Ok so basically what I wanna do is make a bunch of parts which are put together to make a straight line which indicates the route troops will be going on a circular earth map. I think what I wanna do is like generate points in-between those 2 points (the position of the troop and the mouse hit position) as if it were a circle and those generated points would be the line part positions. I think I’ll have to do some math and trigonometry but I suck at that.

You can use pathfinding service to calculate the path, then loop through all of the waypoints and put a part at the position of that waypoint.

local PathfindingService = game:GetService("PathfindingService")
local Point1 = --start position Vector3 value
local Point2 = --end position Vector3 value
path:ComputeAsync(Point1, Point2)
local waypoints = path:GetWaypoints()
for I, waypoint in pairs(waypoints) do
local part = Instance.new("Part", workspace)
part.Position = waypoint.Position
part.Anchored = true
part.Size = Vector3.new(1,1,1)
end

Hmm here’s a solution using rotation between two vectors

Except modified to use a decimal percentage:

local function AngleBetween(vector1, vector2)
return math.acos(math.clamp(vector1.Unit:Dot(vector2.Unit), -1, 1))
end
local function rotateVectorAround( v, amount, axis )
return CFrame.fromAxisAngle(axis, amount):VectorToWorldSpace(v)
end
local function rotateVectorSpherePointsPercentage(point1,point2,centerOfSphere,decimalPercentage)
local radius1 = point1-centerOfSphere
local radius2 = point2-centerOfSphere
local angle = AngleBetween(radius1,radius2)
local rotationAxis = radius1:Cross(radius2)
if not (radius1:Dot(radius2) > 0.99999) then -- if there is a rotation
local radius3 = rotateVectorAround(radius1,angle*decimalPercentage,rotationAxis)
local pointOnSphere = centerOfSphere+radius3
return radius3
end
end

The idea what the rotateVectorSpherePointsPercentage function. By rotating the radius vector of the sphere from point1 to point2.

And here’s the code I used to generate the above image:

local sin, cos, acos = math.sin, math.cos, math.acos
function slerp(p0, p1, t)
--From https://en.wikipedia.org/wiki/Slerp
-- See "Geometric Slerp"
local l = p0.Magnitude
p0 = p0.Unit
p1 = p1.Unit
local Omega = acos(p0:Dot(p1))
return (
p0 * sin( (1 - t) * Omega) / sin(Omega) +
p1 * sin( (t ) * Omega) / sin(Omega)
) * l
end
local steps = 10
local A, B, C = game.Workspace.A, game.Workspace.B, game.Workspace.C
local last_p = A.Position
for i = 1/steps, 1, 1/steps do
local c = C:Clone()
local p = slerp(A.Position, B.Position, i)
local d = (p - last_p).Magnitude
c.Size = Vector3.new(1, 1, d)
c.CFrame = CFrame.new(p, last_p) * CFrame.new(0, 0, -d * 0.5)
c.Parent = game.Workspace
last_p = p
end
C:Destroy()

The slerp function assumes the center of the sphere is (0, 0, 0) and that p0 is on the surface of the sphere. p1 doesn’t have to be on the surface, but it does have to be different from (0, 0, 0). The returned point is along the surface of the sphere from p0 to p1, acting as if p1 were on the surface of the sphere.

The only downside is that I don’t understand it and whenever I try to put code in my game I try to know what it does, how do you even come up with this kind of stuff?

Well I’d heard of “slerp” before and I think I did some spherical geometry for a high school project, but other than that it’s mostly just having strong google-fu