  Unlike many other works, where authors are usually focused on one or two
quality criteria, the current manuscript, which is a generalization of the
article [35] published in Russian, offers a multi-criteria approach to the
assessment of the shape quality of curves that constitute component parts of
the surfaces used for the computer modelling of object shapes in various types
of design. Based on the analysis of point particle motion along a curved path,
requirements for the quality of functional curves are proposed: a high order of
smoothness, a minimum number of curvature extrema, minimization of the maximum
value of curvature and its variation rate, minimization of the potential energy
of the curve, and aesthetic analysis from the standpoint of the laws of
technical aesthetics. The authors do not set themselves the task of giving a
simple and precise mathematical definition of such curves. On the contrary,
this category can include various curves that meet certain quality criteria,
the refinement and addition of which is possible in the near future.
Engineering practice shows that quality criteria can change over time, which
does not diminish the need to develop multi-criteria methods for assessing the
quality of geometric shapes. Technical issues faced during edge rounding in 3D
models that affect the quality of industrial design product shape have been
reviewed as an example of the imperfection of existing CAD systems.
