在Unity中创建二维环形网格

Question

我目前有一个“CreateMesh”脚本，可以将其作为对象的组件放在具有网格渲染器和网格过滤器的物体上，并且根据设置为“tri”或“box”的“MeshType”变量，在网格的尺寸中创建一个带多边形碰撞器的2D网格（分别用于三角形和矩形网格）。我想添加创建圆形网格的功能，但是经过一些研究，我意识到这并不像我最初想象的那么简单。然而，我还没有找到任何有用的东西。

这是我用于矩形和三角形网格的代码：

public float width = 5f;
public float height = 5f;

public string meshType;

public PolygonCollider2D polyCollider;

void Start()
{
    polyCollider = GetComponent<PolygonCollider2D>();
}

// Update is called once per frame
void Update () {
    if (meshType == "tri")
    {
        TriangleMesh(width, height);
    }
    if (meshType == "box")
    {
        BoxMesh(width, height);
    }

}

void TriangleMesh(float width, float height)
{
    MeshFilter mf = GetComponent<MeshFilter>();
    Mesh mesh = new Mesh();
    mf.mesh = mesh;

    //Verticies
    Vector3[] verticies = new Vector3[3]
    {
        new Vector3(0,0,0), new Vector3(width, 0, 0), new Vector3(0, height, 0)
    };

    //Triangles
    int[] tri = new int[3];

    tri[0] = 0;
    tri[1] = 2;
    tri[2] = 1;

    //normals
    Vector3[] normals = new Vector3[3];

    normals[0] = -Vector3.forward;
    normals[1] = -Vector3.forward;
    normals[2] = -Vector3.forward;

    //UVs
    Vector2[] uv = new Vector2[3];

    uv[0] = new Vector2(0, 0);
    uv[0] = new Vector2(1, 0);
    uv[0] = new Vector2(0, 1);

    //initialise
    mesh.vertices = verticies;
    mesh.triangles = tri;
    mesh.normals = normals;
    mesh.uv = uv;

    //setting up collider
    polyCollider.pathCount = 1;

    Vector2[] path = new Vector2[3]
    {
        new Vector2(0,0), new Vector2(0, height), new Vector2(width, 0)
    };

    polyCollider.SetPath(0, path);

}

void BoxMesh(float width, float height)
{
    MeshFilter mf = GetComponent<MeshFilter>();
    Mesh mesh = new Mesh();
    mf.mesh = mesh;

    //Verticies
    Vector3[] verticies = new Vector3[4]
    {
        new Vector3(0,0,0), new Vector3(0, height, 0), new Vector3(width, height, 0), new Vector3(width, 0, 0)
    };

    //Triangles
    int[] tri = new int[6];

    tri[0] = 0;
    tri[1] = 1;
    tri[2] = 3;

    tri[3] = 1;
    tri[4] = 2;
    tri[5] = 3;

    //normals
    Vector3[] normals = new Vector3[4];

    normals[0] = -Vector3.forward;
    normals[1] = -Vector3.forward;
    normals[2] = -Vector3.forward;
    normals[3] = -Vector3.forward;

    //UVs
    Vector2[] uv = new Vector2[4];

    uv[0] = new Vector2(0, 0);
    uv[1] = new Vector2(0, 1);
    uv[2] = new Vector2(1, 1);
    uv[3] = new Vector2(1, 0);

    //initialise
    mesh.vertices = verticies;
    mesh.triangles = tri;
    mesh.normals = normals;
    mesh.uv = uv;

    //setting up collider
    polyCollider.pathCount = 1;

    Vector2[] path = new Vector2[4]
    {
        new Vector2(0,0), new Vector2(0, height), new Vector2(width, height), new Vector2(width, 0)
    };

    polyCollider.SetPath(0, path);

}

所以基本上我想要一个函数，我可以在更新方法中调用它，它将简单地创建一个圆形网格。例如：

void Update () {
   if (meshType == "tri")
   {
       TriangleMesh(width, height);
   }
   if (meshType == "box")
   {
       BoxMesh(width, height);
   }
   if (meshType == "circle")
   {
       CircleMesh(radius);
   }
}

- Tom Ryan

---

自从发布这个问题以来，我已经成功解决了这个问题。我有时间时会提供一个答案。 - Tom Ryan

Answer 1

我找到的解决方案涉及创建一个具有大量边数n的正多边形。我有一个名为PolyMesh的函数，可以创建具有n个边和给定半径的正多边形网格。 生成顶点

对于一个具有n个边的正多边形的每个顶点，相对于多边形中心的坐标如下：x = r*i*sin(θ)和y = r*i*cos(θ)，因此x = r*i*sin(2π/2)和y = r*i*cos(2π/2)。其中i从0迭代到n-1。因此我们可以创建一个分配了顶点的列表，然后将其转换为数组：

    //verticies
    List<Vector3> verticiesList = new List<Vector3> { };
    float x;
    float y;
    for (int i = 0; i < n; i ++)
    {
        x = radius * Mathf.Sin((2 * Mathf.PI * i) / n);
        y = radius * Mathf.Cos((2 * Mathf.PI * i) / n);
        verticiesList.Add(new Vector3(x, y, 0f));
    }
    Vector3[] verticies = verticiesList.ToArray();

生成三角形

给定一个有n个边的正多边形，可以从同一点将其分成n-2个三角形。因此，我们可以按照以下方式生成每个三角形：

    //triangles
    List<int> trianglesList = new List<int> { };
    for(int i = 0; i < (n-2); i++)
    {
        trianglesList.Add(0);
        trianglesList.Add(i+1);
        trianglesList.Add(i+2);
    }
    int[] triangles = trianglesList.ToArray();

生成法线

由于这是一个2D对象，我们可以将每个法线设为-Vector3.forward，如下所示：

    //normals
    List<Vector3> normalsList = new List<Vector3> { };
    for (int i = 0; i < verticies.Length; i++)
    {
        normalsList.Add(-Vector3.forward);
    }
    Vector3[] normals = normalsList.ToArray();

生成碰撞器

我们可以使用一个半径相同的圆形碰撞器，但是为了使此函数适用于较小n值的多边形，我们必须使用PolygonCollider2D。由于顶点已经按顺序在顶点数组中排列，因此我们可以将它们简单地用作PolygonCollider2D的路径。

    //polyCollider
    polyCollider.pathCount = 1;

    List<Vector2> pathList = new List<Vector2> { };
    for (int i = 0; i < n; i++)
    {
        pathList.Add(new Vector2(verticies[i].x, verticies[i].y));
    }
    Vector2[] path = pathList.ToArray();

    polyCollider.SetPath(0, path);

完整的代码应该看起来像这样：

public PolygonCollider2D polyCollider;

void Start()
{
    polyCollider = GetComponent<PolygonCollider2D>();
}

void PolyMesh(float radius, int n)
{
    MeshFilter mf = GetComponent<MeshFilter>();
    Mesh mesh = new Mesh();
    mf.mesh = mesh;

    //verticies
    List<Vector3> verticiesList = new List<Vector3> { };
    float x;
    float y;
    for (int i = 0; i < n; i ++)
    {
        x = radius * Mathf.Sin((2 * Mathf.PI * i) / n);
        y = radius * Mathf.Cos((2 * Mathf.PI * i) / n);
        verticiesList.Add(new Vector3(x, y, 0f));
    }
    Vector3[] verticies = verticiesList.ToArray();

    //triangles
    List<int> trianglesList = new List<int> { };
    for(int i = 0; i < (n-2); i++)
    {
        trianglesList.Add(0);
        trianglesList.Add(i+1);
        trianglesList.Add(i+2);
    }
    int[] triangles = trianglesList.ToArray();

    //normals
    List<Vector3> normalsList = new List<Vector3> { };
    for (int i = 0; i < verticies.Length; i++)
    {
        normalsList.Add(-Vector3.forward);
    }
    Vector3[] normals = normalsList.ToArray();

    //initialise
    mesh.vertices = verticies;
    mesh.triangles = triangles;
    mesh.normals = normals;

    //polyCollider
    polyCollider.pathCount = 1;

    List<Vector2> pathList = new List<Vector2> { };
    for (int i = 0; i < n; i++)
    {
        pathList.Add(new Vector2(verticies[i].x, verticies[i].y));
    }
    Vector2[] path = pathList.ToArray();

    polyCollider.SetPath(0, path);
}

网格介绍

- Tom Ryan

Answer 2

我还没有超过50的声望值，所以无法仅仅评论@Tom Ryan的回答。

话虽如此，要注意他的解决方案并没有包括网格的UV。以下是修改：

//uvs
Vector2[] uvs = new Vector2[vertices.Length];
for (int i = 0; i < uvs.Length; i++)
{
    uvs[i] = new Vector2(vertices[i].x / (radius*2) + 0.5f, vertices[i].y / (radius*2) + 0.5f);
}

// Later...
mesh.uv = uvs;

- Gmanicus