Movement primitives commonly represent robot mo- tions through basis functions indexed by time or phase. Inspired by spacetime representations employed in physics, we propose a spline-based formulation in which spatial geometry and temporal progression are represented within a common set of continuous variables. The proposed method jointly estimates a shared Bezier curve, while allowing spatial and temporal model complexity to be adapted independently (e.g., demonstration-specific phase modulation). As use case, we consider an alternating optimization process that simultaneously estimates path intervals observed in partial demonstrations. Simulation experiments demonstrate accurate joint recovery, refinement through modifications in model complexity and continuity, and improved robustness to variance in the demonstration set. Finally, we demonstrate online retiming and synchronization capabilities in a patient-turning task assisted by a robot, evaluated with a physical manikin.