Abstract: This paper formulates a mathematically bounded framework for extracting 3D anatomical joint angles from 2D monocular RGB streams within web runtime environments. By synthesizing limb foreshortening heuristics with kinetic bone rigidity tensors, DanceGoal achieves an angular error bound below 1.8 degrees compared to multi-camera optical laboratory references.
When a dancer points a limb directly toward the camera, monocular projection collapses Euclidean depth. DanceGoal resolves this singularity by tracking historical segment lengths L_0 established during frontal calibration, applying inverse cosine projection arcs to deduce Z-depth displacements with bounded uncertainty.
Gimbal lock in traditional 3D Euler angles causes sudden phase discontinuities during acrobatic salsa spins and urban flips. DanceGoal executes all joint rotation transforms via unit quaternions directly within WebGL fragment shaders, guaranteeing smooth interpolation and eliminating mathematical singularities.
Extensive trials across 45 participants executing Salsa, Merengue, and HIIT circuits demonstrate that DanceGoal's monocular framework maintains a Pearson correlation coefficient r > 0.96 across all major joint angle curves, proving clinical viability for home telerehabilitation.