说明
地理均分球体,即 GeoSphere,也是一种球体,只是三角网格划分方式与普通经纬度球体不同。
几何
从本质上说,GeoSphere 就是正二十面体经过细分后得到的球体。与前面的正二十面体不同的是:每个点的法线都是独特的,而且细分后新生成的点,会沿法线进行移动,移动到球面上。
从代码角度来讲,更简单了。无需考虑顶点法线不同的问题,也就无需再重复 3 次顶点。法线计算也简单了,直接根据每个点的坐标,进行归一化就可以了。
代码
public static func generateGeoSphere(radius: Float, res: Int = 0) throws -> MeshResource {
let pointCount = 12
var triangles = 20
var vertices = pointCount
var descr = MeshDescriptor()
var meshPositions: [SIMD3<Float>] = []
var indices: [UInt32] = []
var normals: [SIMD3<Float>] = []
var textureMap: [SIMD2<Float>] = []
let phi = (1.0 + sqrtf(5)) * 0.5
let r2 = radius * radius
let den = (1.0 + (1.0 / pow(phi, 2.0)))
let h = sqrt(r2 / (den))
let w = h / phi
let points = [
SIMD3<Float>(0.0, h, w),
SIMD3<Float>(0.0, h, -w),
SIMD3<Float>(0.0, -h, w),
SIMD3<Float>(0.0, -h, -w),
SIMD3<Float>(h, -w, 0.0),
SIMD3<Float>(h, w, 0.0),
SIMD3<Float>(-h, -w, 0.0),
SIMD3<Float>(-h, w, 0.0),
SIMD3<Float>(-w, 0.0, -h),
SIMD3<Float>(w, 0.0, -h),
SIMD3<Float>(-w, 0.0, h),
SIMD3<Float>(w, 0.0, h)
]
meshPositions.append(contentsOf: points)
let index: [UInt32] = [
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
]
indices.append(contentsOf: index)
for _ in 0..<res {
let newTriangles = triangles * 4
let newVertices = vertices + triangles * 3
var newIndices: [UInt32] = []
var pos: SIMD3<Float>
for i in 0..<triangles {
let ai = 3 * i
let bi = 3 * i + 1
let ci = 3 * i + 2
let i0 = indices[ai]
let i1 = indices[bi]
let i2 = indices[ci]
let v0 = meshPositions[Int(i0)]
let v1 = meshPositions[Int(i1)]
let v2 = meshPositions[Int(i2)]
// a
pos = (v0 + v1) * 0.5
pos = simd_normalize(pos) * radius
meshPositions.append(pos)
// b
pos = (v1 + v2) * 0.5
pos = simd_normalize(pos) * radius
meshPositions.append(pos)
// c
pos = (v2 + v0) * 0.5
pos = simd_normalize(pos) * radius
meshPositions.append(pos)
let a = UInt32(ai + vertices)
let b = UInt32(bi + vertices)
let c = UInt32(ci + vertices)
newIndices.append(contentsOf: [
i0, a, c,
a, i1, b,
a, b, c,
c, b, i2
])
}
indices = newIndices
triangles = newTriangles
vertices = newVertices
}
for i in 0..<meshPositions.count {
let p = meshPositions[i]
let n = simd_normalize(p)
normals.append(n)
textureMap.append(SIMD2<Float>(abs(atan2(n.x, n.z)) / .pi, 1 - acos(n.y) / .pi))
}
descr.positions = MeshBuffers.Positions(meshPositions)
descr.normals = MeshBuffers.Normals(normals)
descr.textureCoordinates = MeshBuffers.TextureCoordinates(textureMap)
descr.primitives = .triangles(indices)
return try MeshResource.generate(from: [descr])
}