Fixed custom factors in doc/gtsam.lyx/pdf

[dellaert]

Fixed math to agree with code and added explanation:

[roger-]

Tangentially related question: is there a standard mathematical notation or function for extracting a pose from a transformation matrix? Something like the skew operator in the Lie algebra but for the group?

Like (x, y, theta)^T = somefunc(q) for matrix q?

[dellaert]

Tangentially related question: is there a standard mathematical notation or function for extracting a pose from a transformation matrix? Something like the skew operator in the Lie algebra but for the group?

Like (x, y, theta)^T = somefunc(q) for matrix q?

Not that I know of. The group elements have different representations. We actually use (R, t) internally. You can also use a 4x4 matrix. Typically I switch between them without being explicit about it.

PS1 Another equally valid representation is an 8x8 matrix, which repeats the 4x4 matrix on the diagonal. There is a whole "representation theory" about it that I once was more knowledgeable about, but I forgot most of it :-)

PS2 The generalization of skew is \hat{}. And some people use the "vee" operator to do the reverse.

[xsj01]

LGTM, except for the comments above

[dellaert]

LGTM, except for the comments above

Sorry to rebut both those comments :-/

[roger-]

@dellaert
Above you define the error as:

Could we also define it as:

where

just converts from homogenous to Cartesian coordinates.

I have to double check my math, but I believe this gives a Jacobian similar to the original formulation (I got a negative identity matrix followed by a non-zero last column).

Don't think this is advantageous, but was just curious.

I was also wondering if this error could be defined in the tangent space, but I guess that doesn't make sense since m has no angle.