Few fixes (Thanks to @jonbyte) and some more documentation
Here is the changes: Few fixes and documentation · CodesOtakuYT/CodesOtakuModules@5d6e823 (github.com)
Added tons of new functions, and some fixes 
Also documented everything decently for now
{
--> Practical functions
lerp = lerp, -- takes a range [a -> b] and a t value [0->1]. it returns a value travalling from a to b linearly, where t is the percentage it advanced (Ex: 50% = 0.5)
inverseLerp = inverseLerp, -- takes a range [c -> d] and a value x, it returns the t value of the value in range, basically where the value is relative to the range.
map = map, -- lerp(o1, o2, inverseLerp(i1, i2, x)), remaps a value x from the range [i1->i2] to [o1->o2], can be useful to create sliders.
--> Calculus
compositeDerivative = compositeDerivative, -- (f(g))' = f'(g)*g'
--> Table Math
mapT = mapT, -- Gets a table [x1, x2, x3...xn] and a function, returns [f(x1), f(x2), f(x3)...f(xn)]
filterT = filterT, -- Gets a table and a function, returns a new table with the elements that evaluated the function f(value, key) to true
countT = countT, -- Accumulates the result of a function f(v, k) traversing a table, returns the accumulated value
countMulT = countMulT, -- The same as countT but with multiplication
sampleT = sampleT, -- Sample function output n times from x1 to x2 linearly
----> Vector math
distanceV = distanceV, -- Returns the distance between the position vec1 and vec2
midPosV = midPosV, -- Returns the middle position between the position vec1 and vec2, equivalent to lerp(vec1, vec2, 0.5)
applyV = applyV, -- Returns a new Vector3 by applying a function on the X, Y and Z components of a Vector3
absV = absV, -- Returns a new Vector3 where all the components of the vector are absolute (positive or nil)
-- Helper functions
copyT = copyT, -- Returns a copy of a table
invertT = invertT, -- the keys becomes the values and vice versa, takes a table [y1 = x1, y2 = x2...yn = xn], returns [x1 = y1, x2 = y2...xn = yn]
zipT = zipT, -- takes 2 tables and zip them together {{t1[1], t2[1]}, {t1[2], t2[2]}...{t1[n], t2[n]}}
unzipT = unzipT, -- the inverse of zip, takes 1 table of pairs and unzip it into 2 tables
valuesT = valuesT, -- return a table of all the values inside the table, there is also recursive mode for nested tables
keysT = keysT, -- the same as valuesT, but for table keys
}
Tons of new functions and some fixes! · CodesOtakuYT/CodesOtakuModules@c3bb372 (github.com)
You should add more trigonometric functions like these ones
versin = function(x) return 1 - math.cos(x) end -- versin(θ) = 1 - cos(θ) = 2sin²(θ/2)
coversin = function(x) return 1 - math.sin(x) end -- coversine(θ) = 1 - sin(θ)
exsec = function(x) return (1 / math.cos(x)) - 1 end -- exsecant(θ) = sec(θ) - 1 = 1 / cos(θ) - 1
haversin = function(x) return 1 / 2 * (1 - math.cos(x)) end -- haversine(θ) = sin²(0⁄2) = 1 - cos(θ) / 2
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You can commit it to github and I’ll accept it. otherwise I can add them myself. Thanks for your contribution
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You could also add exponential lerp functions (non-linear)
--Credits to https://github.com/FreyaHolmer/Mathfs/blob/e13700a9636190a118730c09a389aa316d8ec240/Mathfs.cs
eerp = function(a, b, t) --exponential lerp
return a ^ (1 - t) * b ^ t
end
ieerp = function(a, b, t) --inverse exponential lerp
return math.log(a / t) / math.log(a / b)
end
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Ohh, that’s interesting, I’ll add them in the next update for sure, thanks a lot!
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Update: Update Math.lua · CodesOtakuYT/CodesOtakuModules@2981170 (github.com)
New functions:
----> Practical functions
lerpExp = lerpExp, -- exponential lerp
invLerpExp = invLerpExp, inverseLerpExp = invLerpExp, -- inverse exponential lerp
----> Pure mathematical functions
versin = versin, -- versin(θ) = 1 - cos(θ) = 2sin²(θ/2)
coversin = coversin, -- coversine(θ) = 1 - sin(θ)
exsec = exsec, -- exsecant(θ) = sec(θ) - 1 = 1 / cos(θ) - 1
haversin = haversin, -- haversine(θ) = sin²(0⁄2) = 1 - cos(θ) / 2
----> Random
randomItemT = randomItemT, -- Returns a random key in table
random = random, -- returns a random number in range [a,b]
randomN = randomN, -- returns a random integer in range [a,b]
Thanks to @thrixtle for his contribution:
versin, coversin, exsec, haversin, lerpExp, invLerpExp
Looking forward to hear your feedback everyone!
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Am gonna revamp the documentation a bit in the future update, and add with it useful resources like such image links and desmos graphs (the way I personally learn and enjoy math) if needed
I found this cool function while watching this youtube video, and I thought it could be useful.
local function factorial(n)
if (n == 0) then
return 1
else
return n * factorial(n - 1)
end
end
local function fastFactorial(n)
return math.sqrt((2*n + 1/3) * 3.1415926535897932) * (n / 2.718281828459045) ^ n
end
print(fastFactorial(50)) --> 3.0414009581301e+64
print(factorial(50)) --> 3.0414093201713e+64
print(factorial(50) / fastFactorial(50)) --> 1.0000027494044215
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Update:
Update Math.lua · CodesOtakuYT/CodesOtakuModules@58de414 (github.com)
deepCopyT = deepCopyT, -- Returns a copy of the table and all of the tables inside it, if isKeyCopy, then it will also deep copy the keys of the table if they're also tables, it also supports cyclic tables copying.
toRawT = toRawT, -- returns a one dimensional table copy of a complex recursive table
randomV = randomV, -- returns a unit vector3 as a random direction
angleV = angleV, -- Returns the angle between the given vectors or vector
fastFactorial = factorialFast, factorialFast = factorialFast, -- x! but sacrifice accuracy for speed
This update’s contributions:
Bug thrixtle: fastFactorial
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