1 module raylib.raymath; 2 3 import raylib; 4 /********************************************************************************************** 5 * 6 * raymath v1.5 - Math functions to work with Vector2, Vector3, Matrix and Quaternions 7 * 8 * CONFIGURATION: 9 * 10 * #define RAYMATH_IMPLEMENTATION 11 * Generates the implementation of the library into the included file. 12 * If not defined, the library is in header only mode and can be included in other headers 13 * or source files without problems. But only ONE file should hold the implementation. 14 * 15 * #define RAYMATH_STATIC_INLINE 16 * Define static inline functions code, so #include header suffices for use. 17 * This may use up lots of memory. 18 * 19 * CONVENTIONS: 20 * 21 * - Functions are always self-contained, no function use another raymath function inside, 22 * required code is directly re-implemented inside 23 * - Functions input parameters are always received by value (2 unavoidable exceptions) 24 * - Functions use always a "result" variable for return 25 * - Functions are always defined inline 26 * - Angles are always in radians (DEG2RAD/RAD2DEG macros provided for convenience) 27 * 28 * 29 * LICENSE: zlib/libpng 30 * 31 * Copyright (c) 2015-2022 Ramon Santamaria (@raysan5) 32 * 33 * This software is provided "as-is", without any express or implied warranty. In no event 34 * will the authors be held liable for any damages arising from the use of this software. 35 * 36 * Permission is granted to anyone to use this software for any purpose, including commercial 37 * applications, and to alter it and redistribute it freely, subject to the following restrictions: 38 * 39 * 1. The origin of this software must not be misrepresented; you must not claim that you 40 * wrote the original software. If you use this software in a product, an acknowledgment 41 * in the product documentation would be appreciated but is not required. 42 * 43 * 2. Altered source versions must be plainly marked as such, and must not be misrepresented 44 * as being the original software. 45 * 46 * 3. This notice may not be removed or altered from any source distribution. 47 * 48 **********************************************************************************************/ 49 50 extern (C) @nogc nothrow: 51 52 // Function specifiers definition 53 54 // We are building raylib as a Win32 shared library (.dll). 55 56 // We are using raylib as a Win32 shared library (.dll) 57 58 // Provide external definition 59 60 // Functions may be inlined, no external out-of-line definition 61 62 // plain inline not supported by tinycc (See issue #435) // Functions may be inlined or external definition used 63 64 //---------------------------------------------------------------------------------- 65 // Defines and Macros 66 //---------------------------------------------------------------------------------- 67 68 enum PI = 3.14159265358979323846f; 69 70 enum EPSILON = 0.000001f; 71 72 enum DEG2RAD = PI / 180.0f; 73 74 enum RAD2DEG = 180.0f / PI; 75 76 // Get float vector for Matrix 77 78 extern (D) auto MatrixToFloat(T)(auto ref T mat) 79 { 80 return MatrixToFloatV(mat).v; 81 } 82 83 // Get float vector for Vector3 84 85 extern (D) auto Vector3ToFloat(T)(auto ref T vec) 86 { 87 return Vector3ToFloatV(vec).v; 88 } 89 90 //---------------------------------------------------------------------------------- 91 // Types and Structures Definition 92 //---------------------------------------------------------------------------------- 93 94 // Vector2 type 95 96 // Vector3 type 97 98 // Vector4 type 99 100 // Quaternion type 101 102 // Matrix type (OpenGL style 4x4 - right handed, column major) 103 104 // Matrix first row (4 components) 105 // Matrix second row (4 components) 106 // Matrix third row (4 components) 107 // Matrix fourth row (4 components) 108 109 // NOTE: Helper types to be used instead of array return types for *ToFloat functions 110 struct float3 111 { 112 float[3] v; 113 } 114 115 struct float16 116 { 117 float[16] v; 118 } 119 120 // Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), floor(), fminf(), fmaxf(), fabs() 121 122 //---------------------------------------------------------------------------------- 123 // Module Functions Definition - Utils math 124 //---------------------------------------------------------------------------------- 125 126 // Clamp float value 127 float Clamp(float value, float min, float max); 128 129 // Calculate linear interpolation between two floats 130 float Lerp(float start, float end, float amount); 131 132 // Normalize input value within input range 133 float Normalize(float value, float start, float end); 134 135 // Remap input value within input range to output range 136 float Remap( 137 float value, 138 float inputStart, 139 float inputEnd, 140 float outputStart, 141 float outputEnd); 142 143 // Wrap input value from min to max 144 float Wrap(float value, float min, float max); 145 146 // Check whether two given floats are almost equal 147 int FloatEquals(float x, float y); 148 149 //---------------------------------------------------------------------------------- 150 // Module Functions Definition - Vector2 math 151 //---------------------------------------------------------------------------------- 152 153 // Vector with components value 0.0f 154 Vector2 Vector2Zero(); 155 156 // Vector with components value 1.0f 157 Vector2 Vector2One(); 158 159 // Add two vectors (v1 + v2) 160 Vector2 Vector2Add(Vector2 v1, Vector2 v2); 161 162 // Add vector and float value 163 Vector2 Vector2AddValue(Vector2 v, float add); 164 165 // Subtract two vectors (v1 - v2) 166 Vector2 Vector2Subtract(Vector2 v1, Vector2 v2); 167 168 // Subtract vector by float value 169 Vector2 Vector2SubtractValue(Vector2 v, float sub); 170 171 // Calculate vector length 172 float Vector2Length(Vector2 v); 173 174 // Calculate vector square length 175 float Vector2LengthSqr(Vector2 v); 176 177 // Calculate two vectors dot product 178 float Vector2DotProduct(Vector2 v1, Vector2 v2); 179 180 // Calculate distance between two vectors 181 float Vector2Distance(Vector2 v1, Vector2 v2); 182 183 // Calculate square distance between two vectors 184 float Vector2DistanceSqr(Vector2 v1, Vector2 v2); 185 186 // Calculate angle from two vectors 187 float Vector2Angle(Vector2 v1, Vector2 v2); 188 189 // Scale vector (multiply by value) 190 Vector2 Vector2Scale(Vector2 v, float scale); 191 192 // Multiply vector by vector 193 Vector2 Vector2Multiply(Vector2 v1, Vector2 v2); 194 195 // Negate vector 196 Vector2 Vector2Negate(Vector2 v); 197 198 // Divide vector by vector 199 Vector2 Vector2Divide(Vector2 v1, Vector2 v2); 200 201 // Normalize provided vector 202 Vector2 Vector2Normalize(Vector2 v); 203 204 // Transforms a Vector2 by a given Matrix 205 Vector2 Vector2Transform(Vector2 v, Matrix mat); 206 207 // Calculate linear interpolation between two vectors 208 Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount); 209 210 // Calculate reflected vector to normal 211 212 // Dot product 213 Vector2 Vector2Reflect(Vector2 v, Vector2 normal); 214 215 // Rotate vector by angle 216 Vector2 Vector2Rotate(Vector2 v, float angle); 217 218 // Move Vector towards target 219 Vector2 Vector2MoveTowards(Vector2 v, Vector2 target, float maxDistance); 220 221 // Invert the given vector 222 Vector2 Vector2Invert(Vector2 v); 223 224 // Clamp the components of the vector between 225 // min and max values specified by the given vectors 226 Vector2 Vector2Clamp(Vector2 v, Vector2 min, Vector2 max); 227 228 // Clamp the magnitude of the vector between two min and max values 229 Vector2 Vector2ClampValue(Vector2 v, float min, float max); 230 231 // Check whether two given vectors are almost equal 232 int Vector2Equals(Vector2 p, Vector2 q); 233 234 //---------------------------------------------------------------------------------- 235 // Module Functions Definition - Vector3 math 236 //---------------------------------------------------------------------------------- 237 238 // Vector with components value 0.0f 239 Vector3 Vector3Zero(); 240 241 // Vector with components value 1.0f 242 Vector3 Vector3One(); 243 244 // Add two vectors 245 Vector3 Vector3Add(Vector3 v1, Vector3 v2); 246 247 // Add vector and float value 248 Vector3 Vector3AddValue(Vector3 v, float add); 249 250 // Subtract two vectors 251 Vector3 Vector3Subtract(Vector3 v1, Vector3 v2); 252 253 // Subtract vector by float value 254 Vector3 Vector3SubtractValue(Vector3 v, float sub); 255 256 // Multiply vector by scalar 257 Vector3 Vector3Scale(Vector3 v, float scalar); 258 259 // Multiply vector by vector 260 Vector3 Vector3Multiply(Vector3 v1, Vector3 v2); 261 262 // Calculate two vectors cross product 263 Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2); 264 265 // Calculate one vector perpendicular vector 266 267 // Cross product between vectors 268 Vector3 Vector3Perpendicular(Vector3 v); 269 270 // Calculate vector length 271 float Vector3Length(const Vector3 v); 272 273 // Calculate vector square length 274 float Vector3LengthSqr(const Vector3 v); 275 276 // Calculate two vectors dot product 277 float Vector3DotProduct(Vector3 v1, Vector3 v2); 278 279 // Calculate distance between two vectors 280 float Vector3Distance(Vector3 v1, Vector3 v2); 281 282 // Calculate square distance between two vectors 283 float Vector3DistanceSqr(Vector3 v1, Vector3 v2); 284 285 // Calculate angle between two vectors 286 float Vector3Angle(Vector3 v1, Vector3 v2); 287 288 // Negate provided vector (invert direction) 289 Vector3 Vector3Negate(Vector3 v); 290 291 // Divide vector by vector 292 Vector3 Vector3Divide(Vector3 v1, Vector3 v2); 293 294 // Normalize provided vector 295 Vector3 Vector3Normalize(Vector3 v); 296 297 // Orthonormalize provided vectors 298 // Makes vectors normalized and orthogonal to each other 299 // Gram-Schmidt function implementation 300 301 // Vector3Normalize(*v1); 302 303 // Vector3CrossProduct(*v1, *v2) 304 305 // Vector3Normalize(vn1); 306 307 // Vector3CrossProduct(vn1, *v1) 308 void Vector3OrthoNormalize(Vector3* v1, Vector3* v2); 309 310 // Transforms a Vector3 by a given Matrix 311 Vector3 Vector3Transform(Vector3 v, Matrix mat); 312 313 // Transform a vector by quaternion rotation 314 Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q); 315 316 // Rotates a vector around an axis 317 318 // Using Euler-Rodrigues Formula 319 // Ref.: https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Rodrigues_formula 320 321 // Vector3Normalize(axis); 322 323 // Vector3CrossProduct(w, v) 324 325 // Vector3CrossProduct(w, wv) 326 327 // Vector3Scale(wv, 2 * a) 328 329 // Vector3Scale(wwv, 2) 330 Vector3 Vector3RotateByAxisAngle(Vector3 v, Vector3 axis, float angle); 331 332 // Calculate linear interpolation between two vectors 333 Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount); 334 335 // Calculate reflected vector to normal 336 337 // I is the original vector 338 // N is the normal of the incident plane 339 // R = I - (2*N*(DotProduct[I, N])) 340 Vector3 Vector3Reflect(Vector3 v, Vector3 normal); 341 342 // Get min value for each pair of components 343 Vector3 Vector3Min(Vector3 v1, Vector3 v2); 344 345 // Get max value for each pair of components 346 Vector3 Vector3Max(Vector3 v1, Vector3 v2); 347 348 // Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c) 349 // NOTE: Assumes P is on the plane of the triangle 350 351 // Vector3Subtract(b, a) 352 // Vector3Subtract(c, a) 353 // Vector3Subtract(p, a) 354 // Vector3DotProduct(v0, v0) 355 // Vector3DotProduct(v0, v1) 356 // Vector3DotProduct(v1, v1) 357 // Vector3DotProduct(v2, v0) 358 // Vector3DotProduct(v2, v1) 359 Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c); 360 361 // Projects a Vector3 from screen space into object space 362 // NOTE: We are avoiding calling other raymath functions despite available 363 364 // Calculate unproject matrix (multiply view patrix by projection matrix) and invert it 365 // MatrixMultiply(view, projection); 366 367 // Calculate inverted matrix -> MatrixInvert(matViewProj); 368 // Cache the matrix values (speed optimization) 369 370 // Calculate the invert determinant (inlined to avoid double-caching) 371 372 // Create quaternion from source point 373 374 // Multiply quat point by unproject matrix 375 // QuaternionTransform(quat, matViewProjInv) 376 377 // Normalized world points in vectors 378 Vector3 Vector3Unproject(Vector3 source, Matrix projection, Matrix view); 379 380 // Get Vector3 as float array 381 float3 Vector3ToFloatV(Vector3 v); 382 383 // Invert the given vector 384 Vector3 Vector3Invert(Vector3 v); 385 386 // Clamp the components of the vector between 387 // min and max values specified by the given vectors 388 Vector3 Vector3Clamp(Vector3 v, Vector3 min, Vector3 max); 389 390 // Clamp the magnitude of the vector between two values 391 Vector3 Vector3ClampValue(Vector3 v, float min, float max); 392 393 // Check whether two given vectors are almost equal 394 int Vector3Equals(Vector3 p, Vector3 q); 395 396 // Compute the direction of a refracted ray where v specifies the 397 // normalized direction of the incoming ray, n specifies the 398 // normalized normal vector of the interface of two optical media, 399 // and r specifies the ratio of the refractive index of the medium 400 // from where the ray comes to the refractive index of the medium 401 // on the other side of the surface 402 Vector3 Vector3Refract(Vector3 v, Vector3 n, float r); 403 404 //---------------------------------------------------------------------------------- 405 // Module Functions Definition - Matrix math 406 //---------------------------------------------------------------------------------- 407 408 // Compute matrix determinant 409 410 // Cache the matrix values (speed optimization) 411 float MatrixDeterminant(Matrix mat); 412 413 // Get the trace of the matrix (sum of the values along the diagonal) 414 float MatrixTrace(Matrix mat); 415 416 // Transposes provided matrix 417 Matrix MatrixTranspose(Matrix mat); 418 419 // Invert provided matrix 420 421 // Cache the matrix values (speed optimization) 422 423 // Calculate the invert determinant (inlined to avoid double-caching) 424 Matrix MatrixInvert(Matrix mat); 425 426 // Get identity matrix 427 Matrix MatrixIdentity(); 428 429 // Add two matrices 430 Matrix MatrixAdd(Matrix left, Matrix right); 431 432 // Subtract two matrices (left - right) 433 Matrix MatrixSubtract(Matrix left, Matrix right); 434 435 // Get two matrix multiplication 436 // NOTE: When multiplying matrices... the order matters! 437 Matrix MatrixMultiply(Matrix left, Matrix right); 438 439 // Get translation matrix 440 Matrix MatrixTranslate(float x, float y, float z); 441 442 // Create rotation matrix from axis and angle 443 // NOTE: Angle should be provided in radians 444 Matrix MatrixRotate(Vector3 axis, float angle); 445 446 // Get x-rotation matrix 447 // NOTE: Angle must be provided in radians 448 449 // MatrixIdentity() 450 Matrix MatrixRotateX(float angle); 451 452 // Get y-rotation matrix 453 // NOTE: Angle must be provided in radians 454 455 // MatrixIdentity() 456 Matrix MatrixRotateY(float angle); 457 458 // Get z-rotation matrix 459 // NOTE: Angle must be provided in radians 460 461 // MatrixIdentity() 462 Matrix MatrixRotateZ(float angle); 463 464 // Get xyz-rotation matrix 465 // NOTE: Angle must be provided in radians 466 467 // MatrixIdentity() 468 Matrix MatrixRotateXYZ(Vector3 angle); 469 470 // Get zyx-rotation matrix 471 // NOTE: Angle must be provided in radians 472 Matrix MatrixRotateZYX(Vector3 angle); 473 474 // Get scaling matrix 475 Matrix MatrixScale(float x, float y, float z); 476 477 // Get perspective projection matrix 478 Matrix MatrixFrustum( 479 double left, 480 double right, 481 double bottom, 482 double top, 483 double near, 484 double far); 485 486 // Get perspective projection matrix 487 // NOTE: Fovy angle must be provided in radians 488 489 // MatrixFrustum(-right, right, -top, top, near, far); 490 Matrix MatrixPerspective(double fovy, double aspect, double near, double far); 491 492 // Get orthographic projection matrix 493 Matrix MatrixOrtho( 494 double left, 495 double right, 496 double bottom, 497 double top, 498 double near, 499 double far); 500 501 // Get camera look-at matrix (view matrix) 502 503 // Vector3Subtract(eye, target) 504 505 // Vector3Normalize(vz) 506 507 // Vector3CrossProduct(up, vz) 508 509 // Vector3Normalize(x) 510 511 // Vector3CrossProduct(vz, vx) 512 513 // Vector3DotProduct(vx, eye) 514 // Vector3DotProduct(vy, eye) 515 // Vector3DotProduct(vz, eye) 516 Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up); 517 518 // Get float array of matrix data 519 float16 MatrixToFloatV(Matrix mat); 520 521 //---------------------------------------------------------------------------------- 522 // Module Functions Definition - Quaternion math 523 //---------------------------------------------------------------------------------- 524 525 // Add two quaternions 526 Quaternion QuaternionAdd(Quaternion q1, Quaternion q2); 527 528 // Add quaternion and float value 529 Quaternion QuaternionAddValue(Quaternion q, float add); 530 531 // Subtract two quaternions 532 Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2); 533 534 // Subtract quaternion and float value 535 Quaternion QuaternionSubtractValue(Quaternion q, float sub); 536 537 // Get identity quaternion 538 Quaternion QuaternionIdentity(); 539 540 // Computes the length of a quaternion 541 float QuaternionLength(Quaternion q); 542 543 // Normalize provided quaternion 544 Quaternion QuaternionNormalize(Quaternion q); 545 546 // Invert provided quaternion 547 Quaternion QuaternionInvert(Quaternion q); 548 549 // Calculate two quaternion multiplication 550 Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2); 551 552 // Scale quaternion by float value 553 Quaternion QuaternionScale(Quaternion q, float mul); 554 555 // Divide two quaternions 556 Quaternion QuaternionDivide(Quaternion q1, Quaternion q2); 557 558 // Calculate linear interpolation between two quaternions 559 Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount); 560 561 // Calculate slerp-optimized interpolation between two quaternions 562 563 // QuaternionLerp(q1, q2, amount) 564 565 // QuaternionNormalize(q); 566 Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount); 567 568 // Calculates spherical linear interpolation between two quaternions 569 Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount); 570 571 // Calculate quaternion based on the rotation from one vector to another 572 573 // Vector3DotProduct(from, to) 574 // Vector3CrossProduct(from, to) 575 576 // QuaternionNormalize(q); 577 // NOTE: Normalize to essentially nlerp the original and identity to 0.5 578 Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to); 579 580 // Get a quaternion for a given rotation matrix 581 Quaternion QuaternionFromMatrix(Matrix mat); 582 583 // Get a matrix for a given quaternion 584 585 // MatrixIdentity() 586 Matrix QuaternionToMatrix(Quaternion q); 587 588 // Get rotation quaternion for an angle and axis 589 // NOTE: Angle must be provided in radians 590 591 // Vector3Normalize(axis) 592 593 // QuaternionNormalize(q); 594 Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle); 595 596 // Get the rotation angle and axis for a given quaternion 597 598 // QuaternionNormalize(q); 599 600 // This occurs when the angle is zero. 601 // Not a problem: just set an arbitrary normalized axis. 602 void QuaternionToAxisAngle(Quaternion q, Vector3* outAxis, float* outAngle); 603 604 // Get the quaternion equivalent to Euler angles 605 // NOTE: Rotation order is ZYX 606 Quaternion QuaternionFromEuler(float pitch, float yaw, float roll); 607 608 // Get the Euler angles equivalent to quaternion (roll, pitch, yaw) 609 // NOTE: Angles are returned in a Vector3 struct in radians 610 611 // Roll (x-axis rotation) 612 613 // Pitch (y-axis rotation) 614 615 // Yaw (z-axis rotation) 616 Vector3 QuaternionToEuler(Quaternion q); 617 618 // Transform a quaternion given a transformation matrix 619 Quaternion QuaternionTransform(Quaternion q, Matrix mat); 620 621 // Check whether two given quaternions are almost equal 622 int QuaternionEquals(Quaternion p, Quaternion q); 623 624 // RAYMATH_H