A novel cubic-order algorithm for approximating principal direction vectors

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3D Facial Expression Recognition Based on Primitive Surface Feature Distribution (2006, methodology): “Similar to the method in [14], we define the fitting function in the form of”
Ridge-valley lines on meshes via implicit surface fitting (2004, methodology): “The two main approaches to curvature tensor estimation consist of using (cid:2)nite differences [Meyer et al. 2003; Cohen-Steiner and Morvan 2003] and polynomial (cid:2)tting [Cazals and Pouget 2003; Goldfeather and Interrante 2004].”
Extracting lines of curvature from noisy point clouds (2009, background): “, (14; 13; 37), b) discrete differential geometry methods where discrete versions of differential geometry theorems are developed and applied to one-ring, two-ring or N -ring neigh-”
MorphoGraphX: A platform for quantifying morphogenesis in 4D (2015, methodology): “For example, the local tissue curvature ( Goldfeather and Interrante, 2004 ) can be calculated based on the position of the neighbors closer than a given radius and displayed in a manner similar to the growth directions ( Figure 4B and Figure 4—figure supplement 3 ), making it a convenient tool for…”