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Posted: Thu Apr 02, 2020 8:51 am
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Posted: Thu Apr 02, 2020 1:52 pm
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Posted: Fri Apr 03, 2020 3:37 pm
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Posted: Fri Apr 03, 2020 7:10 pm
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Southern Cross Nemesis Vice Captain
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Posted: Sat Apr 04, 2020 9:21 am
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Posted: Sat Apr 04, 2020 10:32 am
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Southern Cross Nemesis Assuming, I correctly remember algebra. sweatdrop 3d objects are multiplied by 3 Volume of a sphere = 4/3 π r^3 Saving you from the math. 33510.32 ft^3 And then divide that by 5 ft^3(the space you allocated for each victim) = 6,702.064 So 6,702 vic's and someone's right pinky toe will be affected by your fireball. Assuming you eliminated the ground from the equation and can shepherd everyone into a freefall ball. i am slitly sceptical as it seems a excedingly large number but you do seem to also know what your talking about and i like your wording.. did you by eny chance use a blender before you placed the "vic's" in to the area of the Fire Ball? if so i commend you for your creativity & dedication to maximum efficiency.
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Posted: Sat Apr 04, 2020 5:41 pm
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Southern Cross Nemesis Vice Captain
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Posted: Sat Apr 04, 2020 7:10 pm
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Posted: Sun Apr 05, 2020 8:55 am
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I think it has to be measured from a crosspoint to be a "true" 5' radius (in cubic space!).
OO OO
For example, in 2D battlefield, a 5' radius spell should only hit 4 targets.
In 3D space, 5' radius would hit 8 targets.
10' radius, it adds another 2x2 set of targets to each face of the above 2x2x2 cube. 8 + 24 = 32 targets.
15' radius, it extends out another 2x2 set of targets (+24), and the existing extension gets another "layer" of cubes around it. They overlap a bit though, so don't double-count. A single second layer gets 2 more cubes on each side, turning it into this thicc cross:
OOO OOOO OOOO OOO
However, each of those second red O's will be shared with another layer extension. How I'm thinking of it at early-o-clock in the morning is +8 for the top layer, +8 for the bottom layer, and +8 for the middle four that don't double up on the top or bottom. Another +24. So we're at 8+24+24+24 = 80 targets.
20' radius, here we go! Extend out another 2x2 on the edge like before (+24), the previous extension will chonk up but be far enough removed from each other to not overlap so 6x8=+48, the previously extended layer chonks a second time:
OOOO OOOOO OOOOOO OOOOOO OOOOO OOOO
The red O's will be shared like in the previous example, so you get the same situation of +8+8+8 (top, bottom, and middle that aren't shared). The blue is it diagonaling out, again getting shared but it only gets counted once for the 8 45-degree parts of this sphere so another +8. My final tally is 8+24+24+24+24+48+24+8 = 184 total targets.
That all said, even though I'm a numbers guy, I'm extremely bad at visualizing math graphically. Generally, spheres aren't measured in cubic intervals so that breaks my brain even more, and I'm not confident of my answer. I ran out of d6s to visualize past the 10' radius example. I know every cube face basically gets another cube stuck to it from the prior example as it expands outwards. If we weren't in a quarantine position, I'd run to the store and get a bunch of marshmallows and toothpicks and make a visual example to post here as a thinly-veiled excuse to get an extreme sugar high later. Alas, not today.
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