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IllidanS4

i_quat.inc

IllidanS4
May 30th, 2016
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  1. /*
  2. The MIT License (MIT)
  3. Copyright (c) 2016-2017 IllidanS4
  4. Permission is hereby granted, free of charge, to any person obtaining a copy
  5. of this software and associated documentation files (the "Software"), to deal
  6. in the Software without restriction, including without limitation the rights
  7. to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  8. copies of the Software, and to permit persons to whom the Software is
  9. furnished to do so, subject to the following conditions:
  10. The above copyright notice and this permission notice shall be included in all
  11. copies or substantial portions of the Software.
  12. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  13. IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  14. FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  15. AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  16. LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  17. OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  18. SOFTWARE.
  19. */
  20. //Documentation: http://forum.sa-mp.com/showthread.php?t=608341
  21. //Version 1.4
  22. /*
  23. native GetVehicleRotationQuatFixed(vehicleid, &Float:w, &Float:x, &Float:y, &Float:z);
  24. native GetVehicleRotation(vehicleid, &Float:x, &Float:y, &Float:z);
  25. native VectorRelToAbsQuat(Float:q[4], Float:v1[3], Float:v2[3]);
  26. native RotationRelToAbsQuat(Float:q[4], Float:r1[3], Float:r2[3]);
  27. native QuaternionRelToAbsQuat(Float:q[4], Float:q1[4], Float:q2[4]);
  28. native VectorRelToAbs(Float:r[3], Float:v1[3], Float:v2[3]);
  29. native RotationRelToAbs(Float:r[3], Float:r1[3], Float:r2[3]);
  30. native QuaternionRelToAbs(Float:r[3], Float:q1[4], Float:q2[4]);
  31. native VectorAbsToRelQuat(Float:q[4], Float:v1[3], Float:v2[3]);
  32. native RotationAbsToRelQuat(Float:q[4], Float:r1[3], Float:r2[3]);
  33. native QuaternionAbsToRelQuat(Float:q[4], Float:q1[4], Float:q2[4]);
  34. native VectorAbsToRel(Float:r[3], Float:v1[3], Float:v2[3]);
  35. native RotationAbsToRel(Float:r[3], Float:r1[3], Float:r2[3]);
  36. native QuaternionAbsToRel(Float:r[3], Float:q1[4], Float:q2[4]);
  37. native IsValidQuaternion(Float:q[4])
  38. native GetQuaternionAngles(Float:w, Float:x, Float:y, Float:z, &Float:xa, &Float:ya, &Float:za)
  39. native GetRotationQuaternion(Float:x, Float:y, Float:z, &Float:qw, &Float:qx, &Float:qy, &Float:qz);
  40. native GetQuaternionVector(Float:qw, Float:qx, Float:qy, Float:qz, &Float:x, &Float:y, &Float:z);
  41. native GetQuaternionAngle(Float:w, &Float:a);
  42. native RotateVectorQuat(Float:v1[3], Float:q[4], Float:v2[3]);
  43. native GetQuatConjugate(Float:q1[4], Float:q2[4]);
  44. native GetQuatInverse(Float:q1[4], Float:q2[4]);
  45. native GetQuatProduct(Float:q1[4], Float:q2[4], Float:q3[4]);
  46. */
  47.  
  48. //Array expansion
  49. #define EXP_A1(%0) %0[0]
  50. #define EXP_A2(%0) EXP_A1(%0),%0[1]
  51. #define EXP_A3(%0) EXP_A2(%0),%0[2]
  52. #define EXP_A4(%0) EXP_A3(%0),%0[3]
  53.  
  54. //Array copy
  55. #define SET_A1(%0,%1) %0[0]=%1[0]
  56. #define SET_A2(%0,%1) SET_A1(%0,%1),%0[1]=%1[1]
  57. #define SET_A3(%0,%1) SET_A2(%0,%1),%0[2]=%1[2]
  58. #define SET_A4(%0,%1) SET_A3(%0,%1),%0[3]=%1[3]
  59.  
  60. //Array operator assignment
  61. #define AOP_A1%2(%0,%1) %0[0]%2=%1[0]
  62. #define AOP_A2%2(%0,%1) AOP_A1%2(%0,%1),%0[1]%2=%1[1]
  63. #define AOP_A3%2(%0,%1) AOP_A2%2(%0,%1),%0[2]%2=%1[2]
  64. #define AOP_A4%2(%0,%1) AOP_A3%2(%0,%1),%0[3]%2=%1[3]
  65.  
  66. //Scalar operator assignment
  67. #define SOP_A1%2(%0,%1) %0[0]%2=%1
  68. #define SOP_A2%2(%0,%1) SOP_A1%2(%0,%1),%0[1]%2=%1
  69. #define SOP_A3%2(%0,%1) SOP_A2%2(%0,%1),%0[2]%2=%1
  70. #define SOP_A4%2(%0,%1) SOP_A3%2(%0,%1),%0[3]%2=%1
  71.  
  72. //Addition
  73. #define ADD_A1(%0,%1) AOP_A1+(%0,%1)
  74. #define ADD_A2(%0,%1) AOP_A2+(%0,%1)
  75. #define ADD_A3(%0,%1) AOP_A3+(%0,%1)
  76. #define ADD_A4(%0,%1) AOP_A4+(%0,%1)
  77.  
  78. //Subtraction
  79. #define SUB_A1(%0,%1) AOP_A1-(%0,%1)
  80. #define SUB_A2(%0,%1) AOP_A2-(%0,%1)
  81. #define SUB_A3(%0,%1) AOP_A3-(%0,%1)
  82. #define SUB_A4(%0,%1) AOP_A4-(%0,%1)
  83.  
  84. //Multiplication
  85. #define MUL_A1(%0,%1) SOP_A1*(%0,%1)
  86. #define MUL_A2(%0,%1) SOP_A2*(%0,%1)
  87. #define MUL_A3(%0,%1) SOP_A3*(%0,%1)
  88. #define MUL_A4(%0,%1) SOP_A4*(%0,%1)
  89.  
  90. //Division
  91. #define DIV_A1(%0,%1) SOP_A1/(%0,%1)
  92. #define DIV_A2(%0,%1) SOP_A2/(%0,%1)
  93. #define DIV_A3(%0,%1) SOP_A3/(%0,%1)
  94. #define DIV_A4(%0,%1) SOP_A4/(%0,%1)
  95.  
  96. #include <a_samp>
  97.  
  98. #if defined GetVehicleMatrix //has to be supplied by YSF or other plugin
  99. static stock near_zero(Float:val)
  100. {
  101.     return Float:(_:val & 0x7FFFFFFF) <= Float:0x1F800000;
  102. }
  103.  
  104. stock GetVehicleRotationQuatFixed(vehicleid, &Float:w, &Float:x, &Float:y, &Float:z)
  105. {
  106.     new Float:matrix[3][3];
  107.     GetVehicleMatrix(vehicleid, matrix[0][0], matrix[0][1], matrix[0][2], matrix[1][0], matrix[1][1], matrix[1][2], matrix[2][0], matrix[2][1], matrix[2][2]);
  108.     if(near_zero(matrix[2][0]) && near_zero(matrix[2][1]) && near_zero(matrix[2][2]))
  109.     {
  110.         matrix[2][0] = matrix[0][1]*matrix[1][2]-matrix[0][2]*matrix[1][1];
  111.         matrix[2][1] = matrix[0][2]*matrix[1][0]-matrix[0][0]*matrix[1][2];
  112.         matrix[2][2] = matrix[0][0]*matrix[1][1]-matrix[0][1]*matrix[1][0];
  113.     }
  114.     w = floatsqroot(1 + matrix[0][0] + matrix[1][1] + matrix[2][2])/2;
  115.     x = (matrix[2][1] - matrix[1][2])/(4*w);
  116.     y = (matrix[0][2] - matrix[2][0])/(4*w);
  117.     z = (matrix[1][0] - matrix[0][1])/(4*w);
  118. }
  119. #else
  120. #define GetVehicleRotationQuatFixed GetVehicleRotationQuat
  121. #endif
  122.  
  123. //Returns a vehicle's rotation in Euler angles
  124. stock GetVehicleRotation(vehicleid, &Float:x, &Float:y, &Float:z)
  125. {
  126.     new Float:qw, Float:qx, Float:qy, Float:qz;
  127.     GetVehicleRotationQuatFixed(vehicleid, qw, qx, qy, qz);
  128.     GetQuaternionAngles(qw, qx, qy, qz, x, y, z);
  129. }
  130.  
  131. //Converts a vector in coordinates relative to a body with rotation specified by a quaternion to a vector in absolute coordinates
  132. stock VectorRelToAbsQuat(Float:q[4], Float:v1[3], Float:v2[3])
  133. {
  134.     new Float:q2[4];
  135.     GetQuatConjugate(q, q2);
  136.     RotateVectorQuat(v1, q2, v2);
  137. }
  138.  
  139. //Converts an Euler rotation relative to a body with rotation specified by a quaternion to an absolute rotation
  140. stock RotationRelToAbsQuat(Float:q[4], Float:r1[3], Float:r2[3])
  141. {
  142.     new Float:rq[4];
  143.     GetRotationQuaternion(r1[0], r1[1], r1[2], rq[0], rq[1], rq[2], rq[3]);
  144.     QuaternionRelToAbsQuat(q, rq, rq);
  145.     GetQuaternionAngles(rq[0], rq[1], rq[2], rq[3], r2[0], r2[1], r2[2]);
  146. }
  147.  
  148. //Converts a quaternion rotation relative to a body with rotation specified by a quaternion to an absolute rotation
  149. stock QuaternionRelToAbsQuat(Float:q[4], Float:q1[4], Float:q2[4])
  150. {
  151.     GetQuatProduct(q1, q, q2);
  152. }
  153.  
  154. //Converts a vector in coordinates relative to a body with rotation specified by Euler angles to a vector in absolute coordinates
  155. stock VectorRelToAbs(Float:r[3], Float:v1[3], Float:v2[3])
  156. {
  157.     new Float:q[4];
  158.     GetRotationQuaternion(r[0], r[1], r[2], q[0], q[1], q[2], q[3]);
  159.     VectorRelToAbsQuat(q, v1, v2);
  160. }
  161.  
  162. //Converts an Euler rotation relative to a body with rotation specified by Euler angles to an absolute rotation
  163. stock RotationRelToAbs(Float:r[3], Float:r1[3], Float:r2[3])
  164. {
  165.     new Float:q[4];
  166.     GetRotationQuaternion(r[0], r[1], r[2], q[0], q[1], q[2], q[3]);
  167.     RotationRelToAbsQuat(q, r1, r2);
  168. }
  169.  
  170. //Converts a quaternion rotation relative to a body with rotation specified by Euler angles to an absolute rotation
  171. stock QuaternionRelToAbs(Float:r[3], Float:q1[4], Float:q2[4])
  172. {
  173.     new Float:q[4];
  174.     GetRotationQuaternion(r[0], r[1], r[2], q[0], q[1], q[2], q[3]);
  175.     QuaternionRelToAbsQuat(q, q1, q2);
  176. }
  177.  
  178. //Converts a vector in absolute coordinates to a vector in coordinates relative to a body with rotation specified by a quaternion
  179. stock VectorAbsToRelQuat(Float:q[4], Float:v1[3], Float:v2[3])
  180. {
  181.     RotateVectorQuat(v1, q, v2);
  182. }
  183.  
  184. //Converts an Euler rotation to a rotation relative to a body with rotation specified by a quaternion
  185. stock RotationAbsToRelQuat(Float:q[4], Float:r1[3], Float:r2[3])
  186. {
  187.     new Float:rq[4];
  188.     GetRotationQuaternion(r1[0], r1[1], r1[2], rq[0], rq[1], rq[2], rq[3]);
  189.     QuaternionAbsToRelQuat(q, rq, rq);
  190.     GetQuaternionAngles(rq[0], rq[1], rq[2], rq[3], r2[0], r2[1], r2[2]);
  191. }
  192.  
  193. //Converts an absolute quaternion rotation to a rotation relative to a body with rotation specified by Euler angles
  194. stock QuaternionAbsToRelQuat(Float:q[4], Float:q1[4], Float:q2[4])
  195. {
  196.     new Float:qi[4];
  197.     GetQuatConjugate(q, qi);
  198.     GetQuatProduct(q1, qi, q2);
  199. }
  200.  
  201. //Converts a vector in absolute coordinates to a vector in coordinates relative to a body with rotation specified by Euler angles
  202. stock VectorAbsToRel(Float:r[3], Float:v1[3], Float:v2[3])
  203. {
  204.     new Float:q[4];
  205.     GetRotationQuaternion(r[0], r[1], r[2], q[0], q[1], q[2], q[3]);
  206.     VectorAbsToRelQuat(q, v1, v2);
  207. }
  208.  
  209. //Converts an Euler rotation to a rotation relative to a body with rotation specified by Euler angles
  210. stock RotationAbsToRel(Float:r[3], Float:r1[3], Float:r2[3])
  211. {
  212.     new Float:q[4];
  213.     GetRotationQuaternion(r[0], r[1], r[2], q[0], q[1], q[2], q[3]);
  214.     RotationAbsToRelQuat(q, r1, r2);
  215. }
  216.  
  217. //Converts an absolute quaternion rotation to a rotation relative to a body with rotation specified by Euler angles
  218. stock QuaternionAbsToRel(Float:r[3], Float:q1[4], Float:q2[4])
  219. {
  220.     new Float:q[4];
  221.     GetRotationQuaternion(r[0], r[1], r[2], q[0], q[1], q[2], q[3]);
  222.     QuaternionAbsToRelQuat(q, q1, q2);
  223. }
  224.  
  225. //Checks if a quaternion is a valid rotation quaternion
  226. stock IsValidQuaternion(Float:q[4])
  227. {
  228.     for(new i = 0; i < sizeof q; i++)
  229.     {
  230.         if(!(-1.0 <= q[i] <= 1.0)) return false;
  231.     }
  232.     return true;
  233. }
  234.  
  235. static stock Float:asin_limit(Float:value)
  236. {
  237.     if(value > 1.0) value = 1.0;
  238.     else if(value < -1.0) value = -1.0;
  239.     return asin(value);
  240. }
  241.  
  242. static stock Float:acos_limit(Float:value)
  243. {
  244.     if(value > 1.0) value = 1.0;
  245.     else if(value < -1.0) value = -1.0;
  246.     return acos(value);
  247. }
  248.  
  249. static stock Float:atan_limit(Float:value)
  250. {
  251.     if(value > 1.0) value = 1.0;
  252.     else if(value < -1.0) value = -1.0;
  253.     return atan(value);
  254. }
  255.  
  256. static stock Float:atan2_limit(Float:x, Float:y)
  257. {
  258.     if(x > 1.0) x = 1.0;
  259.     else if(x < -1.0) x = -1.0;
  260.     if(y > 1.0) y = 1.0;
  261.     else if(y < -1.0) y = -1.0;
  262.     return atan2(x, y);
  263. }
  264.  
  265. //Returns a set of Euler angles from a quaternion
  266. stock GetQuaternionAngles(Float:w, Float:x, Float:y, Float:z, &Float:xa, &Float:ya, &Float:za)
  267. {
  268.     #if defined QUAT_FLOAT_EPSILON
  269.     static const Float:epsilon = QUAT_FLOAT_EPSILON;
  270.     #else
  271.     static const Float:epsilon = 0.00000202655792236328125;
  272.     #endif
  273.    
  274.     new Float:temp = 2*y*z - 2*x*w;
  275.    
  276.     if(temp >= 1-epsilon)
  277.     {
  278.         xa = 90.0;
  279.         ya = -atan2_limit(y, w);
  280.         za = -atan2_limit(z, w);
  281.     }else if(-temp >= 1-epsilon)
  282.     {
  283.         xa = -90.0;
  284.         ya = -atan2_limit(y, w);
  285.         za = -atan2_limit(z, w);
  286.     }else{
  287.         xa = asin_limit(temp);
  288.         ya = -atan2_limit(x*z + y*w, 0.5 - x*x - y*y);
  289.         za = -atan2_limit(x*y + z*w, 0.5 - x*x - z*z);
  290.     }
  291. }
  292.  
  293. //Creates a quaternion from Euler angles
  294. stock GetRotationQuaternion(Float:x, Float:y, Float:z, &Float:qw, &Float:qx, &Float:qy, &Float:qz)
  295. {
  296.     new Float:cx = floatcos(-0.5*x, degrees);
  297.     new Float:sx = floatsin(-0.5*x, degrees);
  298.     new Float:cy = floatcos(-0.5*y, degrees);
  299.     new Float:sy = floatsin(-0.5*y, degrees);
  300.     new Float:cz = floatcos(-0.5*z, degrees);
  301.     new Float:sz = floatsin(-0.5*z, degrees);
  302.     qw = cx * cy * cz + sx * sy * sz;
  303.     qx = cx * sy * sz + sx * cy * cz;
  304.     qy = cx * sy * cz - sx * cy * sz;
  305.     qz = cx * cy * sz - sx * sy * cz;
  306. }
  307.  
  308. //Returns the vector component of a quaternion
  309. stock GetQuaternionVector(Float:qw, Float:qx, Float:qy, Float:qz, &Float:x, &Float:y, &Float:z)
  310. {
  311.     new Float:a;
  312.     GetQuaternionAngle(qw, a);
  313.     new Float:s = floatsin(a/2.0, degrees);
  314.     x = qx/s;
  315.     y = qy/s;
  316.     z = qz/s;
  317. }
  318.  
  319. //Returns the angle component of a quaternion
  320. stock GetQuaternionAngle(Float:w, &Float:a)
  321. {
  322.     a = 2.0*acos_limit(w);
  323. }
  324.  
  325. //Rotates a vector with a specified quaternion performing a conjugation v2 = q v1 q*
  326. stock RotateVectorQuat(Float:v1[3], Float:q[4], Float:v2[3])
  327. {
  328.     new Float:q1[4], Float:q2[4];
  329.     q1 = q;
  330.     q2[1] = v1[0], q2[2] = v1[1], q2[3] = v1[2];
  331.     GetQuatProduct(q1, q2, q2);
  332.     GetQuatConjugate(q1, q1);
  333.     GetQuatProduct(q2, q1, q2);
  334.     v2[0] = q2[1], v2[1] = q2[2], v2[2] = q2[3];
  335. }
  336.  
  337. //Returns a conjugate of a quaternion, with all non-real components inversed
  338. stock GetQuatConjugate(Float:q1[4], Float:q2[4])
  339. {
  340.     q2[0] =  q1[0];
  341.     q2[1] = -q1[1];
  342.     q2[2] = -q1[2];
  343.     q2[3] = -q1[3];
  344. }
  345.  
  346. //Returns the inverse quaternion
  347. stock GetQuatInverse(Float:q1[4], Float:q2[4])
  348. {
  349.     new Float:norm2 = q1[0]*q1[0]+q1[1]*q1[1]+q1[2]*q1[2]+q1[3]*q1[3];
  350.     GetQuatConjugate(q1, q2);
  351.     q2[0] /= norm2, q2[1] /= norm2, q2[2] /= norm2, q2[3] /= norm2;
  352. }
  353.  
  354. //Returns a Hamilton product of two quaternions
  355. stock GetQuatProduct(Float:q1[4], Float:q2[4], Float:q3[4])
  356. {
  357.     new Float:w = q1[0]*q2[0] - q1[1]*q2[1] - q1[2]*q2[2] - q1[3]*q2[3];
  358.     new Float:x = q1[0]*q2[1] + q1[1]*q2[0] + q1[2]*q2[3] - q1[3]*q2[2];
  359.     new Float:y = q1[0]*q2[2] - q1[1]*q2[3] + q1[2]*q2[0] + q1[3]*q2[1];
  360.     new Float:z = q1[0]*q2[3] + q1[1]*q2[2] - q1[2]*q2[1] + q1[3]*q2[0];
  361.     q3[0] = w, q3[1] = x, q3[2] = y, q3[3] = z;
  362. }
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