Using Math to generate Spheres

[xDeltaXen]

@Blokav

local function fibonacci_spiral_sphere(num_points)
	local vectors = {}
	local gr = (math.sqrt(5) + 1) / 2
	local ga = (2 - gr) * (2 * math.pi)
	
	for i = 1, num_points do
		local lat = math.asin(-1 + 2 * i / (num_points + 1))
		local lon = ga * i

		local x = math.cos(lon) * math.cos(lat)
		local y = math.sin(lon) * math.cos(lat)
		local z = math.sin(lat)

		table.insert(vectors, Vector3.new(x, y, z))
	end

	return vectors
end

I still dont see how I can make a sphere out of this

[blokav]

That function returns an array of vectors that outline the surface of the sphere.

Here I placed parts on each position:

local function fibonacci_spiral_sphere(num_points)
	local vectors = {}
	local gr = (math.sqrt(5) + 1) / 2
	local ga = (2 - gr) * (2 * math.pi)
	
	for i = 1, num_points do
		local lat = math.asin(-1 + 2 * i / (num_points + 1))
		local lon = ga * i
		
		local x = math.cos(lon) * math.cos(lat)
		local y = math.sin(lon) * math.cos(lat)
		local z = math.sin(lat)
		
		table.insert(vectors, Vector3.new(x, y, z))
	end
	
	return vectors
end

local radius = 10

local ref = Instance.new("Part")
ref.Anchored = true
ref.Size = Vector3.new(0.2, 0.2, 0.2)

local vec = fibonacci_spiral_sphere(1024)
for _, v in ipairs(vec) do
	local part = ref:Clone()
	part.CFrame = CFrame.new(v.Unit * radius)
	part.Parent = workspace
	wait()
end

Result:

Then it’s just a matter of resizing the nodes or connecting them to smooth out the surface.

[PysephDEV (Pyseph)]

every vector is a point in space: the function returns a list of points in space. Generate a “Ball” part with a size of 0.1, 0.1, 0.1 for each point, and set its position to that point.

[xDeltaXen]

@Blokav

local function fibonacci_spiral_sphere(num_points)
	local vectors = {}
	local gr = (math.sqrt(5) + 1) / 2
	local ga = (2 - gr) * (2 * math.pi)
	
	for i = 1, num_points do
		local lat = math.asin(-1 + 2 * i / (num_points + 1))
		local lon = ga * i
		
		local x = math.cos(lon) * math.cos(lat)
		local y = math.sin(lon) * math.cos(lat)
		local z = math.sin(lat)
		
		table.insert(vectors, Vector3.new(x, y, z))
	end
	
	return vectors
end

local origin = Vector3.new(0, 0, 0)
local radius = 10

local ref = Instance.new("Part")
ref.Anchored = true
ref.Size = Vector3.new(0.2, 0.2, 0.2)

local vec = fibonacci_spiral_sphere(1024)
for _, v in ipairs(vec) do
	local part = ref:Clone()
	part.CFrame = CFrame.new(origin, v) * CFrame.new(0, 0, -radius)
	part.Parent = workspace
	wait()
end

So how would I calculate the Size and amount of points needed for a perfect enclosed sphere?

[blokav]

No idea. You would probably need some method of finding the closest points to any point and creating a triangle between them. That’s why my first solution was a geodesic sphere - I already knew where the triangles were and which points to connect.

[IlyasTawawe]

This is so informative.
I was looking for this for a long time now but i forgot about it lol
Here is what I’ve done with it:

[xDeltaXen]

How did you do that second circle?

[xDeltaXen]

Do you know how I could turn this into terrain?

[IlyasTawawe]

I increased the size (roughly 2 studs) and changed the shape of reference part to “Ball”
and to make a little variation in color. I just used math.random and Color3.fromRGB functions

[xDeltaXen]

Oh dip nice that is 2 studs longer btw