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Message: <blockquote data-quote="EzekielRaiden" data-source="post: 9640594" data-attributes="member: 6790260">Well, properly speaking, they're still spheres, because "a sphere" is "the set of all points that are a fixed distance from a center point." It's just a sphere in so-called "chessboard" geometry, aka Chebyshev geometry, which causes "a cube" (the set of all points a fixed distance horizontally or vertically from a central point") to mean the same thing as "a sphere" (and technically "a right cylinder" too, which is "the set of all points a fixed distance away from a central axis of length equal to twice that fixed distance"). This is kind of a bugaboo point for me, because people were SO INCENSED by this simplifying approximation...but in practice it makes very, very little difference and almost always results in smoother, faster gameplay for a very slight deviation from reality.Just in case you or anyone else doesn't feel like wading through it, I'll spoilerblock it.[SPOILER="An Assemblage of Unnecessary Detail"]Realistically, the difference between a Euclidean-geometry sphere and a Chebyshev-geometry sphere really isn't as big as a lot of folks think--and, more importantly, the difference between a Chebyshev-geometry circle and a Euclidean-geometry circle is smaller still. With the way we approximate these things, you only get a meaningful difference (that is, more than about +/- 10%) when you get out to radii of about 35 feet. That is, because we approximate these things with chunky squares regardless,People throw around terms like "square fireballs" or "firecubes" without actually putting any thought into what they're complaining about, most of the time. "It's utterly ridiculous to have a square-shaped fireBALL!" Okay, but we already have fire"ball"s made of cubical chunks, not an actual sphere to begin with. (Or, rather, 99.9% of the time, we have fire"circle"s made up of a bunch of chunky squares.)We can quantify the difference between the 4e approximation--aka Chebyshev geometry--and a true circle quite easily. It is, always and exactly, (4-π)/π, or about 27.324%. But the difference between a chunky-approximated circle and the 4e approximation is rather less clean, because it's not going to be a perfect amount and it's going to vary as our circles get larger--but, crucially, the chunky-approximated circle is also wrong, albeit often by a smaller degree.As an example: Imagine a circle of radius 15. Per 5e's rules, that circle must be centered at a grid intersection point, and will entirely cover every 5' square which has at least 50% of the area inside the circle. As a result of this, for a circle of radius 15'...the only difference between this "circle" and a 4e-style circle is four corner squares. Indeed, the same applies for a 10' circle as wel. Here's a table for radii from 5' up to 40':<table style='width: 50%'><tr><td style='width: 33.3333%'>Radius (ft)</td><td style='width: 33.3333%'>Diff (5' sq.)</td><td style='width: 33.3333%'>Relative diff (%)</td></tr><tr><td style='width: 33.3333%'>5</td><td style='width: 33.3333%'>0</td><td style='width: 33.3333%'>0</td></tr><tr><td style='width: 33.3333%'>10</td><td style='width: 33.3333%'>4</td><td style='width: 33.3333%'>33.33...%</td></tr><tr><td style='width: 33.3333%'>15</td><td style='width: 33.3333%'>4</td><td style='width: 33.3333%'>12.5%</td></tr><tr><td style='width: 33.3333%'>20</td><td style='width: 33.3333%'>12</td><td style='width: 33.3333%'>23.076923...%</td></tr><tr><td style='width: 33.3333%'>25</td><td style='width: 33.3333%'>20</td><td style='width: 33.3333%'>25%</td></tr><tr><td style='width: 33.3333%'>30</td><td style='width: 33.3333%'>32</td><td style='width: 33.3333%'>28.571428...%</td></tr><tr><td style='width: 33.3333%'>35</td><td style='width: 33.3333%'>40</td><td style='width: 33.3333%'>~25.64%</td></tr><tr><td style='width: 33.3333%'>40</td><td style='width: 33.3333%'>48</td><td style='width: 33.3333%'>23.076923...%</td></tr></table>As you can see, it's dancing around the 27% figure, depending on whether the base circle is an under-estimate (as is the case for 15' and 30') or an over-estimate (as is the case for most circles). While the absolute difference obviously rises without bound, the relative difference is...about a quarter.So people are literally freaking out over this so-called wildly unrealistic approximation...that basically just increases areas by about 25% relative to the approximations we were already using. Indeed, in most cases, the error is actually smaller than 25%, because the "at least 50% covered" thing is also usually an over-estimate, albeit not always.[/SPOILER]TL;DR: People flip out about how unrealistic "square fireballs" are, but they're really only ~25% bigger most of the time, and the tiny number of added squares so rarely make a difference that it's really not a thing to get all worked up about."4e physics" really wouldn't be any different. Now, 4e magic would be quite a bit different! But that's a different story.</blockquote>

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