  This paper surveys and evaluates some popular state of the art methods for
algorithmic curvature and normal estimation. In addition to surveying existing
methods we also propose a new method for robust curvature estimation and
evaluate it against existing methods thus demonstrating its superiority to
existing methods in the case of significant data noise. Throughout this paper
we are concerned with computation in low dimensional spaces (N < 10) and
primarily focus on the computation of the Weingarten map and quantities that
may be derived from this; however, the algorithms discussed are theoretically
applicable in any dimension. One thing that is common to all these methods is
their basis in an estimated graph structure. For any of these methods to work
the local geometry of the manifold must be exploited; however, in the case of
point cloud data it is often difficult to discover a robust manifold structure
underlying the data, even in simple cases, which can greatly influence the
results of these algorithms. We hope that in pushing these algorithms to their
limits we are able to discover, and perhaps resolve, many major pitfalls that
may affect potential users and future researchers hoping to improve these
methods
