User:LindaB Helendale/rot2roll pitch yaw

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

Note that in LlRot2Euler it is imprecisely stated that llRot2Euler returns roll, pitch and yaw angles. However, LSL Euler angles are extrinsic Tait-Bryan angles, in Z Y X order. With extrinsic rotations, after the Z-rotation (yaw) the Y-rotation is done in the world coordinates, rotating the rotated prim vertices around the world Y-axis, and similarly with X. The nautical pitch angle is with respect to the local Y-axis, nose up/down independent of heading. As an example of the difference, with a 90 degree yaw the Y-rotation will actually cause roll around the local X-axis that is aligned with the world Y-axis. If the order of Euler angles in LSL were X Y Z the angles would be proper nautical angles (and llRot2Euler would return the same values as rot2roll_pitch_yaw below), but the order is built-in in the llRot2Euler and llEuler2Rot functions.

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>);
    vector eulerXYZ = < llAtan2(2*(R.s*R.x+R.y*R.z),1-2*(R.x*R.x+R.y*R.y)), 
                        llAtan2(2*(R.s*R.z+R.x*R.y), 1-2*(R.y*R.y+R.z*R.z)) >;
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>);