3J多面体几何并不是绘制所有的面

我正在做我的第一个Three.js项目,遇到了一些奇怪的问题。我在看书 this paper

我已经弄清楚了如何渲染一个二十面体,以及如何将它划分成一个n度的测地线穹顶。然而,当我渲染测地圆顶时,似乎有一些面没有填充(见图)。我在用 THREE.PolyhedronGeometry 看起来所有的面都被定义了,否则没有面的线框的边不应该出现,但是它们确实出现了。。。

这是我生成测地圆顶三角形的代码

// http://www.geometer.org/mathcircles/geodesic.pdf
// Golden Ratio
const g = (1 + Math.sqrt(5)) / 2

type Point = [number, number, number]
type Triangle = [Point, Point, Point]

// Points
const A: Point = [0, 1, g]
const B: Point = [0, -1, g]
const C: Point = [0, -1, -g]
const D: Point = [0, 1, -g]
const E: Point = [g, 0, 1]
const F: Point = [-g, 0, 1]
const G: Point = [-g, 0, -1]
const H: Point = [g, 0, -1]
const I: Point = [1, g, 0]
const J: Point = [-1, g, 0]
const K: Point = [-1, -g, 0]
const L: Point = [1, -g, 0]

// Triangles
const icosahedron: Triangle[] = [
    [A, I, J],
    [A, J, F],
    [A, F, B],
    [A, B, E],
    [A, E, I],
    [B, F, K],
    [B, K, L],
    [B, L, E],
    [C, D, H],
    [C, H, L],
    [C, L, K],
    [C, K, G],
    [C, G, D],
    [D, G, J],
    [D, J, I],
    [D, I, H],
    [E, L, H],
    [E, H, I],
    [F, J, G],
    [F, G, K],
]

const edge = 2
const radius = Math.sqrt(1 + g * g)

function sub(p1: Point, p2: Point): Point {
    return [p1[0] - p2[0], p1[1] - p2[1], p1[2] - p2[2]]
}

function mult(n: number, p1: Point): Point {
    return [p1[0] * n, p1[1] * n, p1[2] * n]
}

function add(p1: Point, p2: Point): Point {
    return [p1[0] + p2[0], p1[1] + p2[1], p1[2] + p2[2]]
}

function distance(p1: Point, p2: Point): number {
    const x = sub(p1, p2)
    return Math.sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2])
}

function split(tri: Triangle): Array<Triangle> {
    const midpoint01 = add(mult(0.5, tri[0]), mult(0.5, tri[1]))
    const midpoint02 = add(mult(0.5, tri[0]), mult(0.5, tri[2]))
    const midpoint12 = add(mult(0.5, tri[1]), mult(0.5, tri[2]))
    const scale = radius / distance(midpoint01, [0, 0, 0])
    const m01 = mult(scale, midpoint01)
    const m02 = mult(scale, midpoint02)
    const m12 = mult(scale, midpoint12)
    return [
        [m01, m02, m12],
        [tri[0], m01, m02],
        [tri[1], m01, m12],
        [tri[2], m02, m12],
    ]
}

const geodome1 = _.flatten(icosahedron.map(split))
const geodome2 = _.flatten(geodome1.map(split))

下面是我绘制多面体的3.js代码:

function trianglesToPoly(triangles: Triangle[]) {
    const points: Point[] = _.uniqWith(_.flatten(triangles), _.isEqual)
    const vertices = _.flatten(points)
    const faces = _.flatten(
        _.flatten(
            triangles.map(triangle => {
                return triangle.map(point => {
                    return points.findIndex(p => _.isEqual(p, point))
                })
            })
        )
    )
    const geometry = new THREE.PolyhedronGeometry(vertices, faces, 10, 0)
    return geometry
}

const scene = new THREE.Scene()
const width = window.innerWidth * 0.8
const height = window.innerHeight * 0.8

const camera = new THREE.PerspectiveCamera(75, width / height, 0.1, 1000)

const renderer = new THREE.WebGLRenderer()
renderer.setSize(width, height)
renderer.domElement.style.height = `${height}px`
renderer.domElement.style.width = `${width}px`
document.body.appendChild(renderer.domElement)

// const geometry = trianglesToPoly(icosahedron)
const geometry = trianglesToPoly(geodome1)
// const geometry = trianglesToPoly(geodome2)

var material = new THREE.MeshPhongMaterial({
    color: 0x0000ff,
    polygonOffset: true,
    polygonOffsetFactor: 1, // positive value pushes polygon further away
    polygonOffsetUnits: 1,
})

const mesh = new THREE.Mesh(geometry, material)
scene.add(mesh)

// https://stackoverflow.com/questions/31539130/display-wireframe-and-solid-color
var geo = new THREE.EdgesGeometry(mesh.geometry) // or WireframeGeometry
var mat = new THREE.LineBasicMaterial({ color: 0xffffff, linewidth: 4 })
var wireframe = new THREE.LineSegments(geo, mat)
mesh.add(wireframe)

camera.position.z = 50

const animate = () => {
    requestAnimationFrame(animate)

    mesh.rotation.x += 0.01
    mesh.rotation.y += 0.01

    renderer.render(scene, camera)
}

animate()

你知道为什么那些脸没有出现吗?我甚至找不到脸的颜色是在哪里定义的,或者我会给它一个颜色让它更明显。

如果克隆my repo,则可以自己运行代码:

git clone https://github.com/ccorcos/geodome.git
cd geodome
npm install
npm start