[2043] | 1 | |
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| 2 | |
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| 3 | /* |
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| 4 | orxonox - the future of 3D-vertical-scrollers |
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| 5 | |
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| 6 | Copyright (C) 2004 orx |
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| 7 | |
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| 8 | This program is free software; you can redistribute it and/or modify |
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| 9 | it under the terms of the GNU General Public License as published by |
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| 10 | the Free Software Foundation; either version 2, or (at your option) |
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| 11 | any later version. |
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| 12 | |
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| 13 | ### File Specific: |
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[2551] | 14 | main-programmer: Christian Meyer |
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| 15 | co-programmer: Patrick Boenzli : Vector::scale() |
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| 16 | Vector::abs() |
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[2190] | 17 | |
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| 18 | Quaternion code borrowed from an Gamasutra article by Nick Bobick and Ken Shoemake |
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[2043] | 19 | */ |
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| 20 | |
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[3605] | 21 | #define DEBUG_SPECIAL_MODULE DEBUG_MODULE_MATH |
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[2043] | 22 | |
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| 23 | #include "vector.h" |
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[3605] | 24 | #include "debug.h" |
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[2043] | 25 | |
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| 26 | using namespace std; |
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| 27 | |
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| 28 | /** |
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| 29 | \brief add two vectors |
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| 30 | \param v: the other vector |
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| 31 | \return the sum of both vectors |
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| 32 | */ |
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| 33 | Vector Vector::operator+ (const Vector& v) const |
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| 34 | { |
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| 35 | Vector r; |
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[2816] | 36 | |
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[2043] | 37 | r.x = x + v.x; |
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| 38 | r.y = y + v.y; |
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| 39 | r.z = z + v.z; |
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| 40 | |
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| 41 | return r; |
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| 42 | } |
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| 43 | |
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| 44 | /** |
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| 45 | \brief subtract a vector from another |
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| 46 | \param v: the other vector |
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| 47 | \return the difference between the vectors |
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| 48 | */ |
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| 49 | Vector Vector::operator- (const Vector& v) const |
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| 50 | { |
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| 51 | Vector r; |
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| 52 | |
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| 53 | r.x = x - v.x; |
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| 54 | r.y = y - v.y; |
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| 55 | r.z = z - v.z; |
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| 56 | |
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| 57 | return r; |
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| 58 | } |
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| 59 | |
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| 60 | /** |
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| 61 | \brief calculate the dot product of two vectors |
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| 62 | \param v: the other vector |
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| 63 | \return the dot product of the vectors |
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| 64 | */ |
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| 65 | float Vector::operator* (const Vector& v) const |
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| 66 | { |
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[3746] | 67 | return x * v.x + y * v.y+ z * v.z; |
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[2043] | 68 | } |
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| 69 | |
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| 70 | /** |
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| 71 | \brief multiply a vector with a float |
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| 72 | \param f: the factor |
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| 73 | \return the vector multipied by f |
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| 74 | */ |
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| 75 | Vector Vector::operator* (float f) const |
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| 76 | { |
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| 77 | Vector r; |
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| 78 | |
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| 79 | r.x = x * f; |
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| 80 | r.y = y * f; |
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| 81 | r.z = z * f; |
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| 82 | |
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| 83 | return r; |
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| 84 | } |
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| 85 | |
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| 86 | /** |
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| 87 | \brief divide a vector with a float |
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| 88 | \param f: the divisor |
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| 89 | \return the vector divided by f |
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| 90 | */ |
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| 91 | Vector Vector::operator/ (float f) const |
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| 92 | { |
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| 93 | Vector r; |
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| 94 | |
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| 95 | if( f == 0.0) |
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| 96 | { |
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| 97 | // Prevent divide by zero |
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| 98 | return Vector (0,0,0); |
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| 99 | } |
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| 100 | |
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| 101 | r.x = x / f; |
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| 102 | r.y = y / f; |
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| 103 | r.z = z / f; |
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| 104 | |
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| 105 | return r; |
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| 106 | } |
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| 107 | |
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| 108 | /** |
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| 109 | \brief calculate the dot product of two vectors |
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| 110 | \param v: the other vector |
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| 111 | \return the dot product of the vectors |
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| 112 | */ |
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| 113 | float Vector::dot (const Vector& v) const |
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| 114 | { |
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| 115 | return x*v.x+y*v.y+z*v.z; |
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| 116 | } |
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| 117 | |
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| 118 | /** |
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| 119 | \brief calculate the cross product of two vectors |
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| 120 | \param v: the other vector |
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| 121 | \return the cross product of the vectors |
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| 122 | */ |
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| 123 | Vector Vector::cross (const Vector& v) const |
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| 124 | { |
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| 125 | Vector r; |
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| 126 | |
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| 127 | r.x = y * v.z - z * v.y; |
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| 128 | r.y = z * v.x - x * v.z; |
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| 129 | r.z = x * v.y - y * v.x; |
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| 130 | |
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| 131 | return r; |
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| 132 | } |
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| 133 | |
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| 134 | /** |
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| 135 | \brief normalizes the vector to lenght 1.0 |
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| 136 | */ |
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| 137 | void Vector::normalize () |
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| 138 | { |
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| 139 | float l = len(); |
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| 140 | |
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| 141 | if( l == 0.0) |
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| 142 | { |
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| 143 | // Prevent divide by zero |
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| 144 | return; |
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| 145 | } |
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| 146 | |
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| 147 | x = x / l; |
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| 148 | y = y / l; |
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| 149 | z = z / l; |
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| 150 | } |
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[2551] | 151 | |
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| 152 | |
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| 153 | /** |
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[3449] | 154 | \brief returns the voctor normalized to length 1.0 |
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[2551] | 155 | */ |
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| 156 | |
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| 157 | Vector* Vector::getNormalized() |
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| 158 | { |
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| 159 | float l = len(); |
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| 160 | if(l != 1.0) |
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| 161 | { |
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| 162 | return this; |
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| 163 | } |
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| 164 | else if(l == 0.0) |
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| 165 | { |
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| 166 | return 0; |
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| 167 | } |
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| 168 | |
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| 169 | Vector *normalizedVector = new Vector(x / l, y /l, z / l); |
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| 170 | return normalizedVector; |
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| 171 | } |
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| 172 | |
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[3449] | 173 | /** |
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| 174 | \brief scales this Vector with Vector v. |
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| 175 | \param v the vector to scale this vector with |
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| 176 | */ |
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[2551] | 177 | void Vector::scale(const Vector& v) |
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| 178 | { |
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| 179 | x *= v.x; |
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| 180 | y *= v.y; |
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| 181 | z *= v.z; |
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| 182 | } |
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| 183 | |
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[2043] | 184 | |
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| 185 | /** |
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| 186 | \brief calculates the lenght of the vector |
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| 187 | \return the lenght of the vector |
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| 188 | */ |
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| 189 | float Vector::len () const |
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| 190 | { |
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| 191 | return sqrt (x*x+y*y+z*z); |
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| 192 | } |
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| 193 | |
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[2551] | 194 | |
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[3449] | 195 | /** |
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| 196 | \brief Vector is looking in the positive direction on all axes after this |
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| 197 | */ |
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[2551] | 198 | Vector Vector::abs() |
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| 199 | { |
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| 200 | Vector v(fabs(x), fabs(y), fabs(z)); |
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| 201 | return v; |
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| 202 | } |
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| 203 | |
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[2043] | 204 | /** |
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| 205 | \brief calculate the angle between two vectors in radiances |
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| 206 | \param v1: a vector |
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| 207 | \param v2: another vector |
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| 208 | \return the angle between the vectors in radians |
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| 209 | */ |
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[3228] | 210 | float angleRad (const Vector& v1, const Vector& v2) |
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[2043] | 211 | { |
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| 212 | return acos( v1 * v2 / (v1.len() * v2.len())); |
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| 213 | } |
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| 214 | |
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[2551] | 215 | |
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[2043] | 216 | /** |
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| 217 | \brief calculate the angle between two vectors in degrees |
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| 218 | \param v1: a vector |
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| 219 | \param v2: another vector |
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| 220 | \return the angle between the vectors in degrees |
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| 221 | */ |
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[3228] | 222 | float angleDeg (const Vector& v1, const Vector& v2) |
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[2043] | 223 | { |
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| 224 | float f; |
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| 225 | f = acos( v1 * v2 / (v1.len() * v2.len())); |
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| 226 | return f * 180 / PI; |
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| 227 | } |
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| 228 | |
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[3605] | 229 | |
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[2043] | 230 | /** |
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[3605] | 231 | \brief Outputs the values of the Vector |
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| 232 | */ |
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| 233 | void Vector::debug(void) |
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| 234 | { |
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| 235 | PRINT(0)("Vector Debug information\n"); |
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| 236 | PRINT(0)("x: %f; y: %f; z: %f", x, y, z); |
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| 237 | PRINT(3)(" lenght: %f", len()); |
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| 238 | PRINT(0)("\n"); |
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| 239 | } |
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| 240 | |
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| 241 | /** |
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[2190] | 242 | \brief creates a multiplicational identity Quaternion |
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| 243 | */ |
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| 244 | Quaternion::Quaternion () |
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| 245 | { |
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| 246 | w = 1; |
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| 247 | v = Vector(0,0,0); |
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| 248 | } |
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| 249 | |
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| 250 | /** |
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| 251 | \brief turns a rotation along an axis into a Quaternion |
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| 252 | \param angle: the amount of radians to rotate |
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| 253 | \param axis: the axis to rotate around |
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| 254 | */ |
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| 255 | Quaternion::Quaternion (float angle, const Vector& axis) |
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| 256 | { |
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| 257 | w = cos(angle/2); |
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| 258 | v = axis * sin(angle/2); |
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| 259 | } |
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| 260 | |
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| 261 | /** |
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[3234] | 262 | \brief calculates a lookAt rotation |
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[2551] | 263 | \param dir: the direction you want to look |
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| 264 | \param up: specify what direction up should be |
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| 265 | |
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| 266 | Mathematically this determines the rotation a (0,0,1)-Vector has to undergo to point |
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| 267 | the same way as dir. If you want to use this with cameras, you'll have to reverse the |
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| 268 | dir Vector (Vector(0,0,0) - your viewing direction) or you'll point the wrong way. You |
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| 269 | can use this for meshes as well (then you do not have to reverse the vector), but keep |
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| 270 | in mind that if you do that, the model's front has to point in +z direction, and left |
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| 271 | and right should be -x or +x respectively or the mesh wont rotate correctly. |
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[2190] | 272 | */ |
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| 273 | Quaternion::Quaternion (const Vector& dir, const Vector& up) |
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[2551] | 274 | { |
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| 275 | Vector z = dir; |
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| 276 | z.normalize(); |
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| 277 | Vector x = up.cross(z); |
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| 278 | x.normalize(); |
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[2190] | 279 | Vector y = z.cross(x); |
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| 280 | |
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| 281 | float m[4][4]; |
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| 282 | m[0][0] = x.x; |
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| 283 | m[0][1] = x.y; |
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| 284 | m[0][2] = x.z; |
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| 285 | m[0][3] = 0; |
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| 286 | m[1][0] = y.x; |
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| 287 | m[1][1] = y.y; |
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| 288 | m[1][2] = y.z; |
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| 289 | m[1][3] = 0; |
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| 290 | m[2][0] = z.x; |
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| 291 | m[2][1] = z.y; |
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| 292 | m[2][2] = z.z; |
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| 293 | m[2][3] = 0; |
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| 294 | m[3][0] = 0; |
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| 295 | m[3][1] = 0; |
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| 296 | m[3][2] = 0; |
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| 297 | m[3][3] = 1; |
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| 298 | |
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| 299 | *this = Quaternion (m); |
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| 300 | } |
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| 301 | |
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| 302 | /** |
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| 303 | \brief calculates a rotation from euler angles |
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| 304 | \param roll: the roll in radians |
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| 305 | \param pitch: the pitch in radians |
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| 306 | \param yaw: the yaw in radians |
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| 307 | |
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[2551] | 308 | I DO HONESTLY NOT EXACTLY KNOW WHICH ANGLE REPRESENTS WHICH ROTATION. And I do not know |
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| 309 | in what order they are applied, I just copy-pasted the code. |
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[2190] | 310 | */ |
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| 311 | Quaternion::Quaternion (float roll, float pitch, float yaw) |
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| 312 | { |
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[2551] | 313 | float cr, cp, cy, sr, sp, sy, cpcy, spsy; |
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| 314 | |
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| 315 | // calculate trig identities |
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| 316 | cr = cos(roll/2); |
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| 317 | cp = cos(pitch/2); |
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| 318 | cy = cos(yaw/2); |
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| 319 | |
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| 320 | sr = sin(roll/2); |
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| 321 | sp = sin(pitch/2); |
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| 322 | sy = sin(yaw/2); |
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| 323 | |
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| 324 | cpcy = cp * cy; |
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| 325 | spsy = sp * sy; |
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| 326 | |
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| 327 | w = cr * cpcy + sr * spsy; |
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| 328 | v.x = sr * cpcy - cr * spsy; |
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| 329 | v.y = cr * sp * cy + sr * cp * sy; |
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[2190] | 330 | v.z = cr * cp * sy - sr * sp * cy; |
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| 331 | } |
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| 332 | |
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| 333 | /** |
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| 334 | \brief rotates one Quaternion by another |
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| 335 | \param q: another Quaternion to rotate this by |
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| 336 | \return a quaternion that represents the first one rotated by the second one (WARUNING: this operation is not commutative! e.g. (A*B) != (B*A)) |
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| 337 | */ |
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| 338 | Quaternion Quaternion::operator*(const Quaternion& q) const |
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[2551] | 339 | { |
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| 340 | float A, B, C, D, E, F, G, H; |
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[2190] | 341 | Quaternion r; |
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[2551] | 342 | |
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| 343 | A = (w + v.x)*(q.w + q.v.x); |
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| 344 | B = (v.z - v.y)*(q.v.y - q.v.z); |
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| 345 | C = (w - v.x)*(q.v.y + q.v.z); |
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| 346 | D = (v.y + v.z)*(q.w - q.v.x); |
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| 347 | E = (v.x + v.z)*(q.v.x + q.v.y); |
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| 348 | F = (v.x - v.z)*(q.v.x - q.v.y); |
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| 349 | G = (w + v.y)*(q.w - q.v.z); |
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| 350 | H = (w - v.y)*(q.w + q.v.z); |
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| 351 | |
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| 352 | r.w = B + (-E - F + G + H)/2; |
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| 353 | r.v.x = A - (E + F + G + H)/2; |
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| 354 | r.v.y = C + (E - F + G - H)/2; |
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[2190] | 355 | r.v.z = D + (E - F - G + H)/2; |
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| 356 | |
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| 357 | return r; |
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| 358 | } |
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| 359 | |
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| 360 | /** |
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| 361 | \brief add two Quaternions |
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| 362 | \param q: another Quaternion |
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| 363 | \return the sum of both Quaternions |
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| 364 | */ |
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| 365 | Quaternion Quaternion::operator+(const Quaternion& q) const |
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| 366 | { |
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| 367 | Quaternion r(*this); |
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| 368 | r.w = r.w + q.w; |
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| 369 | r.v = r.v + q.v; |
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| 370 | return r; |
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| 371 | } |
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| 372 | |
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| 373 | /** |
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| 374 | \brief subtract two Quaternions |
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| 375 | \param q: another Quaternion |
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| 376 | \return the difference of both Quaternions |
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| 377 | */ |
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| 378 | Quaternion Quaternion::operator- (const Quaternion& q) const |
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| 379 | { |
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| 380 | Quaternion r(*this); |
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| 381 | r.w = r.w - q.w; |
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| 382 | r.v = r.v - q.v; |
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| 383 | return r; |
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| 384 | } |
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| 385 | |
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| 386 | /** |
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| 387 | \brief rotate a Vector by a Quaternion |
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| 388 | \param v: the Vector |
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| 389 | \return a new Vector representing v rotated by the Quaternion |
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| 390 | */ |
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| 391 | Vector Quaternion::apply (Vector& v) const |
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| 392 | { |
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| 393 | Quaternion q; |
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| 394 | q.v = v; |
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| 395 | q.w = 0; |
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| 396 | q = *this * q * conjugate(); |
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| 397 | return q.v; |
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| 398 | } |
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| 399 | |
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| 400 | /** |
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| 401 | \brief multiply a Quaternion with a real value |
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| 402 | \param f: a real value |
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| 403 | \return a new Quaternion containing the product |
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| 404 | */ |
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| 405 | Quaternion Quaternion::operator*(const float& f) const |
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| 406 | { |
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| 407 | Quaternion r(*this); |
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| 408 | r.w = r.w*f; |
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| 409 | r.v = r.v*f; |
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| 410 | return r; |
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| 411 | } |
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| 412 | |
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| 413 | /** |
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| 414 | \brief divide a Quaternion by a real value |
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| 415 | \param f: a real value |
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| 416 | \return a new Quaternion containing the quotient |
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| 417 | */ |
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| 418 | Quaternion Quaternion::operator/(const float& f) const |
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| 419 | { |
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| 420 | if( f == 0) return Quaternion(); |
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| 421 | Quaternion r(*this); |
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| 422 | r.w = r.w/f; |
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| 423 | r.v = r.v/f; |
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| 424 | return r; |
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| 425 | } |
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| 426 | |
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| 427 | /** |
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| 428 | \brief calculate the conjugate value of the Quaternion |
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| 429 | \return the conjugate Quaternion |
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| 430 | */ |
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| 431 | Quaternion Quaternion::conjugate() const |
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| 432 | { |
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| 433 | Quaternion r(*this); |
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| 434 | r.v = Vector() - r.v; |
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| 435 | return r; |
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| 436 | } |
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| 437 | |
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| 438 | /** |
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| 439 | \brief calculate the norm of the Quaternion |
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| 440 | \return the norm of The Quaternion |
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| 441 | */ |
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| 442 | float Quaternion::norm() const |
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| 443 | { |
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| 444 | return w*w + v.x*v.x + v.y*v.y + v.z*v.z; |
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| 445 | } |
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| 446 | |
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| 447 | /** |
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| 448 | \brief calculate the inverse value of the Quaternion |
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| 449 | \return the inverse Quaternion |
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| 450 | |
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| 451 | Note that this is equal to conjugate() if the Quaternion's norm is 1 |
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| 452 | */ |
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| 453 | Quaternion Quaternion::inverse() const |
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| 454 | { |
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| 455 | float n = norm(); |
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| 456 | if (n != 0) |
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| 457 | { |
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| 458 | return conjugate() / norm(); |
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| 459 | } |
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| 460 | else return Quaternion(); |
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| 461 | } |
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| 462 | |
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| 463 | /** |
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| 464 | \brief convert the Quaternion to a 4x4 rotational glMatrix |
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| 465 | \param m: a buffer to store the Matrix in |
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| 466 | */ |
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| 467 | void Quaternion::matrix (float m[4][4]) const |
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| 468 | { |
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[2551] | 469 | float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2; |
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| 470 | |
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| 471 | // calculate coefficients |
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| 472 | x2 = v.x + v.x; |
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| 473 | y2 = v.y + v.y; |
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| 474 | z2 = v.z + v.z; |
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| 475 | xx = v.x * x2; xy = v.x * y2; xz = v.x * z2; |
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| 476 | yy = v.y * y2; yz = v.y * z2; zz = v.z * z2; |
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| 477 | wx = w * x2; wy = w * y2; wz = w * z2; |
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| 478 | |
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| 479 | m[0][0] = 1.0 - (yy + zz); m[1][0] = xy - wz; |
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| 480 | m[2][0] = xz + wy; m[3][0] = 0.0; |
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| 481 | |
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| 482 | m[0][1] = xy + wz; m[1][1] = 1.0 - (xx + zz); |
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| 483 | m[2][1] = yz - wx; m[3][1] = 0.0; |
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| 484 | |
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| 485 | m[0][2] = xz - wy; m[1][2] = yz + wx; |
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| 486 | m[2][2] = 1.0 - (xx + yy); m[3][2] = 0.0; |
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| 487 | |
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| 488 | m[0][3] = 0; m[1][3] = 0; |
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| 489 | m[2][3] = 0; m[3][3] = 1; |
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[2190] | 490 | } |
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| 491 | |
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[3449] | 492 | /** |
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| 493 | \brief performs a smooth move. |
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| 494 | \param from from where |
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| 495 | \param to to where |
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| 496 | \param t the time this transformation should take |
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| 497 | \param res The approximation-density |
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| 498 | */ |
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[2551] | 499 | void Quaternion::quatSlerp(const Quaternion* from, const Quaternion* to, float t, Quaternion* res) |
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| 500 | { |
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| 501 | float tol[4]; |
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| 502 | double omega, cosom, sinom, scale0, scale1; |
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| 503 | DELTA = 0.2; |
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| 504 | |
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| 505 | cosom = from->v.x * to->v.x + from->v.y * to->v.y + from->v.z * to->v.z + from->w * to->w; |
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| 506 | |
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| 507 | if( cosom < 0.0 ) |
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| 508 | { |
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| 509 | cosom = -cosom; |
---|
| 510 | tol[0] = -to->v.x; |
---|
| 511 | tol[1] = -to->v.y; |
---|
| 512 | tol[2] = -to->v.z; |
---|
| 513 | tol[3] = -to->w; |
---|
| 514 | } |
---|
| 515 | else |
---|
| 516 | { |
---|
| 517 | tol[0] = to->v.x; |
---|
| 518 | tol[1] = to->v.y; |
---|
| 519 | tol[2] = to->v.z; |
---|
| 520 | tol[3] = to->w; |
---|
| 521 | } |
---|
| 522 | |
---|
| 523 | //if( (1.0 - cosom) > DELTA ) |
---|
| 524 | //{ |
---|
| 525 | omega = acos(cosom); |
---|
| 526 | sinom = sin(omega); |
---|
| 527 | scale0 = sin((1.0 - t) * omega) / sinom; |
---|
| 528 | scale1 = sin(t * omega) / sinom; |
---|
| 529 | //} |
---|
| 530 | /* |
---|
| 531 | else |
---|
| 532 | { |
---|
| 533 | scale0 = 1.0 - t; |
---|
| 534 | scale1 = t; |
---|
| 535 | } |
---|
| 536 | */ |
---|
| 537 | res->v.x = scale0 * from->v.x + scale1 * tol[0]; |
---|
| 538 | res->v.y = scale0 * from->v.y + scale1 * tol[1]; |
---|
| 539 | res->v.z = scale0 * from->v.z + scale1 * tol[2]; |
---|
| 540 | res->w = scale0 * from->w + scale1 * tol[3]; |
---|
| 541 | } |
---|
| 542 | |
---|
| 543 | |
---|
[2190] | 544 | /** |
---|
[2551] | 545 | \brief convert a rotational 4x4 glMatrix into a Quaternion |
---|
| 546 | \param m: a 4x4 matrix in glMatrix order |
---|
[2190] | 547 | */ |
---|
| 548 | Quaternion::Quaternion (float m[4][4]) |
---|
| 549 | { |
---|
[2551] | 550 | |
---|
| 551 | float tr, s, q[4]; |
---|
| 552 | int i, j, k; |
---|
| 553 | |
---|
| 554 | int nxt[3] = {1, 2, 0}; |
---|
| 555 | |
---|
| 556 | tr = m[0][0] + m[1][1] + m[2][2]; |
---|
| 557 | |
---|
| 558 | // check the diagonal |
---|
[2190] | 559 | if (tr > 0.0) |
---|
[2551] | 560 | { |
---|
| 561 | s = sqrt (tr + 1.0); |
---|
| 562 | w = s / 2.0; |
---|
| 563 | s = 0.5 / s; |
---|
| 564 | v.x = (m[1][2] - m[2][1]) * s; |
---|
| 565 | v.y = (m[2][0] - m[0][2]) * s; |
---|
| 566 | v.z = (m[0][1] - m[1][0]) * s; |
---|
[2190] | 567 | } |
---|
| 568 | else |
---|
[2551] | 569 | { |
---|
| 570 | // diagonal is negative |
---|
| 571 | i = 0; |
---|
| 572 | if (m[1][1] > m[0][0]) i = 1; |
---|
| 573 | if (m[2][2] > m[i][i]) i = 2; |
---|
| 574 | j = nxt[i]; |
---|
| 575 | k = nxt[j]; |
---|
| 576 | |
---|
| 577 | s = sqrt ((m[i][i] - (m[j][j] + m[k][k])) + 1.0); |
---|
| 578 | |
---|
| 579 | q[i] = s * 0.5; |
---|
| 580 | |
---|
| 581 | if (s != 0.0) s = 0.5 / s; |
---|
[2190] | 582 | |
---|
[2551] | 583 | q[3] = (m[j][k] - m[k][j]) * s; |
---|
| 584 | q[j] = (m[i][j] + m[j][i]) * s; |
---|
| 585 | q[k] = (m[i][k] + m[k][i]) * s; |
---|
| 586 | |
---|
| 587 | v.x = q[0]; |
---|
| 588 | v.y = q[1]; |
---|
| 589 | v.z = q[2]; |
---|
| 590 | w = q[3]; |
---|
[2190] | 591 | } |
---|
| 592 | } |
---|
| 593 | |
---|
| 594 | /** |
---|
[3605] | 595 | \brief outputs some nice formated debug information about this quaternion |
---|
| 596 | */ |
---|
| 597 | void Quaternion::debug(void) |
---|
| 598 | { |
---|
| 599 | PRINT(0)("Quaternion Debug Information\n"); |
---|
| 600 | PRINT(0)("real a=%f; imag: x=%f y=%f z=%f\n", w, v.x, v.y, v.z); |
---|
| 601 | } |
---|
| 602 | |
---|
| 603 | /** |
---|
[2043] | 604 | \brief create a rotation from a vector |
---|
| 605 | \param v: a vector |
---|
| 606 | */ |
---|
| 607 | Rotation::Rotation (const Vector& v) |
---|
| 608 | { |
---|
| 609 | Vector x = Vector( 1, 0, 0); |
---|
| 610 | Vector axis = x.cross( v); |
---|
| 611 | axis.normalize(); |
---|
[3234] | 612 | float angle = angleRad( x, v); |
---|
[2043] | 613 | float ca = cos(angle); |
---|
| 614 | float sa = sin(angle); |
---|
| 615 | m[0] = 1.0f+(1.0f-ca)*(axis.x*axis.x-1.0f); |
---|
| 616 | m[1] = -axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 617 | m[2] = axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 618 | m[3] = axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 619 | m[4] = 1.0f+(1.0f-ca)*(axis.y*axis.y-1.0f); |
---|
| 620 | m[5] = -axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 621 | m[6] = -axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 622 | m[7] = axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 623 | m[8] = 1.0f+(1.0f-ca)*(axis.z*axis.z-1.0f); |
---|
| 624 | } |
---|
| 625 | |
---|
| 626 | /** |
---|
| 627 | \brief creates a rotation from an axis and an angle (radians!) |
---|
| 628 | \param axis: the rotational axis |
---|
| 629 | \param angle: the angle in radians |
---|
| 630 | */ |
---|
| 631 | Rotation::Rotation (const Vector& axis, float angle) |
---|
| 632 | { |
---|
| 633 | float ca, sa; |
---|
| 634 | ca = cos(angle); |
---|
| 635 | sa = sin(angle); |
---|
| 636 | m[0] = 1.0f+(1.0f-ca)*(axis.x*axis.x-1.0f); |
---|
| 637 | m[1] = -axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 638 | m[2] = axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 639 | m[3] = axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 640 | m[4] = 1.0f+(1.0f-ca)*(axis.y*axis.y-1.0f); |
---|
| 641 | m[5] = -axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 642 | m[6] = -axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 643 | m[7] = axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 644 | m[8] = 1.0f+(1.0f-ca)*(axis.z*axis.z-1.0f); |
---|
| 645 | } |
---|
| 646 | |
---|
| 647 | /** |
---|
| 648 | \brief creates a rotation from euler angles (pitch/yaw/roll) |
---|
| 649 | \param pitch: rotation around z (in radians) |
---|
| 650 | \param yaw: rotation around y (in radians) |
---|
| 651 | \param roll: rotation around x (in radians) |
---|
| 652 | */ |
---|
| 653 | Rotation::Rotation ( float pitch, float yaw, float roll) |
---|
| 654 | { |
---|
| 655 | float cy, sy, cr, sr, cp, sp; |
---|
| 656 | cy = cos(yaw); |
---|
| 657 | sy = sin(yaw); |
---|
| 658 | cr = cos(roll); |
---|
| 659 | sr = sin(roll); |
---|
| 660 | cp = cos(pitch); |
---|
| 661 | sp = sin(pitch); |
---|
| 662 | m[0] = cy*cr; |
---|
| 663 | m[1] = -cy*sr; |
---|
| 664 | m[2] = sy; |
---|
| 665 | m[3] = cp*sr+sp*sy*cr; |
---|
| 666 | m[4] = cp*cr-sp*sr*sy; |
---|
| 667 | m[5] = -sp*cy; |
---|
| 668 | m[6] = sp*sr-cp*sy*cr; |
---|
| 669 | m[7] = sp*cr+cp*sy*sr; |
---|
| 670 | m[8] = cp*cy; |
---|
| 671 | } |
---|
| 672 | |
---|
| 673 | /** |
---|
| 674 | \brief creates a nullrotation (an identity rotation) |
---|
| 675 | */ |
---|
| 676 | Rotation::Rotation () |
---|
| 677 | { |
---|
| 678 | m[0] = 1.0f; |
---|
| 679 | m[1] = 0.0f; |
---|
| 680 | m[2] = 0.0f; |
---|
| 681 | m[3] = 0.0f; |
---|
| 682 | m[4] = 1.0f; |
---|
| 683 | m[5] = 0.0f; |
---|
| 684 | m[6] = 0.0f; |
---|
| 685 | m[7] = 0.0f; |
---|
| 686 | m[8] = 1.0f; |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | /** |
---|
[2190] | 690 | \brief fills the specified buffer with a 4x4 glmatrix |
---|
| 691 | \param buffer: Pointer to an array of 16 floats |
---|
| 692 | |
---|
| 693 | Use this to get the rotation in a gl-compatible format |
---|
| 694 | */ |
---|
| 695 | void Rotation::glmatrix (float* buffer) |
---|
| 696 | { |
---|
| 697 | buffer[0] = m[0]; |
---|
| 698 | buffer[1] = m[3]; |
---|
| 699 | buffer[2] = m[6]; |
---|
| 700 | buffer[3] = m[0]; |
---|
| 701 | buffer[4] = m[1]; |
---|
| 702 | buffer[5] = m[4]; |
---|
| 703 | buffer[6] = m[7]; |
---|
| 704 | buffer[7] = m[0]; |
---|
| 705 | buffer[8] = m[2]; |
---|
| 706 | buffer[9] = m[5]; |
---|
| 707 | buffer[10] = m[8]; |
---|
| 708 | buffer[11] = m[0]; |
---|
| 709 | buffer[12] = m[0]; |
---|
| 710 | buffer[13] = m[0]; |
---|
| 711 | buffer[14] = m[0]; |
---|
| 712 | buffer[15] = m[1]; |
---|
| 713 | } |
---|
| 714 | |
---|
| 715 | /** |
---|
| 716 | \brief multiplies two rotational matrices |
---|
| 717 | \param r: another Rotation |
---|
| 718 | \return the matrix product of the Rotations |
---|
| 719 | |
---|
| 720 | Use this to rotate one rotation by another |
---|
| 721 | */ |
---|
| 722 | Rotation Rotation::operator* (const Rotation& r) |
---|
| 723 | { |
---|
| 724 | Rotation p; |
---|
| 725 | |
---|
| 726 | p.m[0] = m[0]*r.m[0] + m[1]*r.m[3] + m[2]*r.m[6]; |
---|
| 727 | p.m[1] = m[0]*r.m[1] + m[1]*r.m[4] + m[2]*r.m[7]; |
---|
| 728 | p.m[2] = m[0]*r.m[2] + m[1]*r.m[5] + m[2]*r.m[8]; |
---|
| 729 | |
---|
| 730 | p.m[3] = m[3]*r.m[0] + m[4]*r.m[3] + m[5]*r.m[6]; |
---|
| 731 | p.m[4] = m[3]*r.m[1] + m[4]*r.m[4] + m[5]*r.m[7]; |
---|
| 732 | p.m[5] = m[3]*r.m[2] + m[4]*r.m[5] + m[5]*r.m[8]; |
---|
| 733 | |
---|
| 734 | p.m[6] = m[6]*r.m[0] + m[7]*r.m[3] + m[8]*r.m[6]; |
---|
| 735 | p.m[7] = m[6]*r.m[1] + m[7]*r.m[4] + m[8]*r.m[7]; |
---|
| 736 | p.m[8] = m[6]*r.m[2] + m[7]*r.m[5] + m[8]*r.m[8]; |
---|
| 737 | |
---|
| 738 | return p; |
---|
| 739 | } |
---|
| 740 | |
---|
| 741 | |
---|
| 742 | /** |
---|
[2043] | 743 | \brief rotates the vector by the given rotation |
---|
| 744 | \param v: a vector |
---|
| 745 | \param r: a rotation |
---|
| 746 | \return the rotated vector |
---|
| 747 | */ |
---|
[3228] | 748 | Vector rotateVector( const Vector& v, const Rotation& r) |
---|
[2043] | 749 | { |
---|
| 750 | Vector t; |
---|
| 751 | |
---|
| 752 | t.x = v.x * r.m[0] + v.y * r.m[1] + v.z * r.m[2]; |
---|
| 753 | t.y = v.x * r.m[3] + v.y * r.m[4] + v.z * r.m[5]; |
---|
| 754 | t.z = v.x * r.m[6] + v.y * r.m[7] + v.z * r.m[8]; |
---|
| 755 | |
---|
| 756 | return t; |
---|
| 757 | } |
---|
| 758 | |
---|
| 759 | /** |
---|
| 760 | \brief calculate the distance between two lines |
---|
| 761 | \param l: the other line |
---|
| 762 | \return the distance between the lines |
---|
| 763 | */ |
---|
| 764 | float Line::distance (const Line& l) const |
---|
| 765 | { |
---|
| 766 | float q, d; |
---|
| 767 | Vector n = a.cross(l.a); |
---|
| 768 | q = n.dot(r-l.r); |
---|
| 769 | d = n.len(); |
---|
| 770 | if( d == 0.0) return 0.0; |
---|
| 771 | return q/d; |
---|
| 772 | } |
---|
| 773 | |
---|
| 774 | /** |
---|
| 775 | \brief calculate the distance between a line and a point |
---|
| 776 | \param v: the point |
---|
| 777 | \return the distance between the Line and the point |
---|
| 778 | */ |
---|
[3228] | 779 | float Line::distancePoint (const Vector& v) const |
---|
[2043] | 780 | { |
---|
| 781 | Vector d = v-r; |
---|
| 782 | Vector u = a * d.dot( a); |
---|
| 783 | return (d - u).len(); |
---|
| 784 | } |
---|
| 785 | |
---|
| 786 | /** |
---|
| 787 | \brief calculate the two points of minimal distance of two lines |
---|
| 788 | \param l: the other line |
---|
| 789 | \return a Vector[2] (!has to be deleted after use!) containing the two points of minimal distance |
---|
| 790 | */ |
---|
| 791 | Vector* Line::footpoints (const Line& l) const |
---|
| 792 | { |
---|
| 793 | Vector* fp = new Vector[2]; |
---|
| 794 | Plane p = Plane (r + a.cross(l.a), r, r + a); |
---|
[3234] | 795 | fp[1] = p.intersectLine (l); |
---|
[2043] | 796 | p = Plane (fp[1], l.a); |
---|
[3234] | 797 | fp[0] = p.intersectLine (*this); |
---|
[2043] | 798 | return fp; |
---|
| 799 | } |
---|
| 800 | |
---|
| 801 | /** |
---|
| 802 | \brief calculate the length of a line |
---|
| 803 | \return the lenght of the line |
---|
| 804 | */ |
---|
| 805 | float Line::len() const |
---|
| 806 | { |
---|
| 807 | return a.len(); |
---|
| 808 | } |
---|
| 809 | |
---|
| 810 | /** |
---|
| 811 | \brief rotate the line by given rotation |
---|
| 812 | \param rot: a rotation |
---|
| 813 | */ |
---|
| 814 | void Line::rotate (const Rotation& rot) |
---|
| 815 | { |
---|
| 816 | Vector t = a + r; |
---|
[3234] | 817 | t = rotateVector( t, rot); |
---|
| 818 | r = rotateVector( r, rot), |
---|
[2043] | 819 | a = t - r; |
---|
| 820 | } |
---|
| 821 | |
---|
| 822 | /** |
---|
| 823 | \brief create a plane from three points |
---|
| 824 | \param a: first point |
---|
| 825 | \param b: second point |
---|
| 826 | \param c: third point |
---|
| 827 | */ |
---|
| 828 | Plane::Plane (Vector a, Vector b, Vector c) |
---|
| 829 | { |
---|
| 830 | n = (a-b).cross(c-b); |
---|
| 831 | k = -(n.x*b.x+n.y*b.y+n.z*b.z); |
---|
| 832 | } |
---|
| 833 | |
---|
| 834 | /** |
---|
| 835 | \brief create a plane from anchor point and normal |
---|
[3449] | 836 | \param norm: normal vector |
---|
[2043] | 837 | \param p: anchor point |
---|
| 838 | */ |
---|
| 839 | Plane::Plane (Vector norm, Vector p) |
---|
| 840 | { |
---|
| 841 | n = norm; |
---|
| 842 | k = -(n.x*p.x+n.y*p.y+n.z*p.z); |
---|
| 843 | } |
---|
| 844 | |
---|
| 845 | /** |
---|
| 846 | \brief returns the intersection point between the plane and a line |
---|
| 847 | \param l: a line |
---|
| 848 | */ |
---|
[3228] | 849 | Vector Plane::intersectLine (const Line& l) const |
---|
[2043] | 850 | { |
---|
| 851 | if (n.x*l.a.x+n.y*l.a.y+n.z*l.a.z == 0.0) return Vector(0,0,0); |
---|
| 852 | float t = (n.x*l.r.x+n.y*l.r.y+n.z*l.r.z+k) / (n.x*l.a.x+n.y*l.a.y+n.z*l.a.z); |
---|
| 853 | return l.r + (l.a * t); |
---|
| 854 | } |
---|
| 855 | |
---|
| 856 | /** |
---|
| 857 | \brief returns the distance between the plane and a point |
---|
| 858 | \param p: a Point |
---|
| 859 | \return the distance between the plane and the point (can be negative) |
---|
| 860 | */ |
---|
[3228] | 861 | float Plane::distancePoint (const Vector& p) const |
---|
[2043] | 862 | { |
---|
| 863 | float l = n.len(); |
---|
| 864 | if( l == 0.0) return 0.0; |
---|
| 865 | return (n.dot(p) + k) / n.len(); |
---|
| 866 | } |
---|
| 867 | |
---|
| 868 | /** |
---|
| 869 | \brief returns the side a point is located relative to a Plane |
---|
| 870 | \param p: a Point |
---|
| 871 | \return 0 if the point is contained within the Plane, positive(negative) if the point is in the positive(negative) semi-space of the Plane |
---|
| 872 | */ |
---|
[3228] | 873 | float Plane::locatePoint (const Vector& p) const |
---|
[2043] | 874 | { |
---|
| 875 | return (n.dot(p) + k); |
---|
| 876 | } |
---|
[3000] | 877 | |
---|