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Summary: Because rotations and (rotation) quaternions live on curved manifolds, it doesn't make sense to optimize them directly. Having a prominent option to require gradient on random ones may cause people to try, and isn't particularly useful.

Reviewed By: theschnitz

Differential Revision: D29160734

fbshipit-source-id: fc9e320672349fe334747c5b214655882a460a62

Summary:
As reported on github, `matrix_to_quaternion` was incorrect for rotations by 180˚. We resolved the sign of the component `i` based on the sign of `i*r`, assuming `r > 0`, which is untrue if `r == 0`.

This diff handles special cases and ensures we use the non-zero elements to copy the sign from.

Reviewed By: bottler

Differential Revision: D29149465

fbshipit-source-id: cd508cc31567fc37ea3463dd7e8c8e8d5d64a235

Summary: We can represent a rotation as a vector in the axis direction, whose length is the rotation anticlockwise in radians around that axis.

Reviewed By: gkioxari

Differential Revision: D24306293

fbshipit-source-id: 2e0f138eda8329f6cceff600a6e5f17a00e4deb7

Summary: Issue #119. The function `sqrt(max(x, 0))` is not convex and has infinite gradient at 0, but 0 is a subgradient at 0. Here we implement it in such a way as to give 0 as the gradient.

Reviewed By: gkioxari

Differential Revision: D24306294

fbshipit-source-id: 48d136faca083babad4d64970be7ea522dbe9e09

Summary: Conversion to/from the 6D representation of rotation from the paper http://arxiv.org/abs/1812.07035 ; based on David’s implementation.

Reviewed By: davnov134

Differential Revision: D22234397

fbshipit-source-id: 9e25ee93da7e3a2f2068cbe362cb5edc88649ce0

Summary: Address black + isort fbsource linter warnings from D20558374 (previous diff)

Reviewed By: nikhilaravi

Differential Revision: D20558373

fbshipit-source-id: d3607de4a01fb24c0d5269634563a7914bddf1c8

Summary: Ensure copyright header consistency and translation unit name uniqueness.

Reviewed By: nikhilaravi

Differential Revision: D20438802

fbshipit-source-id: 9820cfe4c6efab016a0a8589dfa24bb526692f83

Summary: The shebang line `#!<path to interpreter>` is only required for Python scripts, so remove it on source files for class or function definitions. Additionally explicitly mark as executable the actual Python scripts in the codebase.

Reviewed By: nikhilaravi

Differential Revision: D20095778

fbshipit-source-id: d312599fba485e978a243292f88a180d71e1b55a

Summary:
Lint related fixes: Improve internal/OSS consistency. Fix the fight between black and certain pyre-ignore markers by moving them to the line before.
Use clang-format-8 automatically if present. Small number of pyre fixes.

arc doesn't run pyre at the moment, so I put back the explicit call to pyre. I don't know if there's an option somewhere to change this.

Reviewed By: nikhilaravi

Differential Revision: D19780518

fbshipit-source-id: ef1c243392322fa074130f6cff2dd8a6f7738a7f

Summary: Fixed the rotation matrices generated by the RotateAxisAngle class and updated the tests. Added documentation for Transforms3d to clarify the conventions.

Reviewed By: gkioxari

Differential Revision: D19912903

fbshipit-source-id: c64926ce4e1381b145811557c32b73663d6d92d1

fbshipit-source-id: ad58e416e3ceeca85fae0583308968d04e78fe0d