Abstract : Piecewise Polynomial Reconstruction of Functions from Simplified Morse-Smale complex: The main contribution is the application of a shape
preserving spline surfaces for reconstruction of a scalar field from a given Morse-Smale complex. In particular we approximate the jagged 1-cells on the complex with smooth B-splines. We introduce a C1 monotone Sibson spline interpolant and combine it with a reparameterization to reconstruct the 2-cells individually. The resulting surface piecewise smooth and obeys completely the given MS complex.