]). Three-dimensional kernels for trajectories that produce volumes in geo-time space. Panel a shows a) point space-time density with cylindrical kernels that do not take into account the temporal sequence of points in a trajectory. Panels b), c) and d) show polyline kernels, where there is one kernel for the entire trajectory (and not a separate kernel for each line segment). Distance from each voxel to trajectory in panel b) (shown in kernel with a dashed grey line) is calculated in 3-D, perpendicularly to the trajectory. Distance from each voxel to trajectory in panels c)-d) is measured at a constant moment in time (i.e. horizontally) and is calculated as 2-D distance. Panel d) shows the Brownian bridges version of the stacked 3-D kernel, where the width of the kernel at each moment in time depends on the position on the trajectory between each two consecutive points.