I’m having trouble trying to calculate whether a part is within the boundary or perimeter of a bunch of points. I’ve already tried searching this online and come across a function that works except for certain shapes.

This works but only with a polygon that is convex. Even if it does work, it returns false at positions that should return true because of the polygon not being convex.

local function PointWithinArea(Point, Points)
local Side
for i = 1, #Points do
local Point0 = Points[i]
local Point1 = Points[i == #Points and 1 or i + 1]
local Value = (Point1 - Point0):Cross(Point - Point0).Y > 0
if Side ~= nil and Value ~= Side then
return false
end
Side = Value
end
return true
end

You provided only works for convex polygons. For concave polygons, you’ll need a different way.
One common method for concave polygons is raycasting.
Check if a point is inside a polygon defined by a set of points.

raycasting would only work if there are physical parts surrounding the polygon. I want to avoid this and purely just have positions. Even if I were to do this, how can I detect whether a polygon is convex or concave?

To check for concavity you need to examine the angles formed by adjacent vertices. If any angle is greater than 180 degrees, the polygon is concave.
But yea raycasting typically involves intersecting rays with physical geometry like parts, but it can also be simulated mathematically for non-physical representations like polygons defined by points.

I was able to find the solution by porting this code to Luau, it works flawlessly with both concave and convex polygons.

Here is the ported version:

local function pointInPolygon(point, polygon)
local intersections = 0
local x, y = point.X, point.Z
for i = 1, #polygon do
local x1, y1 = polygon[i].X, polygon[i].Z
local nextVertex = polygon[i+1] or polygon[1]
local x2, y2 = nextVertex.X, nextVertex.Z
if (y < y1) ~= (y < y2) and x < (x2 - x1)*(y - y1)/(y2-y1)+x1 then
intersections += 1
end
end
return intersections % 2 == 1
end