Rigid Transforms & Camera Poses
Frames, conventions, and the six-dimensional space that poses actually live in.
Nobody is confused by the maths of rigid transforms. is orthogonal with determinant ; is a vector; you compose by multiplying. What derails people is bookkeeping: which frame a pose is expressed in, which direction it maps, and which of the four plausible readings of "the camera pose" a given dataset means.
This topic fixes a notation that makes wrong compositions look wrong, then works through the representation choices and the tangent space that optimisers use.
- 01 Frames, and a notation that catches mistakes Foundation 1 interactive 9′ Every pose has a source frame, a target frame, and a direction. Name all three. Repairs The habit of calling a variable `pose` or `T_cam` and reconstructing its meaning from context each time it is used.
- 02 Four ways to write a rotation Core 1 interactive 12′ Matrices, axis–angle, quaternions and Euler angles — each optimal for something, none for everything. Repairs The belief that quaternions are "better" and Euler angles are "bad", rather than each being adapted to a different job.
- 03 Optimising on the manifold Advanced 11′ Why a pose update is six numbers, and why you never add them to a matrix. Repairs The idea that "Lie groups" are advanced theory, rather than the direct answer to "how do I take a derivative with respect to a rotation".