说明
正六面体，也就是立方体。
几何
其实完全可以通过其他方式来构造立方体，贴图也可以有更灵活的选择。这里我们为了保持与其他几何体的一致性，也采用和其实正多面体一样的做法：根据外接球半径，生成正六面体，然后将各个面细分，并采用对称贴图模式。
基本流程和前面的正四面基本一致：
第一步，找到顶点的几何关系；
第二步，计算顶点；
第三步，利用重复顶点，构造三角形或四边形；
第四步，计算初始法线；
第五步，可选步骤，细分每个平面；
第六步，根据顶点位置计算贴图坐标；
顶点位置计算比较简单：
let a: Float = 2 * radius / sqrtf(3)//棱长
let r = a / 2 //内切球半径
let points: [SIMD3<Float>] = [
SIMD3<Float>(r, r, r),
SIMD3<Float>(-r, r, r),
SIMD3<Float>(-r, r, -r),
SIMD3<Float>(r, r, -r),
SIMD3<Float>(r, -r, r),
SIMD3<Float>(-r, -r, r),
SIMD3<Float>(-r, -r, -r),
SIMD3<Float>(r, -r, -r),
]
其他做法也是和前文类似，不同的是，我们采用了 Quads 四边形来直接生成立方体。前面我们都是用三角形来组成网格，其实也可以直接用四边形来生成。不管是索引生成，还是每个面再细分网格，都可以用四边形直接生成。
不过，在很多 3D 引擎中，虽然我们输入的四边形顶点和索引，但最终生成的网格仍是经过优化的三角形，在 RealityKit 中也是如此。当然，这不会影响我们这里的逻辑，只会在最终显示时，RealityKit 会将我们的四边形再分成两个三角形。
代码
/// 正六面体（立方体），radius 为外接球半径，res 四边形平面剖分次数
public static func generateHexahedron(radius: Float, res: Int = 0) throws -> MeshResource {
let pointCount = 8
var quads = 6
var vertices = pointCount * 3
var descr = MeshDescriptor()
var meshPositions: [SIMD3<Float>] = []
var indices: [UInt32] = []
var normals: [SIMD3<Float>] = Array(repeating: .zero, count: vertices)
var textureMap: [SIMD2<Float>] = []
let a: Float = 2 * radius / sqrtf(3)//棱长
let r = a / 2 //内切球半径
let points: [SIMD3<Float>] = [
SIMD3<Float>(r, r, r),
SIMD3<Float>(-r, r, r),
SIMD3<Float>(-r, r, -r),
SIMD3<Float>(r, r, -r),
SIMD3<Float>(r, -r, r),
SIMD3<Float>(-r, -r, r),
SIMD3<Float>(-r, -r, -r),
SIMD3<Float>(r, -r, -r),
]
meshPositions.append(contentsOf: points + points + points)
let index: [UInt32] = [
3, 2, 1, 0,
4, 5, 6, 7,
3, 0, 4, 7,
1, 2, 6, 5,
0, 1, 5, 4,
2, 3, 7, 6
]
var countDict: [UInt32:Int] = [:]
for ind in index {
let count = countDict[ind] ?? 0
indices.append(ind + UInt32(pointCount * count))
countDict[ind] = count + 1
}
for i in 0..<quads {
let ai = 4 * i
let bi = 4 * i + 1
let ci = 4 * i + 2
let di = 4 * i + 3
let i0 = indices[ai]
let i1 = indices[bi]
let i2 = indices[ci]
let i3 = indices[di]
let v0 = meshPositions[Int(i0)]
let v1 = meshPositions[Int(i1)]
let v2 = meshPositions[Int(i2)]
let v3 = meshPositions[Int(i3)]
let faceNormal = simd_normalize((v0 + v1 + v2 + v3) / 4)
normals[Int(i0)] = faceNormal
normals[Int(i1)] = faceNormal
normals[Int(i2)] = faceNormal
normals[Int(i3)] = faceNormal
}
for _ in 0..<res {
let newQuads = quads * 4
let newVertices = vertices + quads * 5
var newIndices: [UInt32] = []
var pos: SIMD3<Float>
for i in 0..<quads {
let ai = 4 * i
let bi = 4 * i + 1
let ci = 4 * i + 2
let di = 4 * i + 3
let i0 = indices[ai]
let i1 = indices[bi]
let i2 = indices[ci]
let i3 = indices[di]
let v0 = meshPositions[Int(i0)]
let v1 = meshPositions[Int(i1)]
let v2 = meshPositions[Int(i2)]
let v3 = meshPositions[Int(i3)]
let faceNormal = normals[Int(i0)]
normals.append(contentsOf: [faceNormal, faceNormal, faceNormal, faceNormal, faceNormal])
pos = (v0 + v1) / 2
meshPositions.append(pos)
pos = (v1 + v2) / 2
meshPositions.append(pos)
pos = (v2 + v3) / 2
meshPositions.append(pos)
pos = (v0 + v3) / 2
meshPositions.append(pos)
pos = (v0 + v1 + v2 + v3) / 4
meshPositions.append(pos)
let a = UInt32(5 * i + vertices)
let b = UInt32(5 * i + 1 + vertices)
let c = UInt32(5 * i + 2 + vertices)
let d = UInt32(5 * i + 3 + vertices)
let center = UInt32(5 * i + 4 + vertices)
newIndices.append(contentsOf: [
i0, a, center, d,
a, i1, b, center,
center, b, i2, c,
d, center, c, i3
])
}
indices = newIndices
quads = newQuads
vertices = newVertices
}
for i in 0..<meshPositions.count {
let p = meshPositions[i]
let n = p
textureMap.append(SIMD2<Float>(abs(atan2(n.x, n.z)) / .pi, 1 - acos(n.y/radius) / .pi))
}
descr.positions = MeshBuffers.Positions(meshPositions)
descr.normals = MeshBuffers.Normals(normals)
descr.textureCoordinates = MeshBuffers.TextureCoordinates(textureMap)
descr.primitives = .trianglesAndQuads(triangles: [], quads: indices)
return try MeshResource.generate(from: [descr])
}
