In designing and building objects, there is a misconception that high-quality work requires a high degree of skill, which itself can only be gained over long periods of time. In practice, I have not found this to be the case. Instead, there are a number of discrete steps which transform raw materials into finished objects, and if the end result appears amateurish, it is usually because a step has been skipped. The shaping of edges is one such step; it is often dismissed as purely decorative, but it is of critical importance to both the visual and mechanical integrity of any object. A properly finished edge is durable, comfortable, and visually striking. The principle can be summed up by the following paradox:
But how can this be achieved? How can something look sharp, without being sharp? The key is to consider the effect of light. As the angle of a surface changes, so does the intensity of the light reflecting off of it. If the surface is a curved edge, this effect produces a visual line which is either bright or dark. In the case of convex edges this line is bright, and will only become brighter with age as any surface coatings are worn away. In the case of concave edges the opposite is true, with the line being dark and only becoming darker as time goes on. While there are theoretically an infinite number of variations and combinations of curves which produce this effect, not all of them are functional; a well-designed edge should project a sufficiently blunt surface to avoid harm to the user and to avoid damage from impacts. With this in mind, I have identified the five types of edges which are most useful, and which I will be using in all upcoming projects.
Square edges are the starting point when working with most materials, since cutting tools tend to produce straight lines. This type of edge is both weak and dangerous; it should never be kept as-is. However, if a square look is desired, or if an object is too small to support any other style, such an edge can be used, provided it is "broken" by introducing a small chamfer or round.
Chamfered edges are the simplest solution to the problem of edge shaping, and are universally applicable. They can be created by any straight-edged cutting tool, and produce a blunt utilitarian aesthetic, in part due to the wide light reflection produced along the chamfer. Their main disadvantage is that they are somewhat rough to the hand.
Rounded edges are the most durable, as they have no corners to be chipped or dented, and they are also the most comfortable to handle. They lack visual sharpness however, and overuse of this type of edge produces a soft, amorphous aesthetic; it is best used in conjunction with steps and beads.
Stepped edges are ideal for platforms and plaques, or anywhere that the shape being defined is a surface. The curved convex area provides durability, while the concave internal corner provides a dark outline. The square external corner is a vulnerability, however, and should always be lightly broken after the initial shaping.
Beaded edges provide equivalent functionality where a large surface is absent, such as on legs or pillars. They are structurally similar to a rounded edge, but with a dark line provided by the grooved area. This groove does weaken the edge however, and under severe impact the bead is liable to bend or break, although the depth of the groove can be adjusted to compensate for this.
Although I believe this list of edges is complete, the usage cases described above are only suggestions. Where each edge is best suited is a design choice specific to each individual project, and this is so open-ended that I don't believe it is useful to make any hard rules in this regard. Likewise, I avoided mentioning any specific materials or tools, as I believe this principle is general enough to apply to any object, and simple enough to be created with any equipment.
The visual improvement brought about by properly shaped edges is immediate and overwhelming, and has the effect of masking imperfections by drawing a sharp border around the project as a whole. By defining and categorizing this subject, my intent is to provide a unified and functional aesthetic for my own projects, and for anyone else who may be struggling with the subject at hand. Future work will continue to test this concept, but at this point I believe it has already greatly improved the quality of my work.