I am trying to create a Goldberg sphere (sphere with hexagons and pentagons) from an icosphere using Godot 4, but some triangles are not appearing: The icosahedron All the vertices exist.
I tried different ways of adding the new vertices to the array new_faces:
appendpush_backI tried coloring differently all the new triangles I create in function subdivide, and it looks like the one I create using the centers of the edges is the one that is missing.
var vertices:PackedVector3Array = []
var faces = []
func generate_icosphere():
var t = (1.0 + sqrt(5.0)) / 2
vertices.push_back(Vector3(-1, t, 0).normalized())
vertices.push_back(Vector3(1, t, 0).normalized())
vertices.push_back(Vector3(-1, -t, 0).normalized())
vertices.push_back(Vector3(1, -t, 0).normalized())
vertices.push_back(Vector3(0, -1, t).normalized())
vertices.push_back(Vector3(0, 1, t).normalized())
vertices.push_back(Vector3(0, -1, -t).normalized())
vertices.push_back(Vector3(0, 1, -t).normalized())
vertices.push_back(Vector3(t, 0, -1).normalized())
vertices.push_back(Vector3(t, 0, 1).normalized())
vertices.push_back(Vector3(-t, 0, -1).normalized())
vertices.push_back(Vector3(-t, 0, 1).normalized())
faces.push_back(Triangle.new(vertices[0], vertices[11], vertices[5]))
faces.push_back(Triangle.new(vertices[0], vertices[5], vertices[1]))
faces.push_back(Triangle.new(vertices[0], vertices[1], vertices[7]))
faces.push_back(Triangle.new(vertices[0], vertices[7], vertices[10]))
faces.push_back(Triangle.new(vertices[0], vertices[10], vertices[11]))
faces.push_back(Triangle.new(vertices[1], vertices[5], vertices[9]))
faces.push_back(Triangle.new(vertices[5], vertices[11], vertices[4]))
faces.push_back(Triangle.new(vertices[11], vertices[10], vertices[2]))
faces.push_back(Triangle.new(vertices[10], vertices[7], vertices[6]))
faces.push_back(Triangle.new(vertices[7], vertices[1], vertices[8]))
faces.push_back(Triangle.new(vertices[3], vertices[9], vertices[4]))
faces.push_back(Triangle.new(vertices[3], vertices[4], vertices[2]))
faces.push_back(Triangle.new(vertices[3], vertices[2], vertices[6]))
faces.push_back(Triangle.new(vertices[3], vertices[6], vertices[8]))
faces.push_back(Triangle.new(vertices[3], vertices[8], vertices[9]))
faces.push_back(Triangle.new(vertices[4], vertices[9], vertices[5]))
faces.push_back(Triangle.new(vertices[2], vertices[4], vertices[11]))
faces.push_back(Triangle.new(vertices[6], vertices[2], vertices[10]))
faces.push_back(Triangle.new(vertices[8], vertices[6], vertices[7]))
faces.push_back(Triangle.new(vertices[9], vertices[8], vertices[1]))
func subdivide(_radius):
var new_faces = []
for face in faces:
var vert0 = face.vertices[0]
var vert1 = face.vertices[1]
var vert2 = face.vertices[2]
var center0_1:Vector3 = lerp(vert0, vert1, 0.5).normalized()
var center1_2:Vector3 = lerp(vert1, vert2, 0.5).normalized()
var center2_0:Vector3 = lerp(vert2, vert0, 0.5).normalized()
new_faces.push_back(Triangle.new(vert0, center0_1, center2_0))
new_faces.push_back(Triangle.new(vert1, center0_1, center1_2))
new_faces.push_back(Triangle.new(vert2, center1_2, center2_0))
new_faces.push_back(Triangle.new(center0_1, center1_2, center2_0))
print(face, new_faces)
return new_faces
func generate(subdivisions,radius):
generate_icosphere()
var result_faces:Array = []
result_faces = subdivide(20)
return result_faces
class Triangle:
var vertices:PackedVector3Array = []
func _init(a, b, c):
vertices.push_back(a)
vertices.push_back(b)
vertices.push_back(c)
Thanks in advance.
I found how to do it with a bit of help from ChatGPT :-). It looks like I needed indices because sometimes two vertices were the same. The code:
func generate_icosahedron():
var t = (1.0 + sqrt(5.0)) / 2.0
var vertices = [
Vector3(-1, t, 0).normalized(), Vector3( 1, t, 0).normalized(), Vector3(-1, -t, 0).normalized(), Vector3( 1, -t, 0).normalized(),
Vector3( 0, -1, t).normalized(), Vector3( 0, 1, t).normalized(), Vector3( 0, -1, -t).normalized(), Vector3( 0, 1, -t).normalized(),
Vector3( t, 0, -1).normalized(), Vector3( t, 0, 1).normalized(), Vector3(-t, 0, -1).normalized(), Vector3(-t, 0, 1).normalized()
]
var faces = [
[0, 11, 5], [0, 5, 1], [0, 1, 7], [0, 7, 10], [0, 10, 11],
[1, 5, 9], [5, 11, 4], [11, 10, 2], [10, 7, 6], [7, 1, 8],
[3, 9, 4], [3, 4, 2], [3, 2, 6], [3, 6, 8], [3, 8, 9],
[4, 9, 5], [2, 4, 11], [6, 2, 10], [8, 6, 7], [9, 8, 1]
]
return [vertices, faces]
func get_face_center(p0: int, p1: int, p2: int, vertex_vertices: Array, vertices: Array):
var point0 = vertex_vertices[p0]
var point1 = vertex_vertices[p1]
var point2 = vertex_vertices[p2]
var middle = (point0 + point1 + point2) / 3.0
middle = middle.normalized()
if vertices.has(middle):
return [vertices.find(middle), middle, false]
var index = vertices.size()
return [index, middle, true]
func generate_icosphere(subdivisions: int):
var data = generate_icosahedron()
var vertices = data[0]
var faces = data[1]
for i in range(subdivisions):
var new_faces = []
var middle_point_cache = {}
for face in faces:
var v1 = face[0]
var v2 = face[1]
var v3 = face[2]
var a = get_middle_point(v1, v2, vertices, middle_point_cache)
var b = get_middle_point(v2, v3, vertices, middle_point_cache)
var c = get_middle_point(v3, v1, vertices, middle_point_cache)
new_faces += [[v1, a, c], [v2, b, a], [v3, c, b], [a, b, c]]
faces = new_faces
for k in range(vertices.size()):
vertices[k] = vertices[k].normalized()
return [vertices, faces]
func get_middle_point(p1: int, p2: int, vertices: Array, cache: Dictionary) -> int:
var smaller_index = min(p1, p2)
var greater_index = max(p1, p2)
var key = str(smaller_index) + "-" + str(greater_index)
if cache.has(key):
return cache[key]
var point1 = vertices[p1]
var point2 = vertices[p2]
var middle = (point1 + point2) / 2.0
middle = middle.normalized()
var index = vertices.size()
vertices.append(middle)
cache[key] = index
return index
So, for anyone interested, it return vertices and an array of faces.