Using Math to generate Cylinders?

[xDeltaXen]

1. What do you want to achieve?
   I want to be able to generate hollow Cylinders using math.

2. What is the issue?
   I do not know the math used to generate Cylinders. I only know the math for a circle and Sphere.

3. What solutions have you tried so far?
   I have tried asking in various discords. Looked on Google and Dev forum.

Circle Generation.

local Radius = 1
local Circle = math.pi * 2
local Amt = 10000

for Number = 1, Amt do
	local Angle = Circle / Amt * Number
	local X = math.sin(Angle) * Radius
	local Z = math.cos(Angle) * Radius
end

Sphere Generation

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

If anyone could help that would be nice (I’m trying to create a game like no man’s sky).

[DrKittyWaffles (x64dbg)]

It’s the same math as generating a circle except you increment the Y position. If it makes sense, cylinders are basically infinitely stacked circles. Just like how a sphere is infinitely many circles, but instead they’re different sizes.

local Radius = 1
local Circle = math.pi * 2
local Amt = 10000
local Height = 10

for Y = 0, Height do
	for Number = 1, Amt do
		local Angle = Circle / Amt * Number
		local X = math.sin(Angle) * Radius
		local Z = math.cos(Angle) * Radius

		local Position = Vector3.new(X, Y, Z)
	end
end

If you’re confusing on what I meant by “infinitely many stacked circles” try reading these. You don’t really need to understand the math, but they explain the concept with nice graphics:

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al)/6%3A_Using_Definite_Integrals/6.2%3A_Using_Definite_Integrals_to_Find_Volume
https://www.mathalino.com/reviewer/derivation-formulas/derivation-formula-volume-sphere-integration

[ImTheBuildGuy]

Why don’t you just use Instance.new? I don’t think there will be much of a difference.

Following content might be considered rude

Very hard math to generate a cylinder.

--hard code to generate clyinder
local thing = Instance.new("Part")
thing.Shape = Enum.PartType.Cylinder

[DrKittyWaffles (x64dbg)]

Maybe he wants a cylinder that is procedurally generated.

@ImTheBuildGuy

Very hard math to generate a cylinder.

--hard code to generate clyinder
local thing = Instance.new("Cylinder")

Cylinder is not an Instance type. Your code will error.

However, it is a PartType.

local Cylinder = Instance.new("Part")

Cylinder.Shape = Enum.PartType.Cylinder

[blokav]

I noticed you have made a couple of posts about shapes, so I feel the need to ask, what is your use case for this? Do you need to just render the surfaces of a cylinder? Or do you have to be able to compute every possible point inside the cylinder? If so then you would have to integrate through the length and radius as @SwagMasterAndrew pointed out.

[xDeltaXen]

No, No, No I want a hollow cylinder generated by many many parts like the sphere code I want that only a cylinder shape

[xDeltaXen]

I need it for a infinite game im making using -perlin noise and custom structurs.,

[EyesInDisguise1]

This is sorta off topic but I am trying to get into generating different shapes as well so I have some questions:

local Radius = 1
local Circle = math.pi * 2
local Amt = 10000
local Height = 10

for Y = 0, Height do
	for Number = 1, Amt do
		local Angle = Circle / Amt * Number
		local X = math.sin(Angle) * Radius
		local Z = math.cos(Angle) * Radius

		local Position = Vector3.new(X, Y, Z)
	end
end

How does multiplying pi by 2 make a circle (in your circle variable)?

Why do you use sin and cos, how does it work?

Also what is it mean if something is procedurally generated?

Thanks!

[xDeltaXen]

math.pi * 2 makes sure th circle is a full circle so math.pi * 1 would be a semi - circle etc

[EyesInDisguise1]

But pi is just a number, 3,14… How can that be a semi-circle?

[xDeltaXen]

because we are diving math.pi by Amt

[Sleazel]

You already have a function to generate a sphere. To generate cylinder with this method, all you have to do is to achieve a constant radius. Remove cosine factors from the coordinates calculations.

Cylinder Generation:

local function spiral_cylinder(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) --remove * math.cos(lat)
		local y = math.sin(lon) --remove * math.cos(lat)
		local z = math.sin(lat)
		
		table.insert(vectors, Vector3.new(x, y, z))
	end
	
	return vectors
end

Hope this helps!

[xDeltaXen]

This does not make a Cylinder?

local function spiral_cylinder(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) --remove * math.cos(lat)
		local y = math.sin(lon) --remove * math.cos(lat)
		local z = math.sin(lat)
		
		table.insert(vectors, Vector3.new(x, y, z))
	end
	
	return vectors
end

local Radius = 100

for Number, Vector3 in pairs(spiral_cylinder(1000)) do
	local Part = Instance.new("Part")
	Part.Anchored = true
	Part.CFrame = CFrame.new(Vector3.Unit * Radius)
	Part.Parent = workspace
end

[Sleazel]

I am not sure what Vector3.Unit is supposed to do, it sure behaves strange. However this works:

for Number, v in pairs(spiral_cylinder(1000)) do
	local Part = Instance.new("Part")
	Part.Anchored = true
	Part.CFrame = CFrame.new(v * Radius)
	Part.Parent = workspace
end

[xDeltaXen]

How would I change the length?

[Sleazel]

You will need to add another parameter for length. Due to way this function works, it will be still dependent on both this and radius though.

local function spiral_cylinder(num_points,length)
	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) 
		local y = math.sin(lon) 
		local z = math.sin(lat) * length
		
		table.insert(vectors, Vector3.new(x, y, z))
	end
	
	return vectors
end

Usage:

for Number, v in pairs(spiral_cylinder(1000,10)) do
	local Part = Instance.new("Part")
	Part.Anchored = true
	Part.CFrame = CFrame.new(v * Radius)
	Part.Parent = workspace
end

[xDeltaXen]

Do you know how to generate a cuboid?

[blokav]

Here’s a sample I just typed up:

(I used the size and position of a brick named “Box” for the parameters)

local function hollow_cuboid(length, width, height, centerPosition, resolution)
	-- 'centerPosition' can be either a Vector3 or a CFrame
	-- (orientation will default to {0, 0, 0} if a Vector3 is used)
	local pos = (typeof(centerPosition) == "CFrame") and centerPosition
		or (typeof(centerPosition) == "Vector3") and CFrame.new(centerPosition)
		or CFrame.new()
	local vectors = {}
	local hl = length / 2
	local hw = width / 2
	local hh = height / 2
	local rr = 1 / resolution -- 'resolution' is points per stud, 'rr' is number of studs between points
	
	-- bottom + top (length * width)
	-- left + right (length * height)
	for i = -hl, hl, rr do
		for j = -hw, hw, rr do
			table.insert(vectors, (pos * CFrame.new(j, -hh, i)).Position)
			table.insert(vectors, (pos * CFrame.new(j, hh, i)).Position)
		end
		for j = -hh, hh, rr do
			table.insert(vectors, (pos * CFrame.new(-hw, j, i)).Position)
			table.insert(vectors, (pos * CFrame.new(hw, j, i)).Position)
		end
	end
	-- front + back (width * height)
	for i = -hw, hw, rr do
		for j = -hh, hh, rr do
			table.insert(vectors, (pos * CFrame.new(i, j, -hl)).Position)
			table.insert(vectors, (pos * CFrame.new(i, j, hl)).Position)
		end
	end
	return vectors
end

local box = workspace.Box.Size
local vs = hollow_cuboid(box.Z, box.X, box.Y, workspace.Box.CFrame, 1)

for _, v in ipairs(vs) do
	local p = Instance.new("Part")
	p.Size = Vector3.new(0.2, 0.2, 0.2)
	p.Anchored = true
	p.CFrame = CFrame.new(v)
	p.Parent = workspace
	--wait()
end

Result:

[xDeltaXen]

WOW! Thanks so much. This will help in my game a lot! btw, In my other thread didn’t you say you had a triangle generator?

[blokav]

It didn’t make triangle prisms like the rectangle script, it just draws a triangle between three vector3 vertices. I originally made it to render the surface of the sphere I mentioned in the last thread.

local function make_triangle(a, b, c, thickness)
	-- sanitize input
	a = (typeof(a) == "Vector3") and a or Vector3.new(0, 0, 0)
	b = (typeof(b) == "Vector3") and b or Vector3.new(1, 0, 0)
	c = (typeof(c) == "Vector3") and c or Vector3.new(0, 1, 0)
	thickness = math.max((tonumber(thickness) or 1), 0.05)

	-- re-order vertices so that AB is the longest side
	local a0, b0, c0 = a, b, c
	local ab = (a - b).Magnitude
	local bc = (b - c).Magnitude
	local ca = (a - c).Magnitude
	if (bc > ab) then
		-- ab not the longest side
		if (ca > bc) then
			-- ca longest
			a = c0
			b = a0
			c = b0
		else
			-- bc longest
			a = b0
			b = c0
			c = a0
		end
	else
		-- ab longer than bc
		if (ca > ab) then
			-- ca longest
			a = c0
			b = a0
			c = b0
		else
			-- ab longest
		end
	end
	ab = (a - b).Magnitude
	bc = (b - c).Magnitude
	ca = (a - c).Magnitude

	local area = (b - a):Cross(c - a).Magnitude / 2
	local h = 2 * area / ab
	local hx = math.sqrt((ca ^ 2) - (h ^ 2))

	-- cframe stuff
	local f = (b - a).Unit
	local u = (c - a).Unit
	local r = f:Cross(u).Unit
	local u2 = r:Cross(f).Unit
	local cf = CFrame.fromMatrix(a, r, u2)

	-- parts
	local p1 = Instance.new("WedgePart")
	p1.Anchored = true
	p1.Size = Vector3.new(thickness, h, hx)
	p1.CFrame = cf * CFrame.new(0, h / 2, -(hx / 2)) * CFrame.Angles(0, math.pi, 0)
	p1.Parent = workspace
	local p2 = Instance.new("WedgePart")
	p2.Anchored = true
	p2.Size = Vector3.new(thickness, h, ab - hx)
	p2.CFrame = cf * CFrame.new(0, h / 2, -(ab + hx) / 2)
	p2.Parent = workspace

	return p1, p2 -- so the user can do more stuff with it
end