inline Real& operator [] ( const size_t i ) |
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| 92 | { |
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| 93 | assert( i < 2 ); |
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| 94 | |
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| 95 | return *(&x+i); |
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| 96 | } |
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| 97 | |
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| 98 | /// Pointer accessor for direct copying |
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| 99 | inline Real* ptr() |
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| 100 | { |
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| 101 | return &x; |
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| 102 | } |
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| 103 | /// Pointer accessor for direct copying |
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| 104 | inline const Real* ptr() const |
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| 105 | { |
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| 106 | return &x; |
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| 107 | } |
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| 108 | |
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| 109 | /** Assigns the value of the other vector. |
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| 110 | @param |
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| 111 | rkVector The other vector |
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| 112 | */ |
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| 113 | inline Vector2& operator = ( const Vector2& rkVector ) |
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| 114 | { |
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| 115 | x = rkVector.x; |
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| 116 | y = rkVector.y; |
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| 117 | |
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| 118 | return *this; |
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| 119 | } |
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| 120 | |
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| 121 | inline Vector2& operator = ( const Real fScalar) |
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| 122 | { |
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| 123 | x = fScalar; |
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| 124 | y = fScalar; |
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| 125 | |
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| 126 | return *this; |
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| 127 | } |
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| 128 | |
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| 129 | inline bool operator == ( const Vector2& rkVector ) const |
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| 130 | { |
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| 131 | return ( x == rkVector.x && y == rkVector.y ); |
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| 132 | } |
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| 133 | |
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| 134 | inline bool operator != ( const Vector2& rkVector ) const |
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| 135 | { |
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| 136 | return ( x != rkVector.x || y != rkVector.y ); |
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| 137 | } |
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| 138 | |
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| 139 | // arithmetic operations |
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| 140 | inline Vector2 operator + ( const Vector2& rkVector ) const |
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| 141 | { |
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| 142 | return Vector2( |
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| 143 | x + rkVector.x, |
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| 144 | y + rkVector.y); |
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| 145 | } |
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| 146 | |
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| 147 | inline Vector2 operator - ( const Vector2& rkVector ) const |
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| 148 | { |
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| 149 | return Vector2( |
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| 150 | x - rkVector.x, |
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| 151 | y - rkVector.y); |
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| 152 | } |
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| 153 | |
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| 154 | inline Vector2 operator * ( const Real fScalar ) const |
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| 155 | { |
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| 156 | return Vector2( |
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| 157 | x * fScalar, |
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| 158 | y * fScalar); |
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| 159 | } |
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| 160 | |
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| 161 | inline Vector2 operator * ( const Vector2& rhs) const |
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| 162 | { |
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| 163 | return Vector2( |
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| 164 | x * rhs.x, |
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| 165 | y * rhs.y); |
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| 166 | } |
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| 167 | |
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| 168 | inline Vector2 operator / ( const Real fScalar ) const |
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| 169 | { |
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| 170 | assert( fScalar != 0.0 ); |
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| 171 | |
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| 172 | Real fInv = 1.0 / fScalar; |
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| 173 | |
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| 174 | return Vector2( |
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| 175 | x * fInv, |
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| 176 | y * fInv); |
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| 177 | } |
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| 178 | |
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| 179 | inline Vector2 operator / ( const Vector2& rhs) const |
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| 180 | { |
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| 181 | return Vector2( |
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| 182 | x / rhs.x, |
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| 183 | y / rhs.y); |
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| 184 | } |
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| 185 | |
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| 186 | inline const Vector2& operator + () const |
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| 187 | { |
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| 188 | return *this; |
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| 189 | } |
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| 190 | |
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| 191 | inline Vector2 operator - () const |
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| 192 | { |
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| 193 | return Vector2(-x, -y); |
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| 194 | } |
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| 195 | |
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| 196 | // overloaded operators to help Vector2 |
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| 197 | inline friend Vector2 operator * ( const Real fScalar, const Vector2& rkVector ) |
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| 198 | { |
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| 199 | return Vector2( |
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| 200 | fScalar * rkVector.x, |
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| 201 | fScalar * rkVector.y); |
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| 202 | } |
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| 203 | |
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| 204 | inline friend Vector2 operator / ( const Real fScalar, const Vector2& rkVector ) |
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| 205 | { |
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| 206 | return Vector2( |
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| 207 | fScalar / rkVector.x, |
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| 208 | fScalar / rkVector.y); |
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| 209 | } |
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| 210 | |
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| 211 | inline friend Vector2 operator + (const Vector2& lhs, const Real rhs) |
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| 212 | { |
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| 213 | return Vector2( |
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| 214 | lhs.x + rhs, |
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| 215 | lhs.y + rhs); |
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| 216 | } |
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| 217 | |
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| 218 | inline friend Vector2 operator + (const Real lhs, const Vector2& rhs) |
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| 219 | { |
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| 220 | return Vector2( |
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| 221 | lhs + rhs.x, |
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| 222 | lhs + rhs.y); |
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| 223 | } |
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| 224 | |
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| 225 | inline friend Vector2 operator - (const Vector2& lhs, const Real rhs) |
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| 226 | { |
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| 227 | return Vector2( |
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| 228 | lhs.x - rhs, |
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| 229 | lhs.y - rhs); |
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| 230 | } |
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| 231 | |
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| 232 | inline friend Vector2 operator - (const Real lhs, const Vector2& rhs) |
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| 233 | { |
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| 234 | return Vector2( |
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| 235 | lhs - rhs.x, |
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| 236 | lhs - rhs.y); |
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| 237 | } |
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| 238 | // arithmetic updates |
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| 239 | inline Vector2& operator += ( const Vector2& rkVector ) |
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| 240 | { |
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| 241 | x += rkVector.x; |
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| 242 | y += rkVector.y; |
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| 243 | |
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| 244 | return *this; |
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| 245 | } |
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| 246 | |
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| 247 | inline Vector2& operator += ( const Real fScaler ) |
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| 248 | { |
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| 249 | x += fScaler; |
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| 250 | y += fScaler; |
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| 251 | |
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| 252 | return *this; |
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| 253 | } |
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| 254 | |
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| 255 | inline Vector2& operator -= ( const Vector2& rkVector ) |
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| 256 | { |
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| 257 | x -= rkVector.x; |
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| 258 | y -= rkVector.y; |
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| 259 | |
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| 260 | return *this; |
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| 261 | } |
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| 262 | |
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| 263 | inline Vector2& operator -= ( const Real fScaler ) |
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| 264 | { |
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| 265 | x -= fScaler; |
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| 266 | y -= fScaler; |
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| 267 | |
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| 268 | return *this; |
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| 269 | } |
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| 270 | |
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| 271 | inline Vector2& operator *= ( const Real fScalar ) |
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| 272 | { |
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| 273 | x *= fScalar; |
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| 274 | y *= fScalar; |
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| 275 | |
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| 276 | return *this; |
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| 277 | } |
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| 278 | |
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| 279 | inline Vector2& operator *= ( const Vector2& rkVector ) |
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| 280 | { |
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| 281 | x *= rkVector.x; |
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| 282 | y *= rkVector.y; |
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| 283 | |
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| 284 | return *this; |
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| 285 | } |
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| 286 | |
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| 287 | inline Vector2& operator /= ( const Real fScalar ) |
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| 288 | { |
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| 289 | assert( fScalar != 0.0 ); |
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| 290 | |
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| 291 | Real fInv = 1.0 / fScalar; |
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| 292 | |
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| 293 | x *= fInv; |
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| 294 | y *= fInv; |
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| 295 | |
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| 296 | return *this; |
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| 297 | } |
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| 298 | |
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| 299 | inline Vector2& operator /= ( const Vector2& rkVector ) |
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| 300 | { |
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| 301 | x /= rkVector.x; |
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| 302 | y /= rkVector.y; |
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| 303 | |
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| 304 | return *this; |
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| 305 | } |
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| 306 | |
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| 307 | /** Returns the length (magnitude) of the vector. |
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| 308 | @warning |
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| 309 | This operation requires a square root and is expensive in |
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| 310 | terms of CPU operations. If you don't need to know the exact |
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| 311 | length (e.g. for just comparing lengths) use squaredLength() |
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| 312 | instead. |
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| 313 | */ |
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| 314 | inline Real length () const |
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| 315 | { |
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| 316 | return Math::Sqrt( x * x + y * y ); |
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| 317 | } |
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| 318 | |
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| 319 | /** Returns the square of the length(magnitude) of the vector. |
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| 320 | @remarks |
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| 321 | This method is for efficiency - calculating the actual |
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| 322 | length of a vector requires a square root, which is expensive |
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| 323 | in terms of the operations required. This method returns the |
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| 324 | square of the length of the vector, i.e. the same as the |
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| 325 | length but before the square root is taken. Use this if you |
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| 326 | want to find the longest / shortest vector without incurring |
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| 327 | the square root. |
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| 328 | */ |
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| 329 | inline Real squaredLength () const |
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| 330 | { |
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| 331 | return x * x + y * y; |
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| 332 | } |
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| 333 | |
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| 334 | /** Calculates the dot (scalar) product of this vector with another. |
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| 335 | @remarks |
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| 336 | The dot product can be used to calculate the angle between 2 |
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| 337 | vectors. If both are unit vectors, the dot product is the |
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| 338 | cosine of the angle; otherwise the dot product must be |
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| 339 | divided by the product of the lengths of both vectors to get |
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| 340 | the cosine of the angle. This result can further be used to |
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| 341 | calculate the distance of a point from a plane. |
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| 342 | @param |
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| 343 | vec Vector with which to calculate the dot product (together |
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| 344 | with this one). |
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| 345 | @returns |
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| 346 | A float representing the dot product value. |
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| 347 | */ |
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| 348 | inline Real dotProduct(const Vector2& vec) const |
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| 349 | { |
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| 350 | return x * vec.x + y * vec.y; |
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| 351 | } |
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| 352 | |
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| 353 | /** Normalises the vector. |
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| 354 | @remarks |
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| 355 | This method normalises the vector such that it's |
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| 356 | length / magnitude is 1. The result is called a unit vector. |
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| 357 | @note |
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| 358 | This function will not crash for zero-sized vectors, but there |
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| 359 | will be no changes made to their components. |
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| 360 | @returns The previous length of the vector. |
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| 361 | */ |
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| 362 | inline Real normalise() |
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| 363 | { |
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| 364 | Real fLength = Math::Sqrt( x * x + y * y); |
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| 365 | |
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| 366 | // Will also work for zero-sized vectors, but will change nothing |
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| 367 | if ( fLength > 1e-08 ) |
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| 368 | { |
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| 369 | Real fInvLength = 1.0 / fLength; |
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| 370 | x *= fInvLength; |
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| 371 | y *= fInvLength; |
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| 372 | } |
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| 373 | |
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| 374 | return fLength; |
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| 375 | } |
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| 376 | |
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| 377 | |
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| 378 | |
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| 379 | /** Returns a vector at a point half way between this and the passed |
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| 380 | in vector. |
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| 381 | */ |
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| 382 | inline Vector2 midPoint( const Vector2& vec ) const |
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| 383 | { |
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| 384 | return Vector2( |
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| 385 | ( x + vec.x ) * 0.5, |
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| 386 | ( y + vec.y ) * 0.5 ); |
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| 387 | } |
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| 388 | |
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| 389 | /** Returns true if the vector's scalar components are all greater |
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| 390 | that the ones of the vector it is compared against. |
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| 391 | */ |
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| 392 | inline bool operator < ( const Vector2& rhs ) const |
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| 393 | { |
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| 394 | if( x < rhs.x && y < rhs.y ) |
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| 395 | return true; |
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| 396 | return false; |
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| 397 | } |
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| 398 | |
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| 399 | /** Returns true if the vector's scalar components are all smaller |
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| 400 | that the ones of the vector it is compared against. |
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| 401 | */ |
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| 402 | inline bool operator > ( const Vector2& rhs ) const |
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| 403 | { |
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| 404 | if( x > rhs.x && y > rhs.y ) |
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| 405 | return true; |
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| 406 | return false; |
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| 407 | } |
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| 408 | |
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| 409 | /** Sets this vector's components to the minimum of its own and the |
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| 410 | ones of the passed in vector. |
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| 411 | @remarks |
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| 412 | 'Minimum' in this case means the combination of the lowest |
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| 413 | value of x, y and z from both vectors. Lowest is taken just |
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| 414 | numerically, not magnitude, so -1 < 0. |
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| 415 | */ |
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| 416 | inline void makeFloor( const Vector2& cmp ) |
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| 417 | { |
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| 418 | if( cmp.x < x ) x = cmp.x; |
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| 419 | if( cmp.y < y ) y = cmp.y; |
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| 420 | } |
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| 421 | |
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| 422 | /** Sets this vector's components to the maximum of its own and the |
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| 423 | ones of the passed in vector. |
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| 424 | @remarks |
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| 425 | 'Maximum' in this case means the combination of the highest |
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| 426 | value of x, y and z from both vectors. Highest is taken just |
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| 427 | numerically, not magnitude, so 1 > -3. |
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| 428 | */ |
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| 429 | inline void makeCeil( const Vector2& cmp ) |
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| 430 | { |
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| 431 | if( cmp.x > x ) x = cmp.x; |
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| 432 | if( cmp.y > y ) y = cmp.y; |
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| 433 | } |
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| 434 | |
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| 435 | /** Generates a vector perpendicular to this vector (eg an 'up' vector). |
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| 436 | @remarks |
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| 437 | This method will return a vector which is perpendicular to this |
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| 438 | vector. There are an infinite number of possibilities but this |
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| 439 | method will guarantee to generate one of them. If you need more |
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| 440 | control you should use the Quaternion class. |
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| 441 | */ |
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| 442 | inline Vector2 perpendicular(void) const |
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| 443 | { |
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| 444 | return Vector2 (-y, x); |
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| 445 | } |
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| 446 | /** Calculates the 2 dimensional cross-product of 2 vectors, which results |
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| 447 | in a single floating point value which is 2 times the area of the triangle. |
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| 448 | */ |
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| 449 | inline Real crossProduct( const Vector2& rkVector ) const |
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| 450 | { |
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| 451 | return x * rkVector.y - y * rkVector.x; |
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| 452 | } |
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| 453 | /** Generates a new random vector which deviates from this vector by a |
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| 454 | given angle in a random direction. |
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| 455 | @remarks |
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| 456 | This method assumes that the random number generator has already |
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| 457 | been seeded appropriately. |
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| 458 | @param |
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| 459 | angle The angle at which to deviate in radians |
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| 460 | @param |
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| 461 | up Any vector perpendicular to this one (which could generated |
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| 462 | by cross-product of this vector and any other non-colinear |
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| 463 | vector). If you choose not to provide this the function will |
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| 464 | derive one on it's own, however if you provide one yourself the |
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| 465 | function will be faster (this allows you to reuse up vectors if |
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| 466 | you call this method more than once) |
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| 467 | @returns |
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| 468 | A random vector which deviates from this vector by angle. This |
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| 469 | vector will not be normalised, normalise it if you wish |
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| 470 | afterwards. |
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| 471 | */ |
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| 472 | inline Vector2 randomDeviant( |
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| 473 | Real angle) const |
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| 474 | { |
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| 475 | |
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| 476 | angle *= Math::UnitRandom() * Math::TWO_PI; |
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| 477 | Real cosa = cos(angle); |
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| 478 | Real sina = sin(angle); |
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| 479 | return Vector2(cosa * x - sina * y, |
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| 480 | sina * x + cosa * y); |
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| 481 | } |
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| 482 | |
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| 483 | /** Returns true if this vector is zero length. */ |
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| 484 | inline bool isZeroLength(void) const |
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| 485 | { |
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| 486 | Real sqlen = (x * x) + (y * y); |
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| 487 | return (sqlen < (1e-06 * 1e-06)); |
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| 488 | |
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| 489 | } |
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| 490 | |
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| 491 | /** As normalise, except that this vector is unaffected and the |
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| 492 | normalised vector is returned as a copy. */ |
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| 493 | inline Vector2 normalisedCopy(void) const |
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| 494 | { |
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| 495 | Vector2 ret = *this; |
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| 496 | ret.normalise(); |
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| 497 | return ret; |
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| 498 | } |
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| 499 | |
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| 500 | /** Calculates a reflection vector to the plane with the given normal . |
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| 501 | @remarks NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not. |
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| 502 | */ |
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| 503 | inline Vector2 reflect(const Vector2& normal) const |
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| 504 | { |
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| 505 | return Vector2( *this - ( 2 * this->dotProduct(normal) * normal ) ); |
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| 506 | } |
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| 507 | |
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| 508 | // special points |
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| 509 | static const Vector2 ZERO; |
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| 510 | static const Vector2 UNIT_X; |
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| 511 | static const Vector2 UNIT_Y; |
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| 512 | static const Vector2 NEGATIVE_UNIT_X; |
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| 513 | static const Vector2 NEGATIVE_UNIT_Y; |
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| 514 | static const Vector2 UNIT_SCALE; |
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| 515 | |
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| 516 | /** Function for writing to a stream. |
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| 517 | */ |
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| 518 | inline _OgreExport friend std::ostream& operator << |
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| 519 | ( std::ostream& o, const Vector2& v ) |
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| 520 | { |
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| 521 | o << "Vector2(" << v.x << ", " << v.y << ")"; |
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| 522 | return o; |
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| 523 | } |
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| 524 | |
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| 525 | }; |
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| 526 | |
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| 527 | } |
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| 528 | #endif |
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