Most of the estimators are based on computing the distances to the k:th nearest neighbors and using that information to compute the estimates. However, zero distances carry no information and can’t be used for the estimation. TIM degrades gracefully in these degenerate cases and ignores the zero distances when computing the estimates.
In a really degenerate case it might happen that all the distances are zero, i.e. all points are located at the same position: in this case TIM returns a NaN (not-a-number). While this might sound a rare case, it becomes a bit more important when considering the temporal estimators.
When using temporal estimators, an estimate is given for each time instant. It might then happen that the estimate is not defined for all time instants. However, having NaNs here and there in a temporal estimate is inconvenient. Instead, TIM behaves as follows. Initially, the undefined temporal estimates are given a NaN. However, after all temporal estimates have been computed, TIM reconstructs the NaNs from surrounding temporal estimates using linear interpolation (and constant interpolation at the edges). This reconstruction assumes that the temporal estimates are continuous in time. If the estimates are undefined at all time instants, an array of NaNs is returned.
Here are examples of the reconstruction:
[ 1, NaN, NaN, NaN, 5] -> [ 1, 2, 3, 4, 5]
[ 1, NaN, NaN, NaN, Nan] -> [ 1, 1, 1, 1, 1]
[NaN, NaN, NaN, NaN, 5] -> [ 5, 5, 5, 5, 5]
[NaN, NaN, 3, NaN, NaN] -> [ 3, 3, 3, 3, 3]
[ 1, NaN, 3, NaN, 5] -> [ 1, 2, 3, 4, 5]
[NaN, NaN, NaN, NaN, NaN] -> [NaN, NaN, NaN, NaN, NaN]