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thewhiteaussie

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  1. thewhiteaussie

    Is the concatenation of a VQS with its inverse commutative?

    SOLVED.   Solution was to ensure all quaternions were normalized, thus representing rotations.
  2. thewhiteaussie

    Is the concatenation of a VQS with its inverse commutative?

    Ok good idea. Here's an example that might help. Incidentally, the issue it seems appears to be with the Inverse(VQS) function. Here's a test case:   T = [(-3.2, 1.6, -10.3) , (-0.52, 0.68, 0.49, 0.32) , 2]   Inverse( Inverse(T) ) = [(-4.0, 2.5, -9.9) , (-0.52, 0.68, 0.49, 0.32) , 2]   Inverse( Inverse(T) ) should return T. The scalar and quaternion components are correct, however the translation vector is off. It looks like the method to find the inverse translation component might be incorrect.
  3. Quaternion concatenation is noncommutative. That is   qa * qb  ?  qb * qa   However   q-1 * q = q * q-1 = Iq   where q-1 is the inverse of q and Iq is the identity quaternion. VQS concatenation is also noncommutative:   TA_B  * TB_C  ?   TB_C * TA_B   Where TA_B represents a VQS transformation. Now, we find the inverse of TA_B like so:   TA_B-1 = TB_A   My question is, is the concatenation of a VQS with its inverse commutative? Ie, is the following statement correct?   TA_B * TB_A = TB_A * TA_B = IVQS   Where IVQS  is the identity VQS. With the implementation I’m using I’m finding   T -1 * T   =   IVQS, whereas T * T -1   ?   IVQS   This seems incorrect; both sould return IVQS.     EDIT:   Here is the implementation of VQS Inverse and concatenation functions I'm using: //-------------------------------------------------------------------------------- // Concatenation //-------------------------------------------------------------------------------- VQS VQS::operator*(const VQS& rhs) const { VQS result; //Combine translation vectors result.v = q.Rotate(rhs.v) * s + v; //Combine quaternions result.q = q * rhs.q; //Combine scales result.s = s * rhs.s; //Return result return result; } //End: VQS::operator*() //-------------------------------------------------------------------------------- // Returns inverse VQS //-------------------------------------------------------------------------------- VQS Inverse(const VQS& other) { VQS temp; //Inverse scale temp.s = 1.0f / other.s; //Inverse quaternion temp.q = Inverse(other.q); //Inverse vector temp.v = temp.q.Rotate(-other.v) * temp.s; return temp; } //End: Inverse()
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