Extension of Andrew Stacey's Quaternion Library

Code Sharing
1

Andrew’s quaternion library didn’t have a slerp function. I’m posting mine here, converted to lua from C# online.

Pass two Quaternions and a temporal value 0…1. Returns Quaternion.

function slerp(qa, qb, t) 
 qm = Quaternion(0,0,0,0)
--    // Calculate angle between them.
    cosHalfTheta = qa.a * qb.a + qa.b * qb.b + qa.c * qb.c + qa.d * qb.d
--    // if qa=qb or qa=-qb then...
    if (math.abs(cosHalfTheta) >= 1.0) then
        qm.a = qa.a
        qm.b = qa.b
        qm.c = qa.c
        qm.d = qa.d
        return qm
    end
 --   // Calculate temporary values.
    halfTheta = math.acos(cosHalfTheta)
    sinHalfTheta = math.sqrt(1.0 - cosHalfTheta*cosHalfTheta)
--    // if theta = 180 degrees then result is not fully defined
--    // we could rotate around any axis normal to qa or qb
    if (math.abs(sinHalfTheta) < 0.001) then  
        qm.a = (qa.a * 0.5 + qb.a * 0.5)
        qm.b = (qa.b * 0.5 + qb.b * 0.5)
        qm.c = (qa.c * 0.5 + qb.c * 0.5)
        qm.d = (qa.d * 0.5 + qb.d * 0.5)
        return qm
    end
    ratioA = math.sin((1 - t) * halfTheta) / sinHalfTheta
    ratioB = math.sin(t * halfTheta) / sinHalfTheta
--    //calculate Quaternion.
    qm.a = (qa.a * ratioA + qb.a * ratioB);
    qm.b = (qa.b * ratioA + qb.b * ratioB)
    qm.c = (qa.c * ratioA + qb.c * ratioB)
    qm.d = (qa.d * ratioA + qb.d * ratioB)
    return qm
end
2

Had to look that up! Nice addition.

3

You’re welcome! I’d ask about that write-up again, but after all this reading…

Just can’t figure out how to get an angle for artillery fire from a Quat angle.

4

Video of Quaternion rendering

http://youtu.be/hwFrDbQSaYg