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This article describes the capabilities of a universal software platform for visualizing class F curves and developing specialized applications for CAD systems based on Microsoft Excel VBA, the software complex FairCurveModeler, and computer algebra systems. Additionally, it demonstrates the use of a software platform for visualizing functional and log-aesthetic curves integrated with CAD Fusion360. The value of the curves is evident in visualizing the qualitative geometry of the product shape in industrial design. Moreover, the requirements for the characteristics of class F curves are emphasized to form a visual purity of shape in industrial design and to provide a positive emotional perception of the visual image of the product by a person.

We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of geometric modeling, we perform an aesthetic analysis of planar Bernstein-Bezier curves from the standpoint of the laws of technical aesthetics. The shape features of the curve segments' geometry were evaluated using the following criteria: conciseness-integrity, expressiveness, proportional consistency, compositional balance, structural organization, imagery, rationality, dynamism, scale, flexibility and harmony. In the non-Russian literature, Bernstein-Bezier curves using a monotonic curvature function (i.e., a class A Bezier curve) are considered to be fair (i.e., beautiful) curves, but their aesthetic analysis has never been performed. The aesthetic analysis performed by the authors of this work means that this is no longer the case. To confirm the conclusions of the authors' research, a survey of the "aesthetic appropriateness" of certain Bernstein-Bezier curve segments was conducted among 240 children, aged 14-17. The results of this survey have shown themselves to be in full accordance with the authors' results.

The article analyzes the humanistic basis of expo-design in conjunction with the ideological problems of modern design and the causes of their occurrence. It reveals the potential of mobile exhibition for social transformation in terms of its structural and ideological aesthetic content. It substantiates the effectiveness of expo-design expression's artistic and aesthetic means in viewer personality moral education. It investigates the features of social problems design presentation in the unity of the formative and design material components features of mobile exhibition.

This article studies families of curves with monotonic curvature function (MC-curves) and their applications in geometric modelling and aesthetic design. Aesthetic analysis and assessment of the structure and plastic qualities of pseudospirals, which are curves with monotonic curvature function, are conducted for the first time in the field of geometric modelling from the position of technical aesthetics laws. The example of car body surface modelling with the use of aesthetics splines is given.