Module skeletal_model::conventions

This module describes the mathematical conventions we adopt throughout the skeletal model.

Coordinate system

We adopt a right hand rule coordinate system:

• Your pointer finger is +X, which points “right”
• Your middle finger is +Y, which points “up”
• Your thumb is +Z, which points “backward”. -Z points “forward”.

This convention is the same as other libraries like SteamVR and OpenGL.

Rotation representation

We use quaternions to represent rotations whenever possible. We try not to use euler angles in our implementation to avoid possible gimbal lock issues.

Frames of reference

There are several different frames of reference (aka spaces) that matter:

• Global space: This is a space that all positional and rotational constraints are specified in.
• Sensor spaces: If there are n sensors, there are n sensor spaces, one for each sensor. For example, each imu has its own sensor space, generally they are automatically aligned to share a gravity vector, but their yaw is unaligned. Note that this is not a requirement and the skeletal model makes no assumption that they are aligned to gravity.
• Local space: Local space means that transforms are described relative to the particular bone in the skeleton. Technically there are many local spaces, one for each bone. We usually omit specifying which bone the space belongs to, as its implied that we are referring to the parent bone.

Functions

forward_vec

A vector in the “forward” or -Z direction

look_towards

Creates a UnitQuat that corresponds to the local frame of an observer standing at the origin and looking toward dir. This is a version of UnitQuat::face_towards() that better matches our mathematical conventions.

right_vec

A vector in the “right” or +X direction

up_vec

A vector in the “up” or +Y direction