Conjugation of frame-kinematic surfaces by fourth degree splines

Smooth conjugation of two surfaces is the most important and difficult task of geometric modeling of complex-shaped objects. There are several approaches and methods for designing a conjugation surface. One of the disadvantages of the existing methods is the lack of versatility. In each specific task you have to choose one or another method. It becomes more complicated when you have to mate three or more surfaces. The authors offer the use of an integro-differential spline of the fourth degree and a frame-kinematic surface based on it for mating surfaces. The article also briefly describes the algorithm for constructing the conjugation. An integro-differential spline of the fourth degree has additional coefficients that are the parameters that provide the ability to control the shape of the mating surface; however, it is not more difficult to be calculated than the traditional cubic splines. And the research concludes that in comparison with other methods of constructing, conjugation is a more multi-purpose one.