LlRotBetween

Return value notes

Returns a rotation that is the shortest rotation between the direction start and the direction end

Specification

start and end are directions and are relative to the origin <0.0, 0.0, 0.0>. If you have coordinates relative to a different origin, subtract that origin from the input vectors.

Note that the input vectors are directions, NOT position coordinates.

Feeding position coordinates will not work, or at minimum be very inaccurate and / or inconsistent.

Caveats

start * llRotBetween(start, end) == end is only true if start and end have the same magnitude and neither have a magnitude of zero (see for a workaround).
- This of course is ignoring floating point precision errors.
The above is true because of vector magnitudes and not a shortcoming of this function. The rotation returned is correct regardless of magnitudes
Rotations are from -PI to +PI around each axis.

Examples

Drop the below script into a prim. This script will cause the object to orient it's positive X axis towards it's owner's avatar when touched.

default
{
    touch_start(integer total_number)
    {
        list lTemp = llGetObjectDetails(llGetOwner(),[OBJECT_POS]); //Get the owner's position (region coordinates)
        vector start = llRot2Fwd(ZERO_ROTATION); //Object's X axis is forward. (Can be substituted with llRot2Left (Y axis) or llRot2Up (Z axis). Negative values (-llRot2Fwd) can be used to spin the prim 180 degrees)
        //start = llRot2Fwd( llAxisAngle2Rot(<0,0,1>,45*DEG_TO_RAD) ); //Uncommenting this line will cause the prim to point one of it's corners towards the avatar, instead of the forward face.
        vector end = llVecNorm(llList2Vector(lTemp,0) - llGetPos()); //Convert the owner's position into a normalized direction vector (relative to the prim).
        llSetLinkPrimitiveParamsFast(LINK_THIS,[PRIM_ROTATION,llRotBetween(start,end)]); //Set the prim's rotation accordingly.
    }
    //llRot2Fwd(ZERO_ROTATION) is equivalent to <1,0,0> , llRot2Left would be <0,1,0> and llRot2Up would be <0,0,1>. Negative values ( -llRot2Fwd(ZERO_ROTATION) ) would be <-1,0,0>, -llRot2Left would be <0,-1,0> and -llRot2Up would be <0,0,-1>
    //Note that a value other than ZERO_ROTATION may cause unexpected results. Unless you know the exact offset you need for your object, then leave this as-is.
} //Jenna Huntsman

llRotBetween(<1.0, 0.0, 0.0>, <0.0, -1.0, 0.0>)
// will return <0.00000, 0.00000, -0.70711, 0.70711> (which represents -90 degrees on the z axis)

llRotBetween(<0.0, 0.0, 0.0>, <0.0, -1.0, 0.0>)
// will return <0.00000, 0.00000, 0.00000, 1.00000> (which represents a zero angle on all axis)
// because <0.0, 0.0, 0.0> does not convey a direction.

Helper functions

This function adjusts the magnitude of the quaternion so start * llRotBetween(start, end) == end is true as long as neither have a magnitude really close to zero. They do not have to have the same magnitude. (If either is too close to zero than this will return an unadjusted quaternion). While this is mathematically correct, it won't help with floating point rounding errors, so it's more accurate to say start * return ≈ end.

rotation RotBetween(vector start, vector end) //adjusts quaternion magnitude so (start * return == end) 
{//Authors note: I have never had a use for this but it's good to know how to do it if I did.
    rotation rot = llRotBetween(start, end);
    float d = start * start;
    if(d)//is 'start' zero?
        if((d = llPow(end * end / d, 0.25)))//is 'end' zero?
            return <rot.x * d, rot.y * d, rot.z * d, rot.s * d>;
    return rot;
}//Strife Onizuka

Notes

Vectors that are near opposite each other in direction may lead to erroneous results.

// First Vector is due north second vector is ALMOST due south.
rotation lRotation = llRotBetween( <0., 1., 0.>, <-0.001, -.1, 0.> );
llSay(0, lRotation );
// Provides a result of <1.00000, 0.00000, 0.00000, 0.00000>.

Shared wiki helpers

The original page also injects shared parameter notes, caveats or issue information through these helpers. Their conditional MediaWiki logic is not reproduced here; inspect the preserved helper source for additional material.

Template:Issues/SVC-4415

Original shared helper source (conditional wiki logic is not evaluated)

{{Issues|SVC-4415|type=bug|[[llRotBetween]] sometimes gives erroneous results.|resolution=wont}}

Template:Issues/SCR-309