Performing k-space variable density sampling is a popular way of reducing scanning time in Magnetic Resonance Imaging (MRI). Un-fortunately, given a sampling trajectory, it is not clear how to traverse it using gradient waveforms. In this paper, we actually show that ex-isting methods [1, 2] can yield large traversal time if the trajectory contains high curvature areas. Therefore, we consider here a new method for gradient waveform design which is based on the pro-jection of unrealistic initial trajectory onto the set of hardware con-straints. Next, we show on realistic simulations that this algorithm allows implementing variable density trajectories resulting from the piecewise linear solution of the Travelling Salesman Problem in a reasonable time. Finally, we demonstrate the application of this ap-proach to 2D MRI reconstruction and 3D angiography in the mouse brain.