chombier

17 ms·

181.
by chombier 10y ago
Think of exponentiation of some number 'a' as in-between its integer powers: 'a^1.5' is kind-of half-way between 'a' and 'a^2'. If you plot all the integer powers of 'a', they all belong to
182.
by chombier 10y ago
I was about to write a similar story, but then I realized you need a Riemannian metric (and exponential) for everything arclength-related. IIRC since the unit circle is a compact Lie group, there is a bi-invariant Riemannian metric whose ex
183.
by chombier 10y ago
For me what made it clicked is realizing that complex numbers are 2D matrices: z = x + i y = [[x -y][y x]]. So really we should be writing z = x * [[1 0][0 1]] + y * [[0 -1][1 0]], but since it's tedious we just call 1 == [[1 0] [0 1
184.
by chombier 10y ago
Alternatively if you don't like coordinates, you may notice that multiplication by a unit complex number is linear and preserves the complex norm (i.e. modulus), so it defines an orthogonal transformation of the plane. Topologically, u
185.
by chombier 10y ago
Especially needed since you can build a nice mouse trackball using dual quaternion exponential :)
186.
by chombier 10y ago
I suggest you start with a recursive least squares filter first, which is fully deterministic and quite easy to derive if you are comfortable with Euclidean geometry. The Kalman filter basically just adds process covariance on top of that,
187.
by chombier 10y ago
Many thanks to the author! I have the exact same feeling described in the introduction when reading anything about statistics, but this article made perfect sense to me.
188.
by chombier 10y ago
The rational parametrization looks like the Cayley transform, which IIRC does not cover the whole circle (you can't reach (-1, 0) with a finite mu). Does this happen here as well?
189.
by chombier 10y ago
Sometimes this is the math way ;) More seriously, Lie group theory puts the light exactly on the shared structure between quaternions and rotations (both are smooth groups related in some way) and ignore the secondary details, so you spend
190.
by chombier 10y ago
Ok this I know, but how to do translations only? (apart from the obvious vector space structure in R4)
191.
by chombier 10y ago
Yes, R^3 and the rotation group SO(3) are not homeomorphic (they have different topologies), meaning you can not cover SO(3) with a single chart. So any representation of rotations by 3 numbers is singular somewhere.
192.
by chombier 10y ago
> Similarly, when a quaternion is defined as representing a translation How do you encode translations with quaternions? Don't you need dual quaternions for that?
193.
by chombier 10y ago
Sure, but the way they play together can also be expressed by the means of two complex numbers (which makes 4 real numbers in total).
194.
by chombier 10y ago
I think you can do that using two rotation axis only (cf. proper Euler angles). And quaternions are made of two complex numbers. edit: typo.
195.
by chombier 10y ago
> but 3d has two planes Why not 3 planes?
196.
by chombier 10y ago
Quaternions are much easier to grasp once you are familiar with basic Lie group theory, in particular the adjoint representation of the group over its Lie algebra. Then the link with rotations becomes obvious and it gets very easy to transp
197.
by chombier 10y ago
Unsurprisingly, this results in the infamous 4 chords C, G, Am, F.
198.
by chombier 10y ago
You might want to check out the Eigen library: http://eigen.tuxfamily.org/
199.
by chombier 10y ago
I thought the very same. I guess the most interesting result they obtain is the slight asymmetry in some of the low-frequency modes, which the Fourier basis does not exhibit.
200.
by chombier 10y ago
There was also a lower turnout rate in the younger population, which I guess the less-educated contribute a lot to. The remain vote was around 60% of total younger population, with around 20% non-voters. The proportion of remain votes drops
201.
by chombier 10y ago
The well-educated people have been promising growth and prosperity to the less-educated for the last 30 years or so. It did work out quite well for the well-educated, but not so well for the less-educated. So now the less-educated beg to di
202.
by chombier 10y ago
worth reading, thanks.
203.
by chombier 10y ago
Yes! If you put the process covariance aside, then Kalman filtering really just is a linear least squares problem solved incrementally, using Woodbury formula to solve the normal equations efficiently.
204.
by chombier 10y ago
Not quite, because in your examples the producer and consumer are different, whereas researchers are to a large extent the main consumers of the knowledge they (as a whole) produce.
205.
by chombier 11y ago
Git for Windows is probably the first thing I install as soon as I log into a new Windows computer. Granted, bash may not be the most intuitive shell ever, but it just works about everywhere and this is a huge advantage when switching OS re
206.
by chombier 11y ago
It depends: rigid/non-rigid objects, stiffness for non-rigid objects, approximate/exact Coulomb model, spatial/ temporal resolutions, and solution precision. On a typical desktop computer, that would probably range from real
207.
by chombier 11y ago
It is difficult, but doable assuming Coulomb friction. The two main issues are that it is computationally expensive, but also that your mechanical modeling has to closely match that of the actual robot (especially the contact model), otherw
208.
by chombier 11y ago
So basically, this means c++ template meta-programming is no longer pure (i.e. side-effects can happen during meta-programs) right ? If so, this is quite big news, similar to when people realised the extent to which SFINAE could be abused.