Veril
Frame Savant
Calculating distance between hit and hurtbubbles:
The z-offset had me stumped for a little while... but I've figured out a fairly simple way of finding the distance between 2 bubbles, assuming you know the true (bone and move specific) offsets and size of both.
space between 2 bubbles = {((x_offset_1-x_offset_2)^2+(z_offset_1-z_offset_2)^2)+(y_offset_1-y_offset_2)^2}^1/2 - (size_1+size_2)
disjoint variant, requires hurtbox1 and hitbox2 anchored to the same bone = {((x_offset_1-x_offset_2)^2+(z_offset_1-z_offset_2)^2)+(y_offset_1-y_offset_2)^2}^1/2 - (size_1-size_2)
This uses the Pythagorean theorum twice. WTF is Veril doing, you ask? Well you didn't actually ask but I'm answering anyway! The value we're trying to get is the distance between the closest points on each sphere. To find that you draw a straight line connecting the center point on each sphere. These points are represented by their respective coordinates on the grid (x,y,z). If you kids were paying in trigonometry you know that finding the distance between any 2 points can be determined with the simple a^2+b^2=length of the line ^2. But but but its got a z offset, so things are a bit more complicated. The "a" here isn't just the difference between the x offsets, because the length of this line is affected by the z offset. "b", which I'm gonna use to represent the vertical side of the right triangle, is unaffected by the z-offset.
So I use another right triangle to get my "a" value. Yayuhz! As I found with RocketPsi, it'll probably be better if I just scan in a visual explanation of this rather than try to write out this part... w/e...
The size component was simple as per the fact that "size"=radius. So I simply take the 1st part of the equation (which describes the line containing the central points of both spheres) and subtract the sum of size_1 and size_2. What's left is the distance between the surface of these bubbles (which IS the value that actually matters).
if the answer is 0 or negative: the bubbles ARE in contact with eachother.
This equation WILL work without bone specific offsets for finding disjointedness IF the two bubbles are grafted to the same bone (so, like, most attacks). I BEG you people to start posting hurtbox data as I have no way to use Tabuu atm (even at school, stupid net framework!).
Older stuff:
I had wondered how the size value in psa translated into actual hitbox size in the game. Rocketpsi gave me an idea as to how to setup a test for whether the size value was the radius or diameter, and I figured out a pretty simple proof that shows some important facts about these values:
Size = hitbubble radius
Here's how I figured that out (Rocketpsi brought up a different method to get the same result and put me on the right track, <3)
If the x offsets of two hitbubbles, grafted to bone 0, are equal to -x AND x respectively
AND size =x
AND y offset is the same for both
*there is hardly ever a z-offset for a bone 0 move
If size=radius
THAN the two hitbubbles will visibly meet at one point because hitbubble hacks appear very very very slightly larger (glow >.>) than the hitbubbles actually are and if size = radius you would have the point (0,0) as a point on the perimeter of both hitbubbles.
2xradius=diameter (for those who are less math savvy)
Proof: Bowser's dair looping hitbubbles are two size 4 hitbubbles with x offsets of 4 and -4 respectively. They visibly barely overlap in the video for Bowser's hitbubbles. Check the video posted in the visible hitbubbles link thread (good ****) for Bowser and look at the dair.
Circle (since we're ignoring the z-axis because the offset is 0)
hitbubble formula if the bone=0: (x-a)^2 + (y-b)^2+(z-c)^2=r^2
a = x offset
b = y offset
r = size = radius
x and y are variables the range of which is dictated by the radius. Here we have a finite number of values, as per there being a limit to the smallest distances measured in smash (the plank length of smash is .01 lol).
Bowser's dair loop hits:
b = y offset = 0
a = 4 or -4
r = 4
we're looking at distance between 2 hitbubbles on the x-axis, so we're going to have y = 0, and since its a circle any value of y has 2 corresponding x values.
(x±4)^2 = 16 for this to be true x = zero, which means for both these hitbubbles, they will land on the 0,0 point if r=size. Yay!
Known from hitbubble analysis: The distance values used for offsets are equal to those used for size. The smallest unit of distance in the game is .01 (the smallest interval for size and offsets). Knowing how hitbubble size mathematically equates to size in game is extremely useful right now because any move with bone 0 (and that includes a whole ton of MK's) can be modeled on an x/y axis perfectly in regards to exactly where the hitbox is.
So, hopefully this helps ppl
formula:
size in PSA=radius of hitbubble
(x-xoffset)^2 + (y-yoffset) = size^2 if bone = 0. (Rocketpsi was talking about doing a bone offset project and that would be amazing if it happened)
you can use this to find real range and graph it using a number of programs, especially if you have access to a school mathlab which I will soon.
hitbubble area = πr^2 (well, really 4/3 • πr^3 but we're ignoring z for now)
The z-offset had me stumped for a little while... but I've figured out a fairly simple way of finding the distance between 2 bubbles, assuming you know the true (bone and move specific) offsets and size of both.
space between 2 bubbles = {((x_offset_1-x_offset_2)^2+(z_offset_1-z_offset_2)^2)+(y_offset_1-y_offset_2)^2}^1/2 - (size_1+size_2)
disjoint variant, requires hurtbox1 and hitbox2 anchored to the same bone = {((x_offset_1-x_offset_2)^2+(z_offset_1-z_offset_2)^2)+(y_offset_1-y_offset_2)^2}^1/2 - (size_1-size_2)
This uses the Pythagorean theorum twice. WTF is Veril doing, you ask? Well you didn't actually ask but I'm answering anyway! The value we're trying to get is the distance between the closest points on each sphere. To find that you draw a straight line connecting the center point on each sphere. These points are represented by their respective coordinates on the grid (x,y,z). If you kids were paying in trigonometry you know that finding the distance between any 2 points can be determined with the simple a^2+b^2=length of the line ^2. But but but its got a z offset, so things are a bit more complicated. The "a" here isn't just the difference between the x offsets, because the length of this line is affected by the z offset. "b", which I'm gonna use to represent the vertical side of the right triangle, is unaffected by the z-offset.
So I use another right triangle to get my "a" value. Yayuhz! As I found with RocketPsi, it'll probably be better if I just scan in a visual explanation of this rather than try to write out this part... w/e...
The size component was simple as per the fact that "size"=radius. So I simply take the 1st part of the equation (which describes the line containing the central points of both spheres) and subtract the sum of size_1 and size_2. What's left is the distance between the surface of these bubbles (which IS the value that actually matters).
if the answer is 0 or negative: the bubbles ARE in contact with eachother.
This equation WILL work without bone specific offsets for finding disjointedness IF the two bubbles are grafted to the same bone (so, like, most attacks). I BEG you people to start posting hurtbox data as I have no way to use Tabuu atm (even at school, stupid net framework!).
Older stuff:
I had wondered how the size value in psa translated into actual hitbox size in the game. Rocketpsi gave me an idea as to how to setup a test for whether the size value was the radius or diameter, and I figured out a pretty simple proof that shows some important facts about these values:
Size = hitbubble radius
Here's how I figured that out (Rocketpsi brought up a different method to get the same result and put me on the right track, <3)
If the x offsets of two hitbubbles, grafted to bone 0, are equal to -x AND x respectively
AND size =x
AND y offset is the same for both
*there is hardly ever a z-offset for a bone 0 move
If size=radius
THAN the two hitbubbles will visibly meet at one point because hitbubble hacks appear very very very slightly larger (glow >.>) than the hitbubbles actually are and if size = radius you would have the point (0,0) as a point on the perimeter of both hitbubbles.
2xradius=diameter (for those who are less math savvy)
Proof: Bowser's dair looping hitbubbles are two size 4 hitbubbles with x offsets of 4 and -4 respectively. They visibly barely overlap in the video for Bowser's hitbubbles. Check the video posted in the visible hitbubbles link thread (good ****) for Bowser and look at the dair.
Circle (since we're ignoring the z-axis because the offset is 0)
hitbubble formula if the bone=0: (x-a)^2 + (y-b)^2+(z-c)^2=r^2
a = x offset
b = y offset
r = size = radius
x and y are variables the range of which is dictated by the radius. Here we have a finite number of values, as per there being a limit to the smallest distances measured in smash (the plank length of smash is .01 lol).
Bowser's dair loop hits:
b = y offset = 0
a = 4 or -4
r = 4
we're looking at distance between 2 hitbubbles on the x-axis, so we're going to have y = 0, and since its a circle any value of y has 2 corresponding x values.
(x±4)^2 = 16 for this to be true x = zero, which means for both these hitbubbles, they will land on the 0,0 point if r=size. Yay!
Known from hitbubble analysis: The distance values used for offsets are equal to those used for size. The smallest unit of distance in the game is .01 (the smallest interval for size and offsets). Knowing how hitbubble size mathematically equates to size in game is extremely useful right now because any move with bone 0 (and that includes a whole ton of MK's) can be modeled on an x/y axis perfectly in regards to exactly where the hitbox is.
So, hopefully this helps ppl
formula:
size in PSA=radius of hitbubble
(x-xoffset)^2 + (y-yoffset) = size^2 if bone = 0. (Rocketpsi was talking about doing a bone offset project and that would be amazing if it happened)
you can use this to find real range and graph it using a number of programs, especially if you have access to a school mathlab which I will soon.
hitbubble area = πr^2 (well, really 4/3 • πr^3 but we're ignoring z for now)
