Commit b6c3684b authored by Joseph Mirabel's avatar Joseph Mirabel Committed by Joseph Mirabel
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[Doc] Add doc for firstOrderNormalize

parent ded514db
......@@ -65,7 +65,13 @@ namespace se3
/// of the normalization function.
///
/// Only additions and multiplications are required. Neither square root nor
/// division are used (except a division by 2).
/// division are used (except a division by 2). Let \f$ \delta = ||q||^2 - 1 \f$.
/// Using the following limited development:
/// \f[ \frac{1}{||q||} = (1 + \delta)^{-\frac{1}{2}} = 1 - \frac{\delta}{2} + \mathcal{O}(\delta^2) \f]
///
/// The output is
/// \f[ q_{out} = q \times \frac{3 - ||q_{in}||^2}{2} \f]
///
/// The output quaternion is guaranted to statisfy the following:
/// \f[ | ||q_{out}|| - 1 | \le \frac{M}{2} ||q_{in}|| ( ||q_{in}||^2 - 1 )^2 \f]
/// where \f$ M = \frac{3}{4} (1 - \epsilon)^{-\frac{5}{2}} \f$
......
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