[1092] | 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) 2000-2005 The OGRE Team
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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 | */
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| 25 | #ifndef __Vector2_H__
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| 26 | #define __Vector2_H__
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| 27 |
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| 28 |
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| 29 | #include "OgrePrerequisites.h"
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| 30 | #include "OgreMath.h"
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| 31 |
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| 32 | namespace Ogre
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| 33 | {
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| 34 |
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| 35 | /** Standard 2-dimensional vector.
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| 36 | @remarks
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| 37 | A direction in 2D space represented as distances along the 2
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| 38 | orthoganal axes (x, y). Note that positions, directions and
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| 39 | scaling factors can be represented by a vector, depending on how
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| 40 | you interpret the values.
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| 41 | */
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| 42 | class _OgreExport Vector2
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| 43 | {
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| 44 | public:
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| 45 | union {
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| 46 | struct {
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| 47 | Real x, y;
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| 48 | };
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| 49 | Real val[2];
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| 50 | };
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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( Real fX, 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 Vector2( Real afCoordinate[2] )
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| 63 | : x( afCoordinate[0] ),
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| 64 | y( afCoordinate[1] )
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| 65 | {
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| 66 | }
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| 67 |
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| 68 | inline Vector2( int afCoordinate[2] )
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| 69 | {
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| 70 | x = (Real)afCoordinate[0];
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| 71 | y = (Real)afCoordinate[1];
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| 72 | }
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| 73 |
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| 74 | inline Vector2( const Real* const r )
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| 75 | : x( r[0] ), y( r[1] )
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| 76 | {
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| 77 | }
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| 78 |
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| 79 | inline Vector2( const Vector2& rkVector )
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| 80 | : x( rkVector.x ), y( rkVector.y )
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| 81 | {
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| 82 | }
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| 83 |
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| 84 | inline Real operator [] ( 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 [] ( 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 | /** Assigns the value of the other vector.
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| 99 | @param
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| 100 | rkVector The other vector
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| 101 | */
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| 102 | inline Vector2& operator = ( const Vector2& rkVector )
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| 103 | {
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| 104 | x = rkVector.x;
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| 105 | y = rkVector.y;
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| 106 |
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| 107 | return *this;
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| 108 | }
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| 109 |
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| 110 | inline bool operator == ( const Vector2& rkVector ) const
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| 111 | {
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| 112 | return ( x == rkVector.x && y == rkVector.y );
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| 113 | }
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| 114 |
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| 115 | inline bool operator != ( const Vector2& rkVector ) const
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| 116 | {
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| 117 | return ( x != rkVector.x || y != rkVector.y );
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| 118 | }
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| 119 |
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| 120 | // arithmetic operations
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| 121 | inline Vector2 operator + ( const Vector2& rkVector ) const
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| 122 | {
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| 123 | Vector2 kSum;
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| 124 |
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| 125 | kSum.x = x + rkVector.x;
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| 126 | kSum.y = y + rkVector.y;
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| 127 |
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| 128 | return kSum;
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| 129 | }
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| 130 |
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| 131 | inline Vector2 operator - ( const Vector2& rkVector ) const
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| 132 | {
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| 133 | Vector2 kDiff;
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| 134 |
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| 135 | kDiff.x = x - rkVector.x;
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| 136 | kDiff.y = y - rkVector.y;
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| 137 |
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| 138 | return kDiff;
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| 139 | }
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| 140 |
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| 141 | inline Vector2 operator * ( Real fScalar ) const
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| 142 | {
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| 143 | Vector2 kProd;
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| 144 |
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| 145 | kProd.x = fScalar*x;
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| 146 | kProd.y = fScalar*y;
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| 147 |
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| 148 | return kProd;
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| 149 | }
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| 150 |
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| 151 | inline Vector2 operator * ( const Vector2& rhs) const
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| 152 | {
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| 153 | Vector2 kProd;
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| 154 |
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| 155 | kProd.x = rhs.x * x;
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| 156 | kProd.y = rhs.y * y;
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| 157 |
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| 158 | return kProd;
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| 159 | }
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| 160 |
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| 161 | inline Vector2 operator / ( Real fScalar ) const
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| 162 | {
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| 163 | assert( fScalar != 0.0 );
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| 164 |
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| 165 | Vector2 kDiv;
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| 166 |
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| 167 | Real fInv = 1.0 / fScalar;
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| 168 | kDiv.x = x * fInv;
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| 169 | kDiv.y = y * fInv;
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| 170 |
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| 171 | return kDiv;
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| 172 | }
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| 173 |
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| 174 | inline Vector2 operator - () const
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| 175 | {
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| 176 | Vector2 kNeg;
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| 177 |
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| 178 | kNeg.x = -x;
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| 179 | kNeg.y = -y;
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| 180 |
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| 181 | return kNeg;
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| 182 | }
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| 183 |
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| 184 | inline friend Vector2 operator * ( Real fScalar, const Vector2& rkVector )
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| 185 | {
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| 186 | Vector2 kProd;
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| 187 |
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| 188 | kProd.x = fScalar * rkVector.x;
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| 189 | kProd.y = fScalar * rkVector.y;
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| 190 |
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| 191 | return kProd;
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| 192 | }
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| 193 |
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| 194 | // arithmetic updates
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| 195 | inline Vector2& operator += ( const Vector2& rkVector )
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| 196 | {
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| 197 | x += rkVector.x;
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| 198 | y += rkVector.y;
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| 199 |
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| 200 | return *this;
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| 201 | }
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| 202 |
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| 203 | inline Vector2& operator -= ( const Vector2& rkVector )
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| 204 | {
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| 205 | x -= rkVector.x;
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| 206 | y -= rkVector.y;
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| 207 |
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| 208 | return *this;
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| 209 | }
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| 210 |
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| 211 | inline Vector2& operator *= ( Real fScalar )
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| 212 | {
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| 213 | x *= fScalar;
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| 214 | y *= fScalar;
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| 215 |
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| 216 | return *this;
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| 217 | }
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| 218 |
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| 219 | inline Vector2& operator /= ( Real fScalar )
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| 220 | {
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| 221 | assert( fScalar != 0.0 );
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| 222 |
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| 223 | Real fInv = 1.0 / fScalar;
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| 224 |
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| 225 | x *= fInv;
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| 226 | y *= fInv;
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| 227 |
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| 228 | return *this;
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| 229 | }
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| 230 |
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| 231 | /** Returns the length (magnitude) of the vector.
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| 232 | @warning
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| 233 | This operation requires a square root and is expensive in
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| 234 | terms of CPU operations. If you don't need to know the exact
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| 235 | length (e.g. for just comparing lengths) use squaredLength()
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| 236 | instead.
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| 237 | */
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| 238 | inline Real length () const
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| 239 | {
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| 240 | return Math::Sqrt( x * x + y * y );
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| 241 | }
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| 242 |
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| 243 | /** Returns the square of the length(magnitude) of the vector.
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| 244 | @remarks
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| 245 | This method is for efficiency - calculating the actual
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| 246 | length of a vector requires a square root, which is expensive
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| 247 | in terms of the operations required. This method returns the
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| 248 | square of the length of the vector, i.e. the same as the
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| 249 | length but before the square root is taken. Use this if you
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| 250 | want to find the longest / shortest vector without incurring
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| 251 | the square root.
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| 252 | */
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| 253 | inline Real squaredLength () const
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| 254 | {
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| 255 | return x * x + y * y;
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| 256 | }
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| 257 |
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| 258 | /** Calculates the dot (scalar) product of this vector with another.
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| 259 | @remarks
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| 260 | The dot product can be used to calculate the angle between 2
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| 261 | vectors. If both are unit vectors, the dot product is the
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| 262 | cosine of the angle; otherwise the dot product must be
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| 263 | divided by the product of the lengths of both vectors to get
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| 264 | the cosine of the angle. This result can further be used to
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| 265 | calculate the distance of a point from a plane.
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| 266 | @param
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| 267 | vec Vector with which to calculate the dot product (together
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| 268 | with this one).
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| 269 | @returns
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| 270 | A float representing the dot product value.
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| 271 | */
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| 272 | inline Real dotProduct(const Vector2& vec) const
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| 273 | {
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| 274 | return x * vec.x + y * vec.y;
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| 275 | }
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| 276 |
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| 277 | /** Normalises the vector.
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| 278 | @remarks
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| 279 | This method normalises the vector such that it's
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| 280 | length / magnitude is 1. The result is called a unit vector.
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| 281 | @note
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| 282 | This function will not crash for zero-sized vectors, but there
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| 283 | will be no changes made to their components.
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| 284 | @returns The previous length of the vector.
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| 285 | */
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| 286 | inline Real normalise()
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| 287 | {
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| 288 | Real fLength = Math::Sqrt( x * x + y * y);
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| 289 |
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| 290 | // Will also work for zero-sized vectors, but will change nothing
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| 291 | if ( fLength > 1e-08 )
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| 292 | {
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| 293 | Real fInvLength = 1.0 / fLength;
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| 294 | x *= fInvLength;
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| 295 | y *= fInvLength;
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| 296 | }
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| 297 |
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| 298 | return fLength;
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| 299 | }
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| 300 |
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| 301 |
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| 302 |
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| 303 | /** Returns a vector at a point half way between this and the passed
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| 304 | in vector.
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| 305 | */
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| 306 | inline Vector2 midPoint( const Vector2& vec ) const
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| 307 | {
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| 308 | return Vector2(
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| 309 | ( x + vec.x ) * 0.5,
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| 310 | ( y + vec.y ) * 0.5 );
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| 311 | }
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| 312 |
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| 313 | /** Returns true if the vector's scalar components are all greater
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| 314 | that the ones of the vector it is compared against.
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| 315 | */
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| 316 | inline bool operator < ( const Vector2& rhs ) const
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| 317 | {
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| 318 | if( x < rhs.x && y < rhs.y )
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| 319 | return true;
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| 320 | return false;
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| 321 | }
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| 322 |
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| 323 | /** Returns true if the vector's scalar components are all smaller
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| 324 | that the ones of the vector it is compared against.
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| 325 | */
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| 326 | inline bool operator > ( const Vector2& rhs ) const
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| 327 | {
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| 328 | if( x > rhs.x && y > rhs.y )
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| 329 | return true;
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| 330 | return false;
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| 331 | }
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| 332 |
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| 333 | /** Sets this vector's components to the minimum of its own and the
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| 334 | ones of the passed in vector.
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| 335 | @remarks
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| 336 | 'Minimum' in this case means the combination of the lowest
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| 337 | value of x, y and z from both vectors. Lowest is taken just
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| 338 | numerically, not magnitude, so -1 < 0.
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| 339 | */
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| 340 | inline void makeFloor( const Vector2& cmp )
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| 341 | {
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| 342 | if( cmp.x < x ) x = cmp.x;
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| 343 | if( cmp.y < y ) y = cmp.y;
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| 344 | }
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| 345 |
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| 346 | /** Sets this vector's components to the maximum of its own and the
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| 347 | ones of the passed in vector.
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| 348 | @remarks
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| 349 | 'Maximum' in this case means the combination of the highest
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| 350 | value of x, y and z from both vectors. Highest is taken just
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| 351 | numerically, not magnitude, so 1 > -3.
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| 352 | */
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| 353 | inline void makeCeil( const Vector2& cmp )
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| 354 | {
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| 355 | if( cmp.x > x ) x = cmp.x;
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| 356 | if( cmp.y > y ) y = cmp.y;
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| 357 | }
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| 358 |
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| 359 | /** Generates a vector perpendicular to this vector (eg an 'up' vector).
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| 360 | @remarks
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| 361 | This method will return a vector which is perpendicular to this
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| 362 | vector. There are an infinite number of possibilities but this
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| 363 | method will guarantee to generate one of them. If you need more
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| 364 | control you should use the Quaternion class.
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| 365 | */
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| 366 | inline Vector2 perpendicular(void) const
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| 367 | {
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| 368 | return Vector2 (-y, x);
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| 369 | }
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| 370 | /** Calculates the cross-product of 2 vectors, i.e. the vector that
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| 371 | lies perpendicular to them both.
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| 372 | @remarks
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| 373 | The cross-product is normally used to calculate the normal
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| 374 | vector of a plane, by calculating the cross-product of 2
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| 375 | non-equivalent vectors which lie on the plane (e.g. 2 edges
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| 376 | of a triangle).
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| 377 | @param
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| 378 | vec Vector which, together with this one, will be used to
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| 379 | calculate the cross-product.
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| 380 | @returns
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| 381 | A vector which is the result of the cross-product. This
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| 382 | vector will <b>NOT</b> be normalised, to maximise efficiency
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| 383 | - call Vector3::normalise on the result if you wish this to
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| 384 | be done. As for which side the resultant vector will be on, the
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| 385 | returned vector will be on the side from which the arc from 'this'
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| 386 | to rkVector is anticlockwise, e.g. UNIT_Y.crossProduct(UNIT_Z)
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| 387 | = UNIT_X, whilst UNIT_Z.crossProduct(UNIT_Y) = -UNIT_X.
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| 388 | @par
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| 389 | For a clearer explanation, look a the left and the bottom edges
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| 390 | of your monitor's screen. Assume that the first vector is the
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| 391 | left edge and the second vector is the bottom edge, both of
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| 392 | them starting from the lower-left corner of the screen. The
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| 393 | resulting vector is going to be perpendicular to both of them
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| 394 | and will go <i>inside</i> the screen, towards the cathode tube
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| 395 | (assuming you're using a CRT monitor, of course).
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| 396 | */
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| 397 | inline Vector2 crossProduct( const Vector2& rkVector ) const
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| 398 | {
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| 399 | return Vector2(-rkVector.y, rkVector.x);
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| 400 | }
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| 401 | /** Generates a new random vector which deviates from this vector by a
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| 402 | given angle in a random direction.
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| 403 | @remarks
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| 404 | This method assumes that the random number generator has already
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| 405 | been seeded appropriately.
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| 406 | @param
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| 407 | angle The angle at which to deviate in radians
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| 408 | @param
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| 409 | up Any vector perpendicular to this one (which could generated
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| 410 | by cross-product of this vector and any other non-colinear
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| 411 | vector). If you choose not to provide this the function will
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| 412 | derive one on it's own, however if you provide one yourself the
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| 413 | function will be faster (this allows you to reuse up vectors if
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| 414 | you call this method more than once)
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| 415 | @returns
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| 416 | A random vector which deviates from this vector by angle. This
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| 417 | vector will not be normalised, normalise it if you wish
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| 418 | afterwards.
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| 419 | */
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| 420 | inline Vector2 randomDeviant(
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| 421 | Real angle) const
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| 422 | {
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| 423 |
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| 424 | angle *= Math::UnitRandom() * Math::TWO_PI;
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| 425 | Real cosa = cos(angle);
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| 426 | Real sina = sin(angle);
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| 427 | return Vector2(cosa * x - sina * y,
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| 428 | sina * x + cosa * y);
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| 429 | }
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| 430 |
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| 431 | /** Returns true if this vector is zero length. */
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| 432 | inline bool isZeroLength(void) const
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| 433 | {
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| 434 | Real sqlen = (x * x) + (y * y);
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| 435 | return (sqlen < (1e-06 * 1e-06));
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| 436 |
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| 437 | }
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| 438 |
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| 439 | /** As normalise, except that this vector is unaffected and the
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| 440 | normalised vector is returned as a copy. */
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| 441 | inline Vector2 normalisedCopy(void) const
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| 442 | {
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| 443 | Vector2 ret = *this;
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| 444 | ret.normalise();
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| 445 | return ret;
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| 446 | }
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| 447 |
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| 448 | /** Calculates a reflection vector to the plane with the given normal .
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| 449 | @remarks NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not.
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| 450 | */
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| 451 | inline Vector2 reflect(const Vector2& normal) const
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| 452 | {
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| 453 | return Vector2( *this - ( 2 * this->dotProduct(normal) * normal ) );
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| 454 | }
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| 455 |
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| 456 | // special points
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| 457 | static const Vector2 ZERO;
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| 458 | static const Vector2 UNIT_X;
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| 459 | static const Vector2 UNIT_Y;
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| 460 | static const Vector2 NEGATIVE_UNIT_X;
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| 461 | static const Vector2 NEGATIVE_UNIT_Y;
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| 462 | static const Vector2 UNIT_SCALE;
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| 463 |
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| 464 | /** Function for writing to a stream.
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| 465 | */
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| 466 | inline _OgreExport friend std::ostream& operator <<
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| 467 | ( std::ostream& o, const Vector2& v )
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| 468 | {
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| 469 | o << "Vector2(" << v.x << ", " << v.y << ")";
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| 470 | return o;
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| 471 | }
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| 472 | };
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| 473 |
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| 474 | }
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| 475 | #endif
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