  Neural implicit surface representations are currently receiving a lot of
interest as a means to achieve high-fidelity surface reconstruction at a low
memory cost, compared to traditional explicit representations.However,
state-of-the-art methods still struggle with excessive memory usage and
non-smooth surfaces. This is particularly problematic in large-scale
applications with sparse inputs, as is common in robotics use cases. To address
these issues, we first introduce a sparse structure, \emph{tri-quadtrees},
which represents the environment using learnable features stored in three
planar quadtree projections. Secondly, we concatenate the learnable features
with a Fourier feature positional encoding. The combined features are then
decoded into signed distance values through a small multi-layer perceptron. We
demonstrate that this approach facilitates smoother reconstruction with a
higher completion ratio with fewer holes. Compared to two recent baselines, one
implicit and one explicit, our approach requires only 10\%--50\% as much
memory, while achieving competitive quality.
