atanXR

atanXR is a term used in extended reality (XR) development to describe a family of orientation utilities that compute angular orientation from three-dimensional direction vectors using arctangent-based methods. It is used to translate sensor or render data into yaw and pitch, enabling proper alignment of virtual content with user gaze, head pose, or scene geometry.

The core concept involves converting a directional vector into Euler angles suitable for controlling camera or reticle transformations. Primary operations include normalizing the vector, then calculating yaw with arctangent-2 to maintain quadrant accuracy (for example, yaw = atan2(x, z)) and computing pitch as a function of the vertical component and the horizontal projection (for example, pitch = atan2(-y, sqrt(x^2 + z^2))). Some implementations provide an optional roll value or derive it from additional orientation data. Conventions vary across engines, so atanXR libraries typically include configuration to select left- or right-handed coordinates and alignment with specific XR platforms.

Implementation and ecosystem: atanXR is typically exposed as a cross-language API with bindings for C++, C#, JavaScript, and Python, designed to integrate with XR engines such as Unity or Unreal. It emphasizes numerical stability, performance, and tolerance to sensor noise, with features such as clamping, smoothing, and calibration hooks. Reference implementations often separate core math from engine adapters to support platform-specific coordinate systems and unit scales.

Usage and context: in gaze tracking, head-mounted display pose estimation, reticle placement, and scene alignment, atanXR provides the mathematical bridge between raw direction data and drawable orientations. While atan2-based approaches offer robust quadrant handling, care must be taken with polar singularities and axis conventions across different XR devices.