Research Initiation: Second Order Continuous Blending of Functional Surfaces

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The problem of second order continuity of blending and fairing surfaces has received only approximate or very restricted solutions, although, it is a major challenge in Computer Aided Design of Naval and Aerospace surfaces, where it is dictated by fluid dynamics. Based upon the result of previous research in Variable Sweep Geometric Modeling, this research will develop a blending strategy that is mathematically exact and insures second order continuity of the blend. The specific research objectives are summarized as follows: (1) Formulate the Variable Sweep representation of the second order continuous blend of two second order continuous surfaces. (2) Define trimming of the second order continuous blend near the ends of the blended edge. (3) Formulate the (possibly recursive) definition of the blend of previously blended surfaces.