Sphere generation bug

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#1

I have the following code to generate a sphere:

local RADIUS = 50

local Mesh = Instance.new("MeshPart")
Mesh.Size = Vector3.new(RADIUS, RADIUS, RADIUS)
Mesh.Anchored = true
Mesh.CanCollide = false

local EditableMesh = Instance.new("EditableMesh")
EditableMesh.Parent = Mesh

local EditableImage = Instance.new("EditableImage")
EditableImage.Parent = Mesh

local function PointOnCubeToPointOnSphere(point: Vector3)
	local x2 = point.X * point.X
	local y2 = point.Y * point.Y
	local z2 = point.Z * point.Z

	local x = point.X * math.sqrt(1 - (y2 + z2) / 2 + (y2 * z2) / 3)
	local y = point.Y * math.sqrt(1 - (z2 + x2) / 2 + (z2 * x2) / 3)
	local z = point.Z * math.sqrt(1 - (x2 + y2) / 2 + (x2 * y2) / 3)

	return Vector3.new(x, y, z)
end

function EarthController:CreateFace(normal: Vector3, resolution: number, name: string)
	local faceMesh = Mesh:Clone()
	faceMesh.Parent = workspace
	faceMesh.Name = name

	local editableMesh: EditableMesh = faceMesh:FindFirstChild("EditableMesh")

	local axisA = Vector3.new(normal.Y, normal.Z, normal.X)
	local axisB = axisA:Cross(normal)

	local vertices = {}

	for x = 1, resolution do
		vertices[x] = {}

		for y = 1, resolution do
			local t = Vector2.new(x, y) / (resolution + 1)
			local point = normal + axisA * (2 * t.X - 1) + axisB * (2 * t.Y - 1)
			local normalised = PointOnCubeToPointOnSphere(point)
			local vertex = editableMesh:AddVertex(normalised)

			vertices[x][y] = vertex
		end
	end

	for x = 1, #vertices do
		for y = 1, #vertices[x] do
			if x == #vertices then continue end
			if y == #vertices[x] then continue end

			local vertex = vertices[x][y]
			local vertex2 = vertices[x + 1][y]
			local vertex3 = vertices[x + 1][y + 1]
			local vertex4 = vertices[x][y + 1]

			editableMesh:AddTriangle(vertex, vertex3, vertex2)
			editableMesh:AddTriangle(vertex3, vertex, vertex4)
		end
	end

	return faceMesh
end

function EarthController:GenerateFaces(resolution: number)
    local faces = {}

	for _, normalId in Enum.NormalId:GetEnumItems() do
		local normal = Vector3.FromNormalId(normalId)
		local mesh = self:CreateFace(normal, resolution, normalId.Name)

		table.insert(faces, mesh)
	end

	return faces
end

function EarthController:KnitStart()
	self:GenerateFaces(2^6)
end

Yet, when generated, it produces this:

1331×795 304 KB

I’ve tried fiddling with offsets but nothing seems to work, can anyone shed any light?

#2

Continuing on…

I got this working through a hack (I just added a arbitrary number multiplier to axisA)

I’ve then created a new sphere which has been divided into tiles… this however, does not work at all:

image
image1322×780 34.9 KB

I don’t know how to fix this strange pattern but there it is, can anyone shed any light as to why?

Here is the code I’m using:

local RADIUS = 50

local EarthModel = Instance.new("Model")
EarthModel.Parent = workspace
EarthModel.Name = "Earth"

local editableImages = {}
local editableMeshes = {}

function CreateFace(resolution: number, normal: Vector3, startTile: Vector2, endTile: Vector2, parent: Instance)
	local vertices = {}

	local Mesh = Instance.new("MeshPart")
	Mesh.Size = Vector3.one
	Mesh.Anchored = true
	Mesh.CanCollide = false
	Mesh.Parent = parent

	local EditableImage = Instance.new("EditableImage")
	EditableImage.Parent = Mesh

	local EditableMesh = Instance.new("EditableMesh")
	EditableMesh.Parent = Mesh

	local axisA = Vector3.new(normal.Y, normal.Z, normal.X)
	local axisB = normal:Cross(axisA)

	local tileY = startTile.Y
	local differenceX = (endTile.X - startTile.X) / resolution
	local differenceY = (endTile.Y - startTile.Y) / resolution

	for x = 1, resolution do
		local tileX = startTile.X
		vertices[x] = {}

		for y = 1, resolution do
			local pointOnUnitCube = normal + (tileX - 0.5) * 2 * axisA + (tileY - 0.5) * 2 * axisB
			local pointOnUnitSphere = pointOnUnitCube.Unit
			local verticePosition = pointOnUnitSphere * RADIUS
			local vertice = EditableMesh:AddVertex(verticePosition)

			vertices[x][y] = vertice
			tileX += differenceX
		end

		tileY += differenceY
	end

	for x = 1, #vertices do
		for y = 1, #vertices[x] do
			if x == #vertices then continue end
			if y == #vertices[x] then continue end

			local vertex = vertices[x][y]
			local vertex2 = vertices[x + 1][y]
			local vertex3 = vertices[x + 1][y + 1]
			EditableMesh:AddTriangle(vertex, vertex3, vertex2)
		end
	end
end

function GenerateMeshes(resolution: number, subdivisions: number)
	local meshes = {}
	local faceCoveragePerSubFace = 1 / subdivisions

	for _, normal in Enum.NormalId:GetEnumItems() do
		local faceNormal = Vector3.FromNormalId(normal)

		local faceModel = Instance.new("Model")
		faceModel.Name = normal.Name
		faceModel.Parent = EarthModel

		for x = 1, subdivisions do
			for y = 1, subdivisions do
				local startTile = Vector2.new(x, y) * faceCoveragePerSubFace
				local endTile = startTile + Vector2.one * faceCoveragePerSubFace
				local face = self:CreateFace(resolution, faceNormal, startTile, endTile, faceModel)

				table.insert(meshes, face)
			end
		end
	end

	return meshes
end

GenerateMeshes(2^6, 7)