It's nice that they issued a series of clarifications. I wonder if they were getting tired of the discussion, or just concerned that teams might get the wrong impression? (Or, in fairness, were they motivated independently?)
Quote:
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Originally Posted by Team Update #8
Finally, we have started to receive a number of questions about “curves” vs. “corners”. The guidance that will be provided to the Robot Inspectors is as follows: Curves are considered infinite vertices or corners, thus any exterior curve must be completely protected by bumpers and be flanked by two six-inch segments of straight bumper.
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However, (isn't there always a "however"?) the definitions of corner and curve presented there are inconsistent with conventional usage. Geometrically, a corner is analogous to a cusp in Cartesian geometry (a discontinuity in the radius of curvature), where the adjoining segments are not mutually tangent at their intersection. By contrast, a (smooth
1) curve has a continuous radius of curvature function. Given these very standard definitions, it's more than a little confusing to invent the fiction that a curve is a corner (or even a series of corners).
Now, I understand the reasoning: we're looking at a curve as a series of segments, sort of like we do in calculus. But that's an approximation of a mathematical construct. In math, it's properly described as the
limit of that relationship—which is most assuredly not piecewise for a smooth curve, but rather a continuous function. And in the physical world, infinitesimal segments lying along a curve do not accurately represent the microscopic structure of an object. Either way, it's a poor approximation: a smooth curve is not
actually a series of segments—to contend otherwise is like saying that because we can represent the Earth's surface as flat on a map, we should assume that in law, the Earth
is flat.
Even accepting the idea of a large number of small segments, consider that as the number of corners goes to infinity, the angle of the infinitesimal corners goes to 180°—this is a series of flat surfaces of infinitesimal length, with corners infinitely close to 180°. You might argue that 180 − ε is not really a corner, since it can't be directly percieved as a corner to an astute observer (the test proposed and repeated by the Q&A).
But I guess we shouldn't mathematician the rules.
And more importantly, since each flat surface has infinitesimal length, there's no way to stick a single 6 in segment of bumper on it. If you're using the many-segments definition of a curve, there's nothing within the rules that would relieve you from the minimum segment length requirement. So you must accept that a single segment of bumper can span multiple facets of the bumper perimeter, as would be necessary to allow curves made of infinitesimal segments. It would follow, then, that you could also bend a 6 in piece of plywood
2 around any other corner (90° or otherwise), leaving 3 in on either side? But, no, the Q&A has ruled against this scenario as well.
And then, even if you accept the idea that you can bend the bumpers around these infinitesimal faces with a single segment, there's still the problem of the statement that a curve must be "flanked by two six-inch [or longer
3] segments of straight bumper". All of the "corners" within the curve don't need two adjacent segments of bumper (and couldn't have them, because the faces are infinitesimally long)—what makes the tangent points (or the nearest "corners") different? Why do these ones need to be flanked by separate segments, and not the others within the curve?
For so many reasons, this small portion of the update is hugely flawed.
What does this all mean, practically speaking? The update titles this section a clarification, and calls the bumper information guidance to inspectors—as distinct from a rule for teams to follow. While that's great to know, I want to know what the enforceability of this is. Does FIRST intend for teams to be declared in violation of <R08> if they do not heed the "guidance that will be provided to the Robot Inspectors"? If it's a rule, say it's a rule—this was a perfect chance to just say so, plainly and clearly.
I'm a little disappointed with the way the bumper rule evolved over the course of the season so far. At the beginning of the year, I was quite happy to see the modifications to the bumper rule, which addressed a few major sticking points from previous seasons. But it looks like the desire to leave <R08> unchanged (the fact that it remains unamended was repeatedly mentioned in the Q&A forum and again in this update) has caused the window for a practical rule change to close. It's now pretty late in the build season; frames and robots are nearing completion. It's awful policy to spring a non-obvious interpretation like this on the teams at this late stage. Even if FIRST feels justified in defining corners and curves in the manner presented in this update, there's a real need to consider whether the teams were also operating under the same definitions. Given that FIRST departs from mathematical convention in the update, I don't see how it would be justified to assume that teams could have expected this interpretation.
There will be a small number of teams that will be forced to redesign their bumpers and frames at this stage, despite having followed the previous Q&A guidance and the rules. These were abundantly clear that there was nothing to prohibit curved bumpers, and provided a straightforward test to compare a curve and a corner. Given that at least one of these understandings appears rescinded (depending on your interpretation of the particulars of Update #8), FIRST may have subjected these teams to an unwarranted and potentially major inconvenience.
1Technically, even a piecewise function is a curve, so I clarify it with "smooth", to put it into the proper context.
2I realize that bending plywood is difficult; that's immaterial. Let's say for argument's sake that the team is using balsa plywood, or lots of steam and pressure.
3We can probably assume this.