Add unit dual quaternion #165
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Draft implementation (class layout and a few functions in b9f0460). |
Codecov Report
@@ Coverage Diff @@
## devel #165 +/- ##
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- Coverage 98.23% 97.39% -0.84%
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Files 37 43 +6
Lines 1130 1190 +60
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+ Hits 1110 1159 +49
- Misses 20 31 +11 |
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We should start by I guess after The trouble will be as always with Jacobians are easy once we have the blocks above. We can try to simplify the expressions resulting from the chain rule. Often we are luck with these simplifications. |
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Nice job BTW! how do you code so quickly? Did you create a template or script for new classes in |
| * @brief Constructor given a translation and a unit quaternion. | ||
| * @param[in] t A translation vector. | ||
| * @param[in] q A unit quaternion. | ||
| * @throws manif::invalid_argument on un-normalized complex number. |
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un-normalized *complex number --> un-normalized quaternion
| template <typename _Derived> | ||
| void DHuBase<_Derived>::normalize() | ||
| { | ||
| const Scalar n = coeffs().template head<4>().norm(); | ||
| coeffs() /= n; | ||
| // real and dual parts are orthogonal | ||
| coeffs().template tail<4>() -= (coeffs().template head<4>().dot(coeffs().template tail<4>())) * coeffs().template head<4>(); | ||
| } |
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I did not understand this part in the paper. What are we to normalize? The rotational quaternion (4 components) and then the translational quaternion by the same scaling (4 more components)? Or all the real+dual quaterninon (8 components)? Or both the real and dual normalized separately?
That is, at the end of normalize(), what should we have:
- | Real | = 1 and | Dual | = anything (just as in the code)
- | (Real,Dual) | = 1
- | Real | = 1 AND | Dual | = 1
??
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In this source the author defines 3 conjugates (Sec.5) and more specifically the second conjugate that "follows from the classical quaternion conjugation": σ∗ = p∗ + ϵq∗. Sec.6 states that "a dual quaternion is unit if σ ⊗ σ∗ = 1" which implies that the real part p must be a unit quaternion and the dual part p must be orthogonal to the real part p. So at the end of normalize() we should have:
4.a |Real| = 1
4.b Real . Dual = 0
These are the conditions I'm checking for at construction (see here). And I'm testing normalize() in this test which seems to pass.
Note that this 'second conjugate' is simply called conjugate() in the code and we have
inverse() { return conjugate(); }
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How is the product in 4b defined? Is it regular quaternion product?
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Sec.6 Eq.21 of the aforementioned reference: p0q0 + p1q1 + p2q2 + p3q3 = 0
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OK I see, so they are orthogonal as 4-vectors: p.tr * q = 0
No I haven't found yet a source for
Ahah that's one of the many advantages of |
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exp can be found in 5.1 here |
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This PR adds the unit dual quaternion group, currently called
DHu.note: I suspect there is a better name than
DHuDraft implementation:
Group
DHu::RandomDHu::InverseDHu::ComposeDHu::normalizeDHu::conjugateDHu::conjugatedualDHu::rotationDHu::translationDHu::isometryDHu::adjDHu::logDHu::actJacobiansDHu::...Tangent
DHuTangent::rjacDHuTangent::ljacDHuTangent::smallAdjDHuTangent::hatDHuTangent::expDHuTangent::...Comes on top of #150.
Closes #164.