In the tutorial about modeling mechanical surfaces, I mentioned that most corners look best if they are rounded. The general term for rounding corners is called filleting (sounds just like it's spelled). The most efficient way to fillet a corner is to use two cp's to define the curve's end points and then adjust their bias values to make the sides straight and orthogonal. But there are a number of ways to treat the magnitudes of the end points to achieve similar results.
The image at right shows two corners filleted using different settings at the end points. The lower corner uses splines with the default mag of 100 while the upper corner uses mags set at 130 to give a near circular shape. Neither of them look very real although the larger mags do give a more rounded corner. They'll work OK if they're 1/16" or 1/8" radii on a locomotive but if they are 3/4" corners on a table top I find the sharp grey-scale transitions from the flat sides to the curved surface very unnatural.
For example, here is a picture of a real 1/2" radius corner in a piece of aluminum. I painted it flat grey to eliminate any specular reflections and it's being lit with a single bulb. Notice how subtle are the light to dark the transitions around the corner. Nowhere near as sharp as in the models above.
When you lathe a circular spline with four cp's A:M assigns a mag of 167 to each cp. Since a filleted edge is just one quarter of a circle I assumed that 167 would be a good value to shape a corner. As can be seen in the wireframe on the right, the shape you get using mags of 167 is anything but circular however the look of the final corner next to the wireframe is sufficiently realistic that I'm willing to accept this level of inaccuracy.
An alternate filleting method uses a technique invented by Yves Poissant. The end points are peaked with mags of 236 to give a near circular shape and gammas of 45 to produce straight sides. I used mags of 465 which more closely matched the shape of smooth splines with mags of 167 and achieved very similar results.
The advantage of using peaked spline is that the shape of your corners do not change if you move neighbouring splines as illustrated in the image to the right. The corners on the upper left use smooth splines while the splines in the lower right are peaked. The spline at the rear of the corners was moved to change their length and the effect on the corners with the smooth splines is clearly visible.
The reason I don't use the peaked splines technique is that unless your bias handles are aligned exactly, you get creasing. In this illustration, as before, the left corner uses smooth splines and the right corner is peaked. In this case the rear spline has been scaled up slightly so it no longer matches its neighbouring spline and the creasing at the peaks is noticeable.
The downside of all these filleting techniques is that the spline layout only allows for the radius of the fillet from the top to the sides to be equal to the radius from the left side to the right side. This is not necessarily always the case on real life objects. So to model a corner that can handle this situation I recommend adding additional patches as shown on the right. The added benefit is that it actually seems to make the corner look more natural.
The real question is whether the differences in these various filleting techniques are really worth our concern.
According to the Hash Technical Reference;
"Many people become frustrated by "not being able to get all the creases out" when ultimately, it won't matter...(since)...a well textured model will not show creases as readily as a single color shaded one. Keep this in mind when you are viewing your models before you have applied textures."
In fact it goes so far as saying;
"For most models, a few creases are acceptable; they just need to be placed properly so that they accent the modeling, rather than detract from it. Creases that occur along the back of a knee or inside an elbow joint can be used to add realism to a model, while creases that occur on the side of a head can be hidden with ears or hair if necessary."
The character-centric bias of A:M shows through as the clear implication is that most of the models you will build will have kness and elbows. Unfortunately most hardware doesn't have convenient places to hide creases. However the effect of applying textures can't be dismissed. The following image shows all the sample corners illustrated in this tutorial with a marble like texture added. The corner using default mags of 100, in my opinion the most unrealistic of the models, is in the lower right corner.
Having laid out the evidence, I leave it to you to decide how obsessive you want to get when you model edges and corners.
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