llRotLookAt

void llRotLookAt(rotation Rotation, float Strength, float Damping)

Cause object to rotate to Rotation, with a force function defined by Strength and Damping parameters. Good strength values are around half the mass of the object and good damping values are less than 1/10th of the strength.

Asymmetrical shapes require smaller damping.

A strength of 0.0 cancels the look at.

Parameters

Rotation (rotation)
Strength (float)
Damping (float)

Technical Details

Return Type: void
Energy: 10

In non-physical objects this function operates effectively the same as llSetLocalRot
Damping seems to be capped at 1.0; greater values are reduced to 1.0
The minimum value for Strength seems to be 0.0445 for the function to have any effect
For physical objects a range between 0.2 and 1 is good for both parameters

Examples

Point the prim’s positive y axis towards a position on the sim

//-- where vPosTarget is the global position of the object you want to "look" at
llRotLookAt( llRotBetween( <0.0,1.0,0.0>, llVecNorm( vPosTarget - llGetPos() ) ), 1.0, 0.4 ); // Point +Y axis towards vPosTarget

Explanation:

vPosTarget - llGetPos() converts the global coordinates of the objects to a local distance and direction from the object pointing
llRotBetween returns a scaled rotation, unless both inputs are equal magnitude (e.g. unit vector)
llVecNorm reduces the magnitude to 1 (so that both are equal magnitude), preventing errors

Constraining the Rotation to One Axis

vector detected = llDetectedPos( 0 );
vector pos = llGetPos();
llRotLookAt( llRotBetween( <0.0, 1.0, 0.0>, llVecNorm( <detected.x, detected.y, pos.z> - pos ) ), 1.0, 0.4 );

Helper Functions

Smooth constant rate rotation (non-physical objects)

If you want a (mostly) smooth constant (rather than damped) rate of motion in a non-physical object:

//-- Rotates Object to vRotTarget at vFltRate (in radians per second)
//-- vFltRate < ~0.00000003rad/sec (~0.00002deg/sec) will result in errors (and is just too slow anyway)
//-- vFltRate >= (PI * 5.0)rad/sec (900deg/sec) will result in a single snap move to vRotTarget
uSteppedRotLookAt( rotation vRotTarget, float vFltRate ){
  if ((integer)(vFltRate = (llAngleBetween( llGetLocalRot(), vRotTarget ) / (vFltRate / 5.0)))){
    rotation vRotStep = llAxisAngle2Rot( llRot2Axis( vRotTarget / llGetLocalRot() ),
                        (1.0 / vFltRate) * llRot2Angle( vRotTarget / llGetLocalRot() ) );
    vFltRate = (integer)vFltRate;
    do{
      llSetLocalRot( vRotStep * llGetLocalRot() );
    }while (--vFltRate);
  }
  llSetLocalRot( vRotTarget );
} //-- for fixed time on any rotation try llSetKeyframedMotion

Notes

Maintains rotation until stopped with llStopLookAt
To change the position in the same manner, use llMoveToTarget
For fixed time on any rotation, consider using llSetKeyframedMotion