With the need for adequate analysis of blood flow dynamics, different imaging modalities have been developed to measure varying blood velocities over time. Due to its numerous advantages, Doppler ultrasound sonography remains one of the most widely used techniques in clinical routine, but requires additional preprocessing to recover 3D velocity information. Despite great progress in the last years, recent approaches do not jointly consider spatial and temporal variation in blood flow. In this work, we present a novel gating- and compounding-free method to simultaneously reconstruct a 3D velocity field and a temporal flow profile from arbitrarily sampled Doppler ultrasound measurements obtained from multiple directions. Based on a laminar flow assumption, a patch-wise B-spline formulation of blood velocity is coupled for the first time with a global waveform model acting as temporal regularization. We evaluated our method on three virtual phantom datasets, demonstrating robustness in terms of noise, angle between measurements and data sparsity, and applied it successfully to five real case datasets of carotid artery examination.