To conclude, we have developed an algorithm and implemented it to analyze the diffusion dynamics along curved membrane surfaces. We have applied our method to two simulated membranes with different topologies-one with only mean curvature and another with additional Gaussian curvature. Our approach is able to resolve the roles of curvature and lipid packing in dynamics in multi-microsecond trajectories on systems spanning dozens of nanometers in size, i.e. on biologically relevant scales. This task is only made possible with the efficient implementation of the distance calculation in our algorithm. The richness of molecular motion revealed by our analysis method reveals details of lateral diffusion that are otherwise obscured by the use of conventional, projected diffusion coefficients. The present results not only shed light on the importance of lipid packing effects on the motion of the particles, but also indicate the fundamental way by which the mean curvature H can affect diffusion. Based on the picture emerging following the analysis, either the mean curvature or the lateral density of lipid headgroups seems to be a reliable indicator of changes in lateral diffusion. Of course, the failure of the continuum models predicting the significance of Gaussian curvature G on the length-scales of our simulated membranes is not unexpected.