Mathematical Background#

This section derives the math behind each analysis capability, alongside the code that implements it — for readers who want to know why an algorithm produces the numbers it does, not just how to call it. For the importable Python API itself, see Python Analysis API; for how to run each plugin from the app, see User guide.

Shared conventions #

Every page below that deals with 3D geometry (Multi-Camera Gaze Fusion, Room (Extrinsic) Calibration, 3D Pose Reconstruction) uses the same conventions, matching room_frame::Mat4 (C++) and ray_math.py’s module docstring (Python):

Convention	Meaning
Units	Positions/lengths in millimetres; angles in the formulas below in radians (APIs that take degrees convert internally).
Rigid transform	A 4×4 homogeneous matrix \([R\,\|\,t]\), applied as \(p_{\text{out}} = R \, p_{\text{in}} + t\).
Storage	Row-major, flattened length-16 (index \(i \cdot 4 + j\) is row i, column j; the bottom row is implicitly \([0,0,0,1]\)).
Reference frame	Camera 0 is always the room-frame origin (identity transform); every other camera’s extrinsic pose is relative to it.