Fig. 4:  A chart showing the different values of curvature range and architectonics

It is easy to see that when low curvature variability is accompanied by an obvious neglect of architectonics (quadrant 1), the resulting curves look very freehand, liberal, humanistic (as this term is defined in my article on fonts). This style can be used in expressive black-and-white artwork intended to introduce a motive of elegant looseness into the composition. An artist's goal in this case should be to fully preserve the laxity of unrestrained lines while making a recognizable sketch of the depicted object. If, however, we try to coordinate low-curvature-range lines with horizontals or verticals, their character changes quite abruptly (quadrant 2). Besides dominant directions, architectonics often imply some general tendency to align or coordinate, some degree of overall symmetry and balance. When combined with the intrinsic symmetry and evenness of low-curvature Beziers, this tendency results in the overall feeling of softness, tranquility, and simple perfection. In design, this motif is most commonly implemented by rounded edges of rectangles which give the composition the characteristic "comfortable" look. In the world of wide curvature ranges, implications change once again. Non-architectonic expressive curves (quadrant 3) are not loose or relaxed as were those in quadrant 1. Instead, they convey the feeling of randomness, expressive unpredictability; they are reminiscent of physical particles' trajectories or complex celestial orbits in the directionless universe with no "top" or "bottom." Of all four quadrants, this one is the most powerful and persuasive realization of the very idea of a free Bezier curve. In quadrant 4, curvature variability and architectonics form an amalgamation which is impressive exactly because the nature of these two fundamental concepts is, to some extent, conflicting. In such curves, we're engaged to observe the opposition of emphatically curved shapes with uncompromisingly orthogonal verticals and horizontals. That's where Gothic architecture, Art Nouveau and Art Deco design styles drew much of their inspiration. So, we see that each part of our four-quadrant scheme has some set of associated meanings and connotations, which is a sign that our basic terms of analysis - curvature range and architectonics - are not irrelevant. Each of the above discussed types of curves has its own uses (and abuses) in design compositions, as we'll see in the next sections.