[eigen] about Transform API

["Gael Guennebaud" <gael.guennebaud@xxxxxxxxx>]

Hi list,

if we still agree that Eigen should be as close as possible to what people
would write on a piece of paper, then I think Transform is poorly designed.

For instance if you want to concatenate a scale S to a transformation T you
would write:

paper:  T' = T * S
or
paper:  T' =  S * T

while in Eigen we currently have to write:

eigen:   T = T.scale(Vector3f(sx,sy,sz));
or
eigen:   T = T.prescale(Vector3f(sx,sy,sz));

What about doing something similar to what I did with rotations and
overloading the correct *= and * operators such that you could write:

eigen:   T = T * Scale3f(sx,sy,sz);
eigen:   T *= Scale3f(sx,sy,sz);
or
eigen:   T = Scale3f(sx,sy,sz) * T;

then if you want to express:

paper: T = S * R * L;

(where L is a translation)
you could write:

eigen:  T = Scale3f(..) * RotationType(....) * Translation3f(...);

(with RotationType in {Quaternion, Matrix, AngleAxis, Rotation2D } )

instead of the current:

eigen:  T.setIdentity();
eigen:  T.scale(...);
eigen:  T.rotate(...);
eigen:  T.translate(...);

ok, actually the rotate, scale and translate methods return a reference to
T, so currently you can still write:

eigen:  T.setIdentity();
eigen:  T.scale(...).rotate(...).translate(...);

that is not too bad in that case, but think about "T = R1 * L * T * R2"
which involves "pre*" versions of the methods:

eigen:  T.pretranslate(L).prerotate(R1).rotate(R2);

IMHO it's quite confusing because it does not give you the idea of the
transformation order: "R1 * L * T * R2".