LlRotBetween

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

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.

• start * llRotBetween(start, end) == end is only true if start and end have the same magnitude and neither have a magnitude of zero (see #Useful Snippets for a workaround).
  • This of course is ignoring floating point precision errors.
• Rotations are from -PI to +PI around each axis.

Important Issues

SVC-4415

[c]

llRotBetween sometimes gives erroneous results.

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 -45 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.

This function adjusts the magnitude of the quaternion so start * llRotBetween(start, end) == end is true as long as neither have a magnitude of zero. They don't have to have the same magnitude.

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);
    if(start)
    {
        if(end)
        {
            float d = llSqrt(llVecMag(end) / llVecMag(start));
            return <rot.x * d, rot.y * d, rot.z * d, rot.s * d>;
        }
    }
    return rot;
}//Strife Onizuka

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>.
 

Functions

//Loosely based on SL source code
rotation llRotBetween(vector start, vector end) { 
    vector v1 = llVecNorm(start);
    vector v2 = llVecNorm(end);
    float dot = v1 * v2;
    vector axis = v1 % v2;
    if (dot < -0.9999999) {
        // 180 degrees or there abouts
        vector ortho_axis = llVecNorm(<1.f, 0.f, 0.f> - (sn * (sn.x / (sn * sn))));
        if (ortho_axis)
            return < ortho_axis.x, ortho_axis.y, ortho_axis.z, 0.f>;
        return <0.0, 0.0, 1.0, 0.0>;
    }
    else if(dot > 0.9999999) {
        //parallel
        return ZERO_ROTATION;
    }
    dot = dot + 1.0;
    float m = 1 / llSqrt((axis * axis) + (dot * dot));
    return <axis.x * m, axis.y * m, axis.z * m, dot * m>;
}

Issues

SVC-4415

[c]

llRotBetween sometimes gives erroneous results.

Source