%Increased Area, how does it work with conical aoe's?
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Warning, slight math ahead.
The formula for the area of a circle is A = pi * r^2 . So, given its radius, the formula for the area of a circle is r = (A / pi)^.5 . The formula for the area of a quartercircle is easy, one quarter of a circle. A = .25 * pi * r^2 . Then, the formula for the radius of a semicircle is r = {4 * A / pi)^.5 , which simplifies to r = 2 * (A / pi)^.5 . So as you can see, mathematically, %increases to area should be 2x as effective on the radius for quarter-circle aoe's. My question is whether this will be the way the game handles it, or if %increases to area will be converted back into %increases to radius before they are applied (meaning the radius is always affected the same way by x% of increased area)? edit: messed up the math, nvm builds: https://www.pathofexile.com/forum/view-thread/1663570/ Last edited by ThatsSoGoodman on Feb 27, 2017, 8:47:30 PM Last bumped on Feb 28, 2017, 12:14:51 AM
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And they said the change was because area would be easier to understand and calculate than radius...
Sorry can't help you my nose is bleeding from the math. | |
" My educated guess is they will just modify the radius by the square root of area bonus, that would likely be the simplest way to do it. So, if you got 40% increased area that will, if you input sqrt(1,4) be the same as having 18,3% increased radius. So, there will be no difference. Wish the armchair developers would go back to developing armchairs. ◄[www.moddb.com/mods/balancedux]► ◄[www.moddb.com/mods/one-vision1]► Last edited by raics on Feb 27, 2017, 6:49:44 PM
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" Your math is not correct. The area for a quartercircle is indeed A = .25 * pi * r^2 . But the resulting formula for the radius is r = ((4 * A)/pi)^.5 . A = .25 * pi * r^2 | * 4 A * 4 = pi * r^2 | / pi (A * 4) / pi = r^2 | ^.5 ((A * 4) / pi)^.5 = r That said, i think its the same because the area of a quartercircle is directly proportional to the area of a full circle. All incresed AoE together are a multiplicator for the Area and then you scale it simply down to a quarter so there should be absolutly no difference in radius, if the radius was the same at the beginning. Last edited by Abelarde on Feb 27, 2017, 7:26:19 PM
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"This is correct. For a simple demonstration of this concept, take the example of a circle with a total area of exactly 4. A quarter-circle with the same radius must have area 1, because it covers exactly one quarter of the area of the whole circle. Both have the same radius, which we'll call r1 - we don't need to calculate the value. If we double the area of the circle, it now has area 8. It also has a larger radius, which we'll call r2. A quarter-circle with the same radius (r2) as this larger circle must by definition have area 2, since again, it's a quarter of the larger circle's area. So we know that increasing the area of the whole circle with radius r1 by 100% (from 4 to 8 area), results in a circle with radius r2. If we start with a quarter-circle of radius r1, we know it has area 1. If we increase that area by 100%, we know it will have area 2 - but we've already shown that a quarter-circle with area 2 has radius r2. So increasing the area of a circle and a quarter circle with the same base radius (r1) results in the same final radius (r2). | |
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Yeah I messed up, the increases to area will be inside the square root. So with 100% increased area,
Circle: r1 = (A / pi)^.5 r2 = (2 * A / pi)^.5 r2 = (2)^.5 * (A / pi)^.5 r2 = (2)^.5 * r1 Quartercircle: r1 = 2 * (A / pi)^.5 r2 = 2 * (2 * A / pi)^.5 r2 = (2)^.5 * r1 And even for a triangular area such as Ground Slam's, to maintain similarity you must multiply the base and height by the same number, so to double area you still multiply those by sqrt(2). Only if the aoe has a fixed heighth or width would increases to area have a disproportionate effect, because then similarity would not be maintained. I thought Bladefall and Flame Surge had fixed-width aoe's, I can't think of any other skills like that? builds: https://www.pathofexile.com/forum/view-thread/1663570/ Last edited by ThatsSoGoodman on Feb 27, 2017, 7:51:15 PM
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" To be super picky, the only error he made was order of operations. In r = (4 * A / pi)^.5 The part in the Parentheses must be calced in full before dealing with the Exponent. Can't pull the 4 out of there. The extra Parentheses added around 4*A really are redundant since Multiply Divide happen left to right unless otherwise indicated. So (4 * (A/pi)) would be needed internal Parentheses, ((4 * A) / pi) are not. Support a free Hong Kong.
I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use. -Galileo Galilei |
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"Pulling out the 4 is fine. 4 is 2 squared, so you can distribute the exponent and do 4^.5 which = 2. You can try it with different square roots like sqrt(28) or sqrt(36) and see that it works. builds: https://www.pathofexile.com/forum/view-thread/1663570/
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" Can you tell I'm rusty ;p I'm going back to bed now. Support a free Hong Kong.
I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use. -Galileo Galilei |
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That's the problem I have with how new AoE modifiers work - square roots.
Before, if I have, say, 30% inc radius, and get another 20%, I can, you know, just instantly estimate - without any tools, just calculate in my head - what effect it will make on my aoe: 20/130 = about 15% more radius (because let's face it, radius is what you use to measure your coverage, not "area"). Now what I have to do in same situation but with "area" instead of "radius": sqrt(130+20)/sqrt(130)-1 = 7.5%. No fucking way I could do this without a calculator. In a meaningful amount of time, at least. Now I understand to plan a build you use not only that but excel and other shit, but just to estimate an effect of one increase I now have to use external tools? This is wrong way to do it, GGG. I shudder to think what lies ahead if this is the path you've taken for solving modifier-stacking problems. And worst change is putting almost all bosses in new version of maps into fucking small areas, where you can't kite well or dodge stuff. What a terrible idiot invented that I want say to him: dude flick you, seriously flick you very much.
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