A mathematical design and evaluation of Bernstein-Bezier curves' shape features using the laws of technical aesthetics

摘要

We present some notes on the definition of mathematical design as well as onthe methods of mathematical modeling which are used in the process of theartistic design of the environment and its components. For the first time inthe field of geometric modeling, we perform an aesthetic analysis of planarBernstein-Bezier curves from the standpoint of the laws of technicalaesthetics. The shape features of the curve segments' geometry were evaluatedusing the following criteria: conciseness-integrity, expressiveness,proportional consistency, compositional balance, structural organization,imagery, rationality, dynamism, scale, flexibility and harmony. In thenon-Russian literature, Bernstein-Bezier curves using a monotonic curvaturefunction (i.e., a class A Bezier curve) are considered to be fair (i.e.,beautiful) curves, but their aesthetic analysis has never been performed. Theaesthetic analysis performed by the authors of this work means that this is nolonger the case. To confirm the conclusions of the authors' research, a surveyof the "aesthetic appropriateness" of certain Bernstein-Bezier curve segmentswas conducted among 240 children, aged 14-17. The results of this survey haveshown themselves to be in full accordance with the authors' results.