[2043] | 1 | |
---|
| 2 | |
---|
| 3 | /* |
---|
| 4 | orxonox - the future of 3D-vertical-scrollers |
---|
| 5 | |
---|
| 6 | Copyright (C) 2004 orx |
---|
| 7 | |
---|
| 8 | This program is free software; you can redistribute it and/or modify |
---|
| 9 | it under the terms of the GNU General Public License as published by |
---|
| 10 | the Free Software Foundation; either version 2, or (at your option) |
---|
| 11 | any later version. |
---|
| 12 | |
---|
| 13 | ### File Specific: |
---|
[2551] | 14 | main-programmer: Christian Meyer |
---|
| 15 | co-programmer: Patrick Boenzli : Vector::scale() |
---|
| 16 | Vector::abs() |
---|
[2190] | 17 | |
---|
| 18 | Quaternion code borrowed from an Gamasutra article by Nick Bobick and Ken Shoemake |
---|
[2043] | 19 | */ |
---|
| 20 | |
---|
[3590] | 21 | #define DEBUG_SPECIAL_MODULE DEBUG_MODULE_MATH |
---|
[2043] | 22 | |
---|
| 23 | #include "vector.h" |
---|
[3541] | 24 | #include "debug.h" |
---|
[3814] | 25 | #include "stdincl.h" |
---|
[2043] | 26 | |
---|
| 27 | using namespace std; |
---|
| 28 | |
---|
| 29 | /** |
---|
| 30 | \brief add two vectors |
---|
| 31 | \param v: the other vector |
---|
| 32 | \return the sum of both vectors |
---|
| 33 | */ |
---|
| 34 | |
---|
[3818] | 35 | //Vector Vector::operator+ (const Vector& v) const |
---|
| 36 | |
---|
| 37 | |
---|
[2043] | 38 | /** |
---|
| 39 | \brief subtract a vector from another |
---|
| 40 | \param v: the other vector |
---|
| 41 | \return the difference between the vectors |
---|
| 42 | */ |
---|
[3818] | 43 | //Vector Vector::operator- (const Vector& v) const |
---|
[2043] | 44 | |
---|
[3818] | 45 | |
---|
[2043] | 46 | /** |
---|
| 47 | \brief calculate the dot product of two vectors |
---|
| 48 | \param v: the other vector |
---|
| 49 | \return the dot product of the vectors |
---|
| 50 | */ |
---|
[3818] | 51 | //float Vector::operator* (const Vector& v) const |
---|
[2043] | 52 | |
---|
[3818] | 53 | |
---|
[2043] | 54 | /** |
---|
| 55 | \brief multiply a vector with a float |
---|
| 56 | \param f: the factor |
---|
| 57 | \return the vector multipied by f |
---|
| 58 | */ |
---|
[3818] | 59 | //Vector Vector::operator* (float f) const |
---|
[2043] | 60 | |
---|
[3818] | 61 | |
---|
[2043] | 62 | /** |
---|
| 63 | \brief divide a vector with a float |
---|
| 64 | \param f: the divisor |
---|
| 65 | \return the vector divided by f |
---|
| 66 | */ |
---|
| 67 | Vector Vector::operator/ (float f) const |
---|
| 68 | { |
---|
[3814] | 69 | __UNLIKELY_IF( f == 0.0) |
---|
[2043] | 70 | { |
---|
| 71 | // Prevent divide by zero |
---|
| 72 | return Vector (0,0,0); |
---|
| 73 | } |
---|
[3814] | 74 | return Vector(x / f, y / f, z / f); |
---|
[2043] | 75 | } |
---|
| 76 | |
---|
| 77 | /** |
---|
| 78 | \brief calculate the dot product of two vectors |
---|
| 79 | \param v: the other vector |
---|
| 80 | \return the dot product of the vectors |
---|
| 81 | */ |
---|
| 82 | float Vector::dot (const Vector& v) const |
---|
| 83 | { |
---|
| 84 | return x*v.x+y*v.y+z*v.z; |
---|
| 85 | } |
---|
| 86 | |
---|
| 87 | /** |
---|
| 88 | \brief calculate the cross product of two vectors |
---|
| 89 | \param v: the other vector |
---|
| 90 | \return the cross product of the vectors |
---|
| 91 | */ |
---|
| 92 | Vector Vector::cross (const Vector& v) const |
---|
| 93 | { |
---|
[3814] | 94 | return Vector(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x ); |
---|
[2043] | 95 | } |
---|
| 96 | |
---|
| 97 | /** |
---|
| 98 | \brief normalizes the vector to lenght 1.0 |
---|
| 99 | */ |
---|
| 100 | void Vector::normalize () |
---|
| 101 | { |
---|
| 102 | float l = len(); |
---|
| 103 | |
---|
[3814] | 104 | __UNLIKELY_IF( l == 0.0) |
---|
[2043] | 105 | { |
---|
| 106 | // Prevent divide by zero |
---|
| 107 | return; |
---|
| 108 | } |
---|
| 109 | |
---|
| 110 | x = x / l; |
---|
| 111 | y = y / l; |
---|
| 112 | z = z / l; |
---|
| 113 | } |
---|
[2551] | 114 | |
---|
| 115 | |
---|
| 116 | /** |
---|
[3449] | 117 | \brief returns the voctor normalized to length 1.0 |
---|
[2551] | 118 | */ |
---|
| 119 | |
---|
| 120 | Vector* Vector::getNormalized() |
---|
| 121 | { |
---|
| 122 | float l = len(); |
---|
[3814] | 123 | __UNLIKELY_IF(l != 1.0) |
---|
[2551] | 124 | { |
---|
| 125 | return this; |
---|
| 126 | } |
---|
[3814] | 127 | else __UNLIKELY_IF(l == 0.0) |
---|
[2551] | 128 | { |
---|
| 129 | return 0; |
---|
| 130 | } |
---|
[3814] | 131 | |
---|
| 132 | return new Vector(x / l, y /l, z / l); |
---|
[2551] | 133 | } |
---|
| 134 | |
---|
[3449] | 135 | /** |
---|
| 136 | \brief scales this Vector with Vector v. |
---|
| 137 | \param v the vector to scale this vector with |
---|
| 138 | */ |
---|
[2551] | 139 | void Vector::scale(const Vector& v) |
---|
| 140 | { |
---|
| 141 | x *= v.x; |
---|
| 142 | y *= v.y; |
---|
| 143 | z *= v.z; |
---|
| 144 | } |
---|
| 145 | |
---|
[2043] | 146 | |
---|
| 147 | /** |
---|
| 148 | \brief calculates the lenght of the vector |
---|
| 149 | \return the lenght of the vector |
---|
| 150 | */ |
---|
| 151 | float Vector::len () const |
---|
| 152 | { |
---|
| 153 | return sqrt (x*x+y*y+z*z); |
---|
| 154 | } |
---|
| 155 | |
---|
[2551] | 156 | |
---|
[3449] | 157 | /** |
---|
| 158 | \brief Vector is looking in the positive direction on all axes after this |
---|
| 159 | */ |
---|
[2551] | 160 | Vector Vector::abs() |
---|
| 161 | { |
---|
| 162 | Vector v(fabs(x), fabs(y), fabs(z)); |
---|
| 163 | return v; |
---|
| 164 | } |
---|
| 165 | |
---|
[2043] | 166 | /** |
---|
| 167 | \brief calculate the angle between two vectors in radiances |
---|
| 168 | \param v1: a vector |
---|
| 169 | \param v2: another vector |
---|
| 170 | \return the angle between the vectors in radians |
---|
| 171 | */ |
---|
[3228] | 172 | float angleRad (const Vector& v1, const Vector& v2) |
---|
[2043] | 173 | { |
---|
| 174 | return acos( v1 * v2 / (v1.len() * v2.len())); |
---|
| 175 | } |
---|
| 176 | |
---|
[2551] | 177 | |
---|
[2043] | 178 | /** |
---|
| 179 | \brief calculate the angle between two vectors in degrees |
---|
| 180 | \param v1: a vector |
---|
| 181 | \param v2: another vector |
---|
| 182 | \return the angle between the vectors in degrees |
---|
| 183 | */ |
---|
[3228] | 184 | float angleDeg (const Vector& v1, const Vector& v2) |
---|
[2043] | 185 | { |
---|
| 186 | float f; |
---|
| 187 | f = acos( v1 * v2 / (v1.len() * v2.len())); |
---|
| 188 | return f * 180 / PI; |
---|
| 189 | } |
---|
| 190 | |
---|
[3541] | 191 | |
---|
[2043] | 192 | /** |
---|
[3541] | 193 | \brief Outputs the values of the Vector |
---|
| 194 | */ |
---|
| 195 | void Vector::debug(void) |
---|
| 196 | { |
---|
| 197 | PRINT(0)("Vector Debug information\n"); |
---|
| 198 | PRINT(0)("x: %f; y: %f; z: %f", x, y, z); |
---|
| 199 | PRINT(3)(" lenght: %f", len()); |
---|
| 200 | PRINT(0)("\n"); |
---|
| 201 | } |
---|
| 202 | |
---|
| 203 | /** |
---|
[2190] | 204 | \brief creates a multiplicational identity Quaternion |
---|
| 205 | */ |
---|
| 206 | Quaternion::Quaternion () |
---|
| 207 | { |
---|
| 208 | w = 1; |
---|
| 209 | v = Vector(0,0,0); |
---|
| 210 | } |
---|
| 211 | |
---|
| 212 | /** |
---|
| 213 | \brief turns a rotation along an axis into a Quaternion |
---|
| 214 | \param angle: the amount of radians to rotate |
---|
| 215 | \param axis: the axis to rotate around |
---|
| 216 | */ |
---|
| 217 | Quaternion::Quaternion (float angle, const Vector& axis) |
---|
| 218 | { |
---|
| 219 | w = cos(angle/2); |
---|
| 220 | v = axis * sin(angle/2); |
---|
| 221 | } |
---|
| 222 | |
---|
| 223 | /** |
---|
[3234] | 224 | \brief calculates a lookAt rotation |
---|
[2551] | 225 | \param dir: the direction you want to look |
---|
| 226 | \param up: specify what direction up should be |
---|
| 227 | |
---|
| 228 | Mathematically this determines the rotation a (0,0,1)-Vector has to undergo to point |
---|
| 229 | the same way as dir. If you want to use this with cameras, you'll have to reverse the |
---|
| 230 | dir Vector (Vector(0,0,0) - your viewing direction) or you'll point the wrong way. You |
---|
| 231 | can use this for meshes as well (then you do not have to reverse the vector), but keep |
---|
| 232 | in mind that if you do that, the model's front has to point in +z direction, and left |
---|
| 233 | and right should be -x or +x respectively or the mesh wont rotate correctly. |
---|
[2190] | 234 | */ |
---|
| 235 | Quaternion::Quaternion (const Vector& dir, const Vector& up) |
---|
[2551] | 236 | { |
---|
| 237 | Vector z = dir; |
---|
| 238 | z.normalize(); |
---|
| 239 | Vector x = up.cross(z); |
---|
| 240 | x.normalize(); |
---|
[2190] | 241 | Vector y = z.cross(x); |
---|
| 242 | |
---|
| 243 | float m[4][4]; |
---|
| 244 | m[0][0] = x.x; |
---|
| 245 | m[0][1] = x.y; |
---|
| 246 | m[0][2] = x.z; |
---|
| 247 | m[0][3] = 0; |
---|
| 248 | m[1][0] = y.x; |
---|
| 249 | m[1][1] = y.y; |
---|
| 250 | m[1][2] = y.z; |
---|
| 251 | m[1][3] = 0; |
---|
| 252 | m[2][0] = z.x; |
---|
| 253 | m[2][1] = z.y; |
---|
| 254 | m[2][2] = z.z; |
---|
| 255 | m[2][3] = 0; |
---|
| 256 | m[3][0] = 0; |
---|
| 257 | m[3][1] = 0; |
---|
| 258 | m[3][2] = 0; |
---|
| 259 | m[3][3] = 1; |
---|
| 260 | |
---|
| 261 | *this = Quaternion (m); |
---|
| 262 | } |
---|
| 263 | |
---|
| 264 | /** |
---|
| 265 | \brief calculates a rotation from euler angles |
---|
| 266 | \param roll: the roll in radians |
---|
| 267 | \param pitch: the pitch in radians |
---|
| 268 | \param yaw: the yaw in radians |
---|
| 269 | |
---|
[2551] | 270 | I DO HONESTLY NOT EXACTLY KNOW WHICH ANGLE REPRESENTS WHICH ROTATION. And I do not know |
---|
| 271 | in what order they are applied, I just copy-pasted the code. |
---|
[2190] | 272 | */ |
---|
| 273 | Quaternion::Quaternion (float roll, float pitch, float yaw) |
---|
| 274 | { |
---|
[2551] | 275 | float cr, cp, cy, sr, sp, sy, cpcy, spsy; |
---|
| 276 | |
---|
| 277 | // calculate trig identities |
---|
| 278 | cr = cos(roll/2); |
---|
| 279 | cp = cos(pitch/2); |
---|
| 280 | cy = cos(yaw/2); |
---|
| 281 | |
---|
| 282 | sr = sin(roll/2); |
---|
| 283 | sp = sin(pitch/2); |
---|
| 284 | sy = sin(yaw/2); |
---|
| 285 | |
---|
| 286 | cpcy = cp * cy; |
---|
| 287 | spsy = sp * sy; |
---|
| 288 | |
---|
| 289 | w = cr * cpcy + sr * spsy; |
---|
| 290 | v.x = sr * cpcy - cr * spsy; |
---|
| 291 | v.y = cr * sp * cy + sr * cp * sy; |
---|
[2190] | 292 | v.z = cr * cp * sy - sr * sp * cy; |
---|
| 293 | } |
---|
| 294 | |
---|
| 295 | /** |
---|
| 296 | \brief rotates one Quaternion by another |
---|
| 297 | \param q: another Quaternion to rotate this by |
---|
| 298 | \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)) |
---|
| 299 | */ |
---|
| 300 | Quaternion Quaternion::operator*(const Quaternion& q) const |
---|
[2551] | 301 | { |
---|
| 302 | float A, B, C, D, E, F, G, H; |
---|
[2190] | 303 | Quaternion r; |
---|
[2551] | 304 | |
---|
| 305 | A = (w + v.x)*(q.w + q.v.x); |
---|
| 306 | B = (v.z - v.y)*(q.v.y - q.v.z); |
---|
| 307 | C = (w - v.x)*(q.v.y + q.v.z); |
---|
| 308 | D = (v.y + v.z)*(q.w - q.v.x); |
---|
| 309 | E = (v.x + v.z)*(q.v.x + q.v.y); |
---|
| 310 | F = (v.x - v.z)*(q.v.x - q.v.y); |
---|
| 311 | G = (w + v.y)*(q.w - q.v.z); |
---|
| 312 | H = (w - v.y)*(q.w + q.v.z); |
---|
| 313 | |
---|
| 314 | r.w = B + (-E - F + G + H)/2; |
---|
| 315 | r.v.x = A - (E + F + G + H)/2; |
---|
| 316 | r.v.y = C + (E - F + G - H)/2; |
---|
[2190] | 317 | r.v.z = D + (E - F - G + H)/2; |
---|
| 318 | |
---|
| 319 | return r; |
---|
| 320 | } |
---|
| 321 | |
---|
| 322 | /** |
---|
| 323 | \brief add two Quaternions |
---|
| 324 | \param q: another Quaternion |
---|
| 325 | \return the sum of both Quaternions |
---|
| 326 | */ |
---|
| 327 | Quaternion Quaternion::operator+(const Quaternion& q) const |
---|
| 328 | { |
---|
[3814] | 329 | Quaternion r(*this); |
---|
| 330 | r.w = r.w + q.w; |
---|
| 331 | r.v = r.v + q.v; |
---|
| 332 | return r; |
---|
[2190] | 333 | } |
---|
| 334 | |
---|
| 335 | /** |
---|
[3814] | 336 | \brief subtract two Quaternions |
---|
| 337 | \param q: another Quaternion |
---|
| 338 | \return the difference of both Quaternions |
---|
[2190] | 339 | */ |
---|
| 340 | Quaternion Quaternion::operator- (const Quaternion& q) const |
---|
| 341 | { |
---|
[3814] | 342 | Quaternion r(*this); |
---|
| 343 | r.w = r.w - q.w; |
---|
| 344 | r.v = r.v - q.v; |
---|
| 345 | return r; |
---|
[2190] | 346 | } |
---|
| 347 | |
---|
| 348 | /** |
---|
[3814] | 349 | \brief rotate a Vector by a Quaternion |
---|
| 350 | \param v: the Vector |
---|
| 351 | \return a new Vector representing v rotated by the Quaternion |
---|
[2190] | 352 | */ |
---|
| 353 | Vector Quaternion::apply (Vector& v) const |
---|
| 354 | { |
---|
[3814] | 355 | Quaternion q; |
---|
| 356 | q.v = v; |
---|
| 357 | q.w = 0; |
---|
| 358 | q = *this * q * conjugate(); |
---|
| 359 | return q.v; |
---|
[2190] | 360 | } |
---|
| 361 | |
---|
| 362 | /** |
---|
[3814] | 363 | \brief multiply a Quaternion with a real value |
---|
| 364 | \param f: a real value |
---|
| 365 | \return a new Quaternion containing the product |
---|
[2190] | 366 | */ |
---|
| 367 | Quaternion Quaternion::operator*(const float& f) const |
---|
| 368 | { |
---|
[3814] | 369 | Quaternion r(*this); |
---|
| 370 | r.w = r.w*f; |
---|
| 371 | r.v = r.v*f; |
---|
| 372 | return r; |
---|
[2190] | 373 | } |
---|
| 374 | |
---|
| 375 | /** |
---|
[3814] | 376 | \brief divide a Quaternion by a real value |
---|
| 377 | \param f: a real value |
---|
| 378 | \return a new Quaternion containing the quotient |
---|
[2190] | 379 | */ |
---|
| 380 | Quaternion Quaternion::operator/(const float& f) const |
---|
| 381 | { |
---|
[3814] | 382 | if( f == 0) return Quaternion(); |
---|
| 383 | Quaternion r(*this); |
---|
| 384 | r.w = r.w/f; |
---|
| 385 | r.v = r.v/f; |
---|
| 386 | return r; |
---|
[2190] | 387 | } |
---|
| 388 | |
---|
| 389 | /** |
---|
[3814] | 390 | \brief calculate the conjugate value of the Quaternion |
---|
| 391 | \return the conjugate Quaternion |
---|
[2190] | 392 | */ |
---|
| 393 | Quaternion Quaternion::conjugate() const |
---|
| 394 | { |
---|
[3814] | 395 | Quaternion r(*this); |
---|
| 396 | r.v = Vector() - r.v; |
---|
| 397 | return r; |
---|
[2190] | 398 | } |
---|
| 399 | |
---|
| 400 | /** |
---|
[3814] | 401 | \brief calculate the norm of the Quaternion |
---|
| 402 | \return the norm of The Quaternion |
---|
[2190] | 403 | */ |
---|
| 404 | float Quaternion::norm() const |
---|
| 405 | { |
---|
[3814] | 406 | return w*w + v.x*v.x + v.y*v.y + v.z*v.z; |
---|
[2190] | 407 | } |
---|
| 408 | |
---|
| 409 | /** |
---|
[3814] | 410 | \brief calculate the inverse value of the Quaternion |
---|
| 411 | \return the inverse Quaternion |
---|
| 412 | |
---|
[2190] | 413 | Note that this is equal to conjugate() if the Quaternion's norm is 1 |
---|
| 414 | */ |
---|
| 415 | Quaternion Quaternion::inverse() const |
---|
| 416 | { |
---|
[3814] | 417 | float n = norm(); |
---|
| 418 | if (n != 0) |
---|
| 419 | { |
---|
| 420 | return conjugate() / norm(); |
---|
| 421 | } |
---|
| 422 | else return Quaternion(); |
---|
[2190] | 423 | } |
---|
| 424 | |
---|
| 425 | /** |
---|
[3814] | 426 | \brief convert the Quaternion to a 4x4 rotational glMatrix |
---|
| 427 | \param m: a buffer to store the Matrix in |
---|
[2190] | 428 | */ |
---|
| 429 | void Quaternion::matrix (float m[4][4]) const |
---|
| 430 | { |
---|
[2551] | 431 | float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2; |
---|
| 432 | |
---|
| 433 | // calculate coefficients |
---|
| 434 | x2 = v.x + v.x; |
---|
| 435 | y2 = v.y + v.y; |
---|
| 436 | z2 = v.z + v.z; |
---|
| 437 | xx = v.x * x2; xy = v.x * y2; xz = v.x * z2; |
---|
| 438 | yy = v.y * y2; yz = v.y * z2; zz = v.z * z2; |
---|
| 439 | wx = w * x2; wy = w * y2; wz = w * z2; |
---|
| 440 | |
---|
| 441 | m[0][0] = 1.0 - (yy + zz); m[1][0] = xy - wz; |
---|
| 442 | m[2][0] = xz + wy; m[3][0] = 0.0; |
---|
| 443 | |
---|
| 444 | m[0][1] = xy + wz; m[1][1] = 1.0 - (xx + zz); |
---|
| 445 | m[2][1] = yz - wx; m[3][1] = 0.0; |
---|
| 446 | |
---|
| 447 | m[0][2] = xz - wy; m[1][2] = yz + wx; |
---|
| 448 | m[2][2] = 1.0 - (xx + yy); m[3][2] = 0.0; |
---|
| 449 | |
---|
| 450 | m[0][3] = 0; m[1][3] = 0; |
---|
| 451 | m[2][3] = 0; m[3][3] = 1; |
---|
[2190] | 452 | } |
---|
| 453 | |
---|
[3449] | 454 | /** |
---|
| 455 | \brief performs a smooth move. |
---|
| 456 | \param from from where |
---|
| 457 | \param to to where |
---|
| 458 | \param t the time this transformation should take |
---|
| 459 | \param res The approximation-density |
---|
| 460 | */ |
---|
[2551] | 461 | void Quaternion::quatSlerp(const Quaternion* from, const Quaternion* to, float t, Quaternion* res) |
---|
| 462 | { |
---|
| 463 | float tol[4]; |
---|
| 464 | double omega, cosom, sinom, scale0, scale1; |
---|
| 465 | DELTA = 0.2; |
---|
| 466 | |
---|
| 467 | cosom = from->v.x * to->v.x + from->v.y * to->v.y + from->v.z * to->v.z + from->w * to->w; |
---|
| 468 | |
---|
| 469 | if( cosom < 0.0 ) |
---|
| 470 | { |
---|
| 471 | cosom = -cosom; |
---|
| 472 | tol[0] = -to->v.x; |
---|
| 473 | tol[1] = -to->v.y; |
---|
| 474 | tol[2] = -to->v.z; |
---|
| 475 | tol[3] = -to->w; |
---|
| 476 | } |
---|
| 477 | else |
---|
| 478 | { |
---|
| 479 | tol[0] = to->v.x; |
---|
| 480 | tol[1] = to->v.y; |
---|
| 481 | tol[2] = to->v.z; |
---|
| 482 | tol[3] = to->w; |
---|
| 483 | } |
---|
| 484 | |
---|
| 485 | //if( (1.0 - cosom) > DELTA ) |
---|
| 486 | //{ |
---|
| 487 | omega = acos(cosom); |
---|
| 488 | sinom = sin(omega); |
---|
| 489 | scale0 = sin((1.0 - t) * omega) / sinom; |
---|
| 490 | scale1 = sin(t * omega) / sinom; |
---|
| 491 | //} |
---|
| 492 | /* |
---|
| 493 | else |
---|
| 494 | { |
---|
| 495 | scale0 = 1.0 - t; |
---|
| 496 | scale1 = t; |
---|
| 497 | } |
---|
| 498 | */ |
---|
| 499 | res->v.x = scale0 * from->v.x + scale1 * tol[0]; |
---|
| 500 | res->v.y = scale0 * from->v.y + scale1 * tol[1]; |
---|
| 501 | res->v.z = scale0 * from->v.z + scale1 * tol[2]; |
---|
| 502 | res->w = scale0 * from->w + scale1 * tol[3]; |
---|
| 503 | } |
---|
| 504 | |
---|
| 505 | |
---|
[2190] | 506 | /** |
---|
[2551] | 507 | \brief convert a rotational 4x4 glMatrix into a Quaternion |
---|
| 508 | \param m: a 4x4 matrix in glMatrix order |
---|
[2190] | 509 | */ |
---|
| 510 | Quaternion::Quaternion (float m[4][4]) |
---|
| 511 | { |
---|
[2551] | 512 | |
---|
| 513 | float tr, s, q[4]; |
---|
| 514 | int i, j, k; |
---|
| 515 | |
---|
| 516 | int nxt[3] = {1, 2, 0}; |
---|
| 517 | |
---|
| 518 | tr = m[0][0] + m[1][1] + m[2][2]; |
---|
| 519 | |
---|
| 520 | // check the diagonal |
---|
[2190] | 521 | if (tr > 0.0) |
---|
[2551] | 522 | { |
---|
| 523 | s = sqrt (tr + 1.0); |
---|
| 524 | w = s / 2.0; |
---|
| 525 | s = 0.5 / s; |
---|
| 526 | v.x = (m[1][2] - m[2][1]) * s; |
---|
| 527 | v.y = (m[2][0] - m[0][2]) * s; |
---|
| 528 | v.z = (m[0][1] - m[1][0]) * s; |
---|
[2190] | 529 | } |
---|
| 530 | else |
---|
[2551] | 531 | { |
---|
| 532 | // diagonal is negative |
---|
| 533 | i = 0; |
---|
| 534 | if (m[1][1] > m[0][0]) i = 1; |
---|
| 535 | if (m[2][2] > m[i][i]) i = 2; |
---|
| 536 | j = nxt[i]; |
---|
| 537 | k = nxt[j]; |
---|
| 538 | |
---|
| 539 | s = sqrt ((m[i][i] - (m[j][j] + m[k][k])) + 1.0); |
---|
| 540 | |
---|
| 541 | q[i] = s * 0.5; |
---|
| 542 | |
---|
| 543 | if (s != 0.0) s = 0.5 / s; |
---|
[2190] | 544 | |
---|
[2551] | 545 | q[3] = (m[j][k] - m[k][j]) * s; |
---|
| 546 | q[j] = (m[i][j] + m[j][i]) * s; |
---|
| 547 | q[k] = (m[i][k] + m[k][i]) * s; |
---|
| 548 | |
---|
| 549 | v.x = q[0]; |
---|
| 550 | v.y = q[1]; |
---|
| 551 | v.z = q[2]; |
---|
| 552 | w = q[3]; |
---|
[2190] | 553 | } |
---|
| 554 | } |
---|
| 555 | |
---|
| 556 | /** |
---|
[3541] | 557 | \brief outputs some nice formated debug information about this quaternion |
---|
| 558 | */ |
---|
| 559 | void Quaternion::debug(void) |
---|
| 560 | { |
---|
| 561 | PRINT(0)("Quaternion Debug Information\n"); |
---|
| 562 | PRINT(0)("real a=%f; imag: x=%f y=%f z=%f\n", w, v.x, v.y, v.z); |
---|
| 563 | } |
---|
| 564 | |
---|
| 565 | /** |
---|
[2043] | 566 | \brief create a rotation from a vector |
---|
| 567 | \param v: a vector |
---|
| 568 | */ |
---|
| 569 | Rotation::Rotation (const Vector& v) |
---|
| 570 | { |
---|
| 571 | Vector x = Vector( 1, 0, 0); |
---|
| 572 | Vector axis = x.cross( v); |
---|
| 573 | axis.normalize(); |
---|
[3234] | 574 | float angle = angleRad( x, v); |
---|
[2043] | 575 | float ca = cos(angle); |
---|
| 576 | float sa = sin(angle); |
---|
| 577 | m[0] = 1.0f+(1.0f-ca)*(axis.x*axis.x-1.0f); |
---|
| 578 | m[1] = -axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 579 | m[2] = axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 580 | m[3] = axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 581 | m[4] = 1.0f+(1.0f-ca)*(axis.y*axis.y-1.0f); |
---|
| 582 | m[5] = -axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 583 | m[6] = -axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 584 | m[7] = axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 585 | m[8] = 1.0f+(1.0f-ca)*(axis.z*axis.z-1.0f); |
---|
| 586 | } |
---|
| 587 | |
---|
| 588 | /** |
---|
| 589 | \brief creates a rotation from an axis and an angle (radians!) |
---|
| 590 | \param axis: the rotational axis |
---|
| 591 | \param angle: the angle in radians |
---|
| 592 | */ |
---|
| 593 | Rotation::Rotation (const Vector& axis, float angle) |
---|
| 594 | { |
---|
| 595 | float ca, sa; |
---|
| 596 | ca = cos(angle); |
---|
| 597 | sa = sin(angle); |
---|
| 598 | m[0] = 1.0f+(1.0f-ca)*(axis.x*axis.x-1.0f); |
---|
| 599 | m[1] = -axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 600 | m[2] = axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 601 | m[3] = axis.z*sa+(1.0f-ca)*axis.x*axis.y; |
---|
| 602 | m[4] = 1.0f+(1.0f-ca)*(axis.y*axis.y-1.0f); |
---|
| 603 | m[5] = -axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 604 | m[6] = -axis.y*sa+(1.0f-ca)*axis.x*axis.z; |
---|
| 605 | m[7] = axis.x*sa+(1.0f-ca)*axis.y*axis.z; |
---|
| 606 | m[8] = 1.0f+(1.0f-ca)*(axis.z*axis.z-1.0f); |
---|
| 607 | } |
---|
| 608 | |
---|
| 609 | /** |
---|
| 610 | \brief creates a rotation from euler angles (pitch/yaw/roll) |
---|
| 611 | \param pitch: rotation around z (in radians) |
---|
| 612 | \param yaw: rotation around y (in radians) |
---|
| 613 | \param roll: rotation around x (in radians) |
---|
| 614 | */ |
---|
| 615 | Rotation::Rotation ( float pitch, float yaw, float roll) |
---|
| 616 | { |
---|
| 617 | float cy, sy, cr, sr, cp, sp; |
---|
| 618 | cy = cos(yaw); |
---|
| 619 | sy = sin(yaw); |
---|
| 620 | cr = cos(roll); |
---|
| 621 | sr = sin(roll); |
---|
| 622 | cp = cos(pitch); |
---|
| 623 | sp = sin(pitch); |
---|
| 624 | m[0] = cy*cr; |
---|
| 625 | m[1] = -cy*sr; |
---|
| 626 | m[2] = sy; |
---|
| 627 | m[3] = cp*sr+sp*sy*cr; |
---|
| 628 | m[4] = cp*cr-sp*sr*sy; |
---|
| 629 | m[5] = -sp*cy; |
---|
| 630 | m[6] = sp*sr-cp*sy*cr; |
---|
| 631 | m[7] = sp*cr+cp*sy*sr; |
---|
| 632 | m[8] = cp*cy; |
---|
| 633 | } |
---|
| 634 | |
---|
| 635 | /** |
---|
| 636 | \brief creates a nullrotation (an identity rotation) |
---|
| 637 | */ |
---|
| 638 | Rotation::Rotation () |
---|
| 639 | { |
---|
| 640 | m[0] = 1.0f; |
---|
| 641 | m[1] = 0.0f; |
---|
| 642 | m[2] = 0.0f; |
---|
| 643 | m[3] = 0.0f; |
---|
| 644 | m[4] = 1.0f; |
---|
| 645 | m[5] = 0.0f; |
---|
| 646 | m[6] = 0.0f; |
---|
| 647 | m[7] = 0.0f; |
---|
| 648 | m[8] = 1.0f; |
---|
| 649 | } |
---|
| 650 | |
---|
| 651 | /** |
---|
[2190] | 652 | \brief fills the specified buffer with a 4x4 glmatrix |
---|
| 653 | \param buffer: Pointer to an array of 16 floats |
---|
| 654 | |
---|
| 655 | Use this to get the rotation in a gl-compatible format |
---|
| 656 | */ |
---|
| 657 | void Rotation::glmatrix (float* buffer) |
---|
| 658 | { |
---|
| 659 | buffer[0] = m[0]; |
---|
| 660 | buffer[1] = m[3]; |
---|
| 661 | buffer[2] = m[6]; |
---|
| 662 | buffer[3] = m[0]; |
---|
| 663 | buffer[4] = m[1]; |
---|
| 664 | buffer[5] = m[4]; |
---|
| 665 | buffer[6] = m[7]; |
---|
| 666 | buffer[7] = m[0]; |
---|
| 667 | buffer[8] = m[2]; |
---|
| 668 | buffer[9] = m[5]; |
---|
| 669 | buffer[10] = m[8]; |
---|
| 670 | buffer[11] = m[0]; |
---|
| 671 | buffer[12] = m[0]; |
---|
| 672 | buffer[13] = m[0]; |
---|
| 673 | buffer[14] = m[0]; |
---|
| 674 | buffer[15] = m[1]; |
---|
| 675 | } |
---|
| 676 | |
---|
| 677 | /** |
---|
| 678 | \brief multiplies two rotational matrices |
---|
| 679 | \param r: another Rotation |
---|
| 680 | \return the matrix product of the Rotations |
---|
| 681 | |
---|
| 682 | Use this to rotate one rotation by another |
---|
| 683 | */ |
---|
| 684 | Rotation Rotation::operator* (const Rotation& r) |
---|
| 685 | { |
---|
| 686 | Rotation p; |
---|
| 687 | |
---|
| 688 | p.m[0] = m[0]*r.m[0] + m[1]*r.m[3] + m[2]*r.m[6]; |
---|
| 689 | p.m[1] = m[0]*r.m[1] + m[1]*r.m[4] + m[2]*r.m[7]; |
---|
| 690 | p.m[2] = m[0]*r.m[2] + m[1]*r.m[5] + m[2]*r.m[8]; |
---|
| 691 | |
---|
| 692 | p.m[3] = m[3]*r.m[0] + m[4]*r.m[3] + m[5]*r.m[6]; |
---|
| 693 | p.m[4] = m[3]*r.m[1] + m[4]*r.m[4] + m[5]*r.m[7]; |
---|
| 694 | p.m[5] = m[3]*r.m[2] + m[4]*r.m[5] + m[5]*r.m[8]; |
---|
| 695 | |
---|
| 696 | p.m[6] = m[6]*r.m[0] + m[7]*r.m[3] + m[8]*r.m[6]; |
---|
| 697 | p.m[7] = m[6]*r.m[1] + m[7]*r.m[4] + m[8]*r.m[7]; |
---|
| 698 | p.m[8] = m[6]*r.m[2] + m[7]*r.m[5] + m[8]*r.m[8]; |
---|
| 699 | |
---|
| 700 | return p; |
---|
| 701 | } |
---|
| 702 | |
---|
| 703 | |
---|
| 704 | /** |
---|
[2043] | 705 | \brief rotates the vector by the given rotation |
---|
| 706 | \param v: a vector |
---|
| 707 | \param r: a rotation |
---|
| 708 | \return the rotated vector |
---|
| 709 | */ |
---|
[3228] | 710 | Vector rotateVector( const Vector& v, const Rotation& r) |
---|
[2043] | 711 | { |
---|
| 712 | Vector t; |
---|
| 713 | |
---|
| 714 | t.x = v.x * r.m[0] + v.y * r.m[1] + v.z * r.m[2]; |
---|
| 715 | t.y = v.x * r.m[3] + v.y * r.m[4] + v.z * r.m[5]; |
---|
| 716 | t.z = v.x * r.m[6] + v.y * r.m[7] + v.z * r.m[8]; |
---|
| 717 | |
---|
| 718 | return t; |
---|
| 719 | } |
---|
| 720 | |
---|
| 721 | /** |
---|
| 722 | \brief calculate the distance between two lines |
---|
| 723 | \param l: the other line |
---|
| 724 | \return the distance between the lines |
---|
| 725 | */ |
---|
| 726 | float Line::distance (const Line& l) const |
---|
| 727 | { |
---|
| 728 | float q, d; |
---|
| 729 | Vector n = a.cross(l.a); |
---|
| 730 | q = n.dot(r-l.r); |
---|
| 731 | d = n.len(); |
---|
| 732 | if( d == 0.0) return 0.0; |
---|
| 733 | return q/d; |
---|
| 734 | } |
---|
| 735 | |
---|
| 736 | /** |
---|
| 737 | \brief calculate the distance between a line and a point |
---|
| 738 | \param v: the point |
---|
| 739 | \return the distance between the Line and the point |
---|
| 740 | */ |
---|
[3228] | 741 | float Line::distancePoint (const Vector& v) const |
---|
[2043] | 742 | { |
---|
| 743 | Vector d = v-r; |
---|
| 744 | Vector u = a * d.dot( a); |
---|
| 745 | return (d - u).len(); |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | /** |
---|
| 749 | \brief calculate the two points of minimal distance of two lines |
---|
| 750 | \param l: the other line |
---|
| 751 | \return a Vector[2] (!has to be deleted after use!) containing the two points of minimal distance |
---|
| 752 | */ |
---|
| 753 | Vector* Line::footpoints (const Line& l) const |
---|
| 754 | { |
---|
| 755 | Vector* fp = new Vector[2]; |
---|
| 756 | Plane p = Plane (r + a.cross(l.a), r, r + a); |
---|
[3234] | 757 | fp[1] = p.intersectLine (l); |
---|
[2043] | 758 | p = Plane (fp[1], l.a); |
---|
[3234] | 759 | fp[0] = p.intersectLine (*this); |
---|
[2043] | 760 | return fp; |
---|
| 761 | } |
---|
| 762 | |
---|
| 763 | /** |
---|
| 764 | \brief calculate the length of a line |
---|
| 765 | \return the lenght of the line |
---|
| 766 | */ |
---|
| 767 | float Line::len() const |
---|
| 768 | { |
---|
| 769 | return a.len(); |
---|
| 770 | } |
---|
| 771 | |
---|
| 772 | /** |
---|
| 773 | \brief rotate the line by given rotation |
---|
| 774 | \param rot: a rotation |
---|
| 775 | */ |
---|
| 776 | void Line::rotate (const Rotation& rot) |
---|
| 777 | { |
---|
| 778 | Vector t = a + r; |
---|
[3234] | 779 | t = rotateVector( t, rot); |
---|
| 780 | r = rotateVector( r, rot), |
---|
[2043] | 781 | a = t - r; |
---|
| 782 | } |
---|
| 783 | |
---|
| 784 | /** |
---|
| 785 | \brief create a plane from three points |
---|
| 786 | \param a: first point |
---|
| 787 | \param b: second point |
---|
| 788 | \param c: third point |
---|
| 789 | */ |
---|
| 790 | Plane::Plane (Vector a, Vector b, Vector c) |
---|
| 791 | { |
---|
| 792 | n = (a-b).cross(c-b); |
---|
| 793 | k = -(n.x*b.x+n.y*b.y+n.z*b.z); |
---|
| 794 | } |
---|
| 795 | |
---|
| 796 | /** |
---|
| 797 | \brief create a plane from anchor point and normal |
---|
[3449] | 798 | \param norm: normal vector |
---|
[2043] | 799 | \param p: anchor point |
---|
| 800 | */ |
---|
| 801 | Plane::Plane (Vector norm, Vector p) |
---|
| 802 | { |
---|
| 803 | n = norm; |
---|
| 804 | k = -(n.x*p.x+n.y*p.y+n.z*p.z); |
---|
| 805 | } |
---|
| 806 | |
---|
| 807 | /** |
---|
| 808 | \brief returns the intersection point between the plane and a line |
---|
| 809 | \param l: a line |
---|
| 810 | */ |
---|
[3228] | 811 | Vector Plane::intersectLine (const Line& l) const |
---|
[2043] | 812 | { |
---|
| 813 | if (n.x*l.a.x+n.y*l.a.y+n.z*l.a.z == 0.0) return Vector(0,0,0); |
---|
| 814 | 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); |
---|
| 815 | return l.r + (l.a * t); |
---|
| 816 | } |
---|
| 817 | |
---|
| 818 | /** |
---|
| 819 | \brief returns the distance between the plane and a point |
---|
| 820 | \param p: a Point |
---|
| 821 | \return the distance between the plane and the point (can be negative) |
---|
| 822 | */ |
---|
[3228] | 823 | float Plane::distancePoint (const Vector& p) const |
---|
[2043] | 824 | { |
---|
| 825 | float l = n.len(); |
---|
| 826 | if( l == 0.0) return 0.0; |
---|
| 827 | return (n.dot(p) + k) / n.len(); |
---|
| 828 | } |
---|
| 829 | |
---|
| 830 | /** |
---|
| 831 | \brief returns the side a point is located relative to a Plane |
---|
| 832 | \param p: a Point |
---|
| 833 | \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 |
---|
| 834 | */ |
---|
[3228] | 835 | float Plane::locatePoint (const Vector& p) const |
---|
[2043] | 836 | { |
---|
| 837 | return (n.dot(p) + k); |
---|
| 838 | } |
---|
[3000] | 839 | |
---|