Naming things is really hard! I’m discovering the different geometric types of the library and just realized that the
Isometry type is what I was trying to define myself as extrinsic parameters of cameras. Except in theory it shouldn’t. Isometries are the elements of the Eclidean group also written
E(3) (in dim 3). While extrinsic parameters are parameters of rigid body motions, which are transformations of the Special Euclidean group
SE(3). The tiny difference between
SE(3) is that isometries can contain reflexions (mirrors) which have determinant of (-1), while rigid body motions, which can be written as the combination of rotation and translation, all have determinant of (+1).
I guess the difference is subtle enough, and “isometry” much more common than “rigid body motion” or “Special Euclidean”, to have the tradoff in favor of keeping the current name. I was thinking that it was worth mentionning in the documentation though?