User:LindaB Helendale/rot2roll pitch yaw

Roll, pitch and yaw are commonly used object related rotations (intrinsic Tait-Bryan angles) in avionics, sailing and navigation. Here are conversion functions between LSL rotation and roll, pitch and yaw angles.

<source lang="lsl2"> vector rot2roll_pitch_yaw(rotation R) {

   /*
   Convert rotation to roll, pitch and yaw angles 
   (c) LindaB Helendale
   Permission to use this code in any way granted
   
   Input: rotation (quaternion) R
   Output: vector <roll,pitch,yaw> 
   
   Roll, pitch and yaw are body-related rotations (intrinsic Tait-Bryan angles): 
   first yaw to the heading, then pitch around the local Y-axis and then roll 
   around the local X-axis (nose direction). This is equivalent to world coordinate 
   rotations (extrinsic Tait-Bryan angles, or LSL Euler angles) in order roll, pitch and yaw. 
   Thus the rotation R is recovered from the roll, pitch and yaw angles by inverting 
   the order of the rotations (since in LSL they are in Z Y X or yaw, pitch, roll order):
       rotation R = llEuler2Rot(<roll,0,0>) * llEuler2Rot(<0,pitch,0>) * llEuler2Rot(<0,0,yaw>);
       
   Reference: http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
   */
   vector eulerXYZ = < llAtan2(2*(R.s*R.x+R.y*R.z),1-2*(R.x*R.x+R.y*R.y)), 
                       llAsin(2*(R.s*R.y-R.z*R.x)), 
                       llAtan2(2*(R.s*R.z+R.x*R.y), 1-2*(R.y*R.y+R.z*R.z)) >;
   return(eulerXYZ);

}

rotation roll_pitch_yaw2rot(vector R) {

   // convert vector <roll,pitch,yaw> to LSL rotation
   return llEuler2Rot(<R.x,0,0>) * llEuler2Rot(<0,R.y,0>) * llEuler2Rot(<0,0,R.z>);

}

</source>