Solid blends of high order continuity

Solid blending with the n^th order continuity is investigated in this paper. We use up to the n^th partial derivatives to define the continuity at the boundary surfaces between the blended solids and the blending solid, and introduce basic functions to transform the original boundary conditions into simpler ones. The mathematical description of a blending solid is discussed and a set of linear algebraic equations is derived to determine the unknown constants in the constructed function of the blending solid. Several numerical examples are given to demonstrate both the applications of the proposed approach in solid blending and the effects of different continuities on the smoothness between the blending solid and blended solids.