Discrete robust features on piecewise linear surfaces

Resumen

Surfaces in R3 have features that capture key aspects of their local differential geometry, called robust features, which can be followed when the surface is deformed, that is, the features persist on the deformed surfaces. Amongst these robust features, we have the parabolic and ridge curves. Given a smooth surface M in R3, the parabolic set of M is the zero set of its Gaussian curvature. The ridge is the set of points on M where a principal curvature is extremal along its own lines of principal curvature (colored red for one principal curvature and blue for the other). We consider here discrete robust features of discrete surfaces S in R3. Usually, this is done by discretizing the robust features of a smooth approximation of the discrete surface. In our study, we work directly with discrete surfaces using tools from Discrete Differential Geometry. Our surfaces are piecewise linear surface meshes.