Re: [Plib-devel] Quaternions in plib

[Steve B. <sjb...@ai...>]

Sam Stickland wrote:

> Quaternions have the
> advantage that they don't need to be reorthoganised _ever_,

...but they *do* have to be renormalized - and in theory, that's
just as arbitary as orthoganalization.

> ...and from my
> prespective four floats is a damn site better than twelve for network
> transmission (OK, so it's a naive implementation - you could get away with
> transmitting a single unsigned int if you used a lookup table.  Again
> quaternions would be quicker to lookup).

* For 3D rotation only, you only need nine floats to send a matrix - and for
  a quaternion, you only need to send three floats plus a sign bit.  Of
  course, Eulers only need three floats - so in terms of network
  bandwidth, they beat Quaternions by over 1% !   :-)

* Comparing a 4x4 matrix to a quaternion isn't fair.  A matrix can to
  a heck of a lot more than a quaternion - translation, scaling, perspective,
  shearing, projection onto an arbitary plane, *and* rotation.  Quaternions
  can only do the latter.

* Multiplying matrices together is faster than quaternions despite the
  larger number of terms because the math is simpler.

* Transforming vertices using a Quaternion is a *nightmare* compared to
  using a matrix.

* Quaternions score for interpolation, extrapolation and so forth.

Quaternions have their place - so do Matrices *and* Eulers...I have
rather a soft-spot for Quaternions - and what other mathematical
entity every had a bridge erected in honor of it's multiplication rule?

-- 
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