We propose a new method to construct a real piecewise algebraic hypersurface of a given degree with a prescribed smoothness and topology. The method is based on the smooth blending theory and the Viro method for construction of Bernstein-Bézier algebraic hypersurface piece on a simplex.
"The Viro Method for Construction of Piecewise Algebraic Hypersurfaces." Abstr. Appl. Anal. 2013 (SI57) 1 - 7, 2013. https://doi.org/10.1155/2013/690341