We introduce a geometric method for online subspace adaptation
in the context of projection-based nonlinear model reduction.
The approach works in combination with masked projection schemes like the
missing point estimation or the discrete empirical interpolation method.
Both of these approaches aim at restricting the evaluation of a discretized nonlinear function
to a small subset of grid points in the spatial domain.
It is demonstrated that the selection of the point subset has a major
impact on the quality of the resulting approximations.
We derive error bounds for point selection schemes that can
serve as objective functions in greedy point selection algorithms.
Finally, we discuss ways to accelerate the greedy point selection strategies.