Recovering the underlying function f inside its different regions of smoothness.
Furthermore, the path calculated has good safety and smoothness characteristics.
The importance of this map is that it defines the natural parametric domain for analysing the smoothness of the surface at the extraordinary vertex.
While assessing the various types we incorporate the notions of local support and support size, smoothness and approximation order.
Thus, a piecewise smooth f is in fact a collection of several intervals of smoothness which do not communicate among themselves.
The difficulty with the canonical projection is that, owing to its dependence on traces on subsimplices, it is not bounded on spaces with insufficient smoothness.
This guarantees continuous dependence on parameters, global extensibility of solutions and sufficient smoothness of the flow.
Like the bandwidth, the parameter > 0 controls the smoothness of the fit.
