When it comes to form, designers often follow rules and criteria, rooted deeply in art theory and geometry. A small part of this relates to curve and surface continuity or in other words; how well shapes flow. Good and bad examples of this can be observed through quality of reflections when we pass cars or hold reflective plastic objects. This is the simplest way to evaluate if shapes flow well and to spot any imperfections. In this blog post we will take a look at four levels of how two surfaces can meet and what that means practically.
The most primitive level of continuity is when two surfaces share their meeting position, but are not tangent. In this case the reflection simply breaks at the border and we are left with a sharp edge. This type of continuity is aesthetically not problematic, since there is no actual continuity, hence the name G0.
Moving on to the next type of edge, we have two surfaces that share not only position but also direction, meaning they are tangent. In the cross section above, that means that they share the same direction vector at their meeting point. This type of edge serves its function perfectly fine, as it is no longer sharp. However, aesthetically tangent fillets have a flaw of having a fixed radius, which means that at the meeting point there is a sudden change of curvature. When observing reflection on such surfaces, you can spot a sudden break, even though at first these surfaces seem to flow into another just fine.
The solution to this flaw is to design surfaces in a manner where they do not only share the same position and tangency, but also the same curvature. This effectively solves the issue of abrupt reflection. If you were to turn such object under a light, instead of a sudden break, the reflection would now flow smoothly from on surface into another.
G2 continuity is still not perfect. Even though surfaces are now tangent and share the same curvature, they do not have the same curvature acceleration. If you take a look at the image above, the G2 curvature combs coincide, but they change abruptly. Matching the curvature acceleration makes reflection even smoother. This level of surface quality is standard in automotive design and in well-designed consumer electronics.
When talking about surface quality, we are not talking about good or bad design. A product could have perfectly executed surfaces, but still not meet the functional or aesthetical needs of a certain use case and vice versa. Surface quality itself doesn't make design good, but it does make good design better.