Introduction:
Model:
VectorN vs Vector3:
VectorN supports any amount of dimensions without losing on functionality. Vector3 merges all XYZ to a single binary value, VectorN stores data to a buffer and is more optimized for extremely large vectors.
VectorN also includes 10+ different formats to store data with differing pricision and new functions such as Project for projecting across dimensions and Rotate.
Is this a drop in replacement?
This would work very well as a drop in replacement as it extends Vector3s existing abilities. But because support N dimensions is a priority functions like :Cross have been dropped.
VectorN is slower than native Vector3 because it is running in a Luau container unlike Vector3s which are in C++. Vector3 also uses less memory because it does not package information such as dimensions and byte style. This does not mean VectorN is slow, VectorN is extremely performant especially for large databases.
Documentation
.new functions
new: (...number|{number}) -> VectorN
Create a normal multidimensional vector stored in i8’s. Divides & Multiplies by 10 for decimals.
newInt16: (...number|{number}) -> VectorN
Uses i16 instead of i8s.
newInt32: (...number|{number}) -> VectorN
Uses i32 instead of i8s or i16.
newUint16: (...number|{number}) -> VectorN
Like newInt16 but does not support negatives in exchange for more range.
newUint32: (...number|{number}) -> VectorN
Like newInt32 but does not support negatives in exchange for more range.
newF32: (...number|{number}) -> VectorN
Like i32 but supports decimals similar to normal .new but instead it does not use division + multiplication.
newF64: (...number|{number}) -> VectorN
Like f32 but more range.
newInt16d10: (...number|{number}) -> VectorN
Like Int16 but also supports decimals by dividing and multiplying. Has less range.
newInt32d10: (...number|{number}) -> VectorN
Like Int32 but also supports decimals by dividing and multiplying. Has less range.
newUint16d10: (...number|{number}) -> VectorN
Like Uint16 but also supports decimals by dividing and multiplying. Has less range.
newUint32d10: (...number|{number}) -> VectorN
Like Uint32 but also supports decimals by dividing and multiplying. Has less range.
Functions
Abs: (VectorN) -> VectorN
Returns absolute value for each axis in a new vector.
Floor: (VectorN) -> VectorN
Returns floored value for each axis in a new vector.
Ceil: (VectorN) -> VectorN
Returns value ran on math.ceil for each axis in a new vector.
Sign: (VectorN) -> VectorN
Returns 1,0, or -1 for each axis depending on if it is negative, zero, or positive.
NormalizeMagnitude: (VectorN) -> VectorN
Returns the same vector but with if x == 1 then 1 elseif x == 2 then -1.
Lerp: (VectorN, VectorN, number) -> VectorN
Linear lerping from the first vector to the second vector with the number (alpha) being the time 0-1.
Max: (VectorN, VectorN) -> VectorN
Return a vector with the largest of each axis
Min: (VectorN, VectorN) -> VectorN
Return a vector with the smallest of each axis
Dot: (VectorN, VectorN) -> number
Calculates dot product of 2 vectors
FuzzyEq: (VectorN, VectorN, number) -> boolean
Calculates if the vectors are within a tolerance
Rotate: (VectorN, number, number, number) -> VectorN
Rotates ‘vector’ by angle on dim1 and dim2
Interpret: (VectorN) -> VectorN
Returns the vector projected with one less dimension (ex: 4D → 3D)
Project: (VectorN, number) -> VectorN
Returns the vector projected from any dimension to a lesser dimension (ex: 5D → 3D)
Examples:
-- magnitude.luau
local VectorN
local V1 = VectorN.new(1,2,3.2,4)
local V2 = VectorN.new(5,4,1.7,2)
print(V1, V2, (V1-V2).Magnitude)
NOTE: This example is ported from @GrimDarkLord7’s version here
-- 4d.luau
-- includes code from: https://devforum.roblox.com/t/rotating-4d-cube/1576197
local VectorN
local Object = {}
local xSize, ySize, zSize, wSize = 3,3,3,3
local Offset3d = Vector3.new(0,5,0)
local Speed = 1/24
for x = 1, 2 do
for y = 1, 2 do
for z = 1, 2 do
for w = 1, 2 do
for f = 1, 2 do
Object[VectorN.newF64(x,y,z,w):NormalizeMagnitude()] = Instance.new("Attachment", workspace.Base)
end
end
end
end
end
for Vector, Attachment0 in pairs(Object) do
for secondVector, Attachment1 in pairs(Object) do
if Vector ~= secondVector then
if (Vector - secondVector).Magnitude == 2 then
local Rod = Instance.new("RodConstraint", workspace.Base)
Rod.Attachment0 = Attachment0
Rod.Attachment1 = Attachment1
Rod.Visible = true
Rod.Color = BrickColor.new("Cyan")
Rod.Thickness = 0.2
end
end
end
end
for Vector, _ in pairs(Object) do
Vector[1] *= xSize
Vector[2] *= ySize
Vector[3] *= zSize
Vector[4] *= wSize
end
local rotatingDim1 = 4
local rotatingDim2 = 1
while true do
for i = 1, 360 / Speed do
task.wait()
for Vector, Attachment in pairs(Object) do
local RotatedVector = Vector:Rotate(i * Speed, rotatingDim1, rotatingDim2)
Attachment.WorldPosition = RotatedVector:Project(3):To("Vector3") + Offset3d
--print(RotatedVector)
end
end
end
