Modeling exponential interpolation curves in point calculus

   In engineering geometry the problem of creating flexible curves incident to given points is relevant. The article describes a method for modeling interpolation curves in point calculus based on Bezier curves. The basis for modifying Bezier curves is replacing the simplex of control points in the curve equation with interpolation nodes. This method utilizes a uniform distribution of parameter values, ensuring that the incidence condition for the given points is satisfied. However, the use of Bezier curves does not always allow for the effective modeling of objects and processes with exponential change. Therefore, it is proposed to use the same method to define interpolation curves obtained from exponential functions in point calculus. The result is a new class of exponential interpolation curves which shape is determined using coefficients ki. The advantage of this approach is flexibility in shape control and the ability to create curves with predetermined geometric properties by solving minimax problems for the coefficients ki. The proposed method expands the geometric modeling toolkit in CAD systems and also it can be used for modeling and digitally supporting the lifecycle of complex products and forecasting processes with exponential growth.

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