Unity中如何获取顺序正确的顶点世界坐标？

我有一些代表省份边界的顶点，希望在Unity中获取它们顺序正确的世界坐标。目前用以下代码能获取顶点世界坐标，但顺序不正确，通过LineRenderer渲染时无法正确呈现边界。

[SerializeField] private MeshFilter _mesh;
[SerializeField] private LineRenderer _lineRenderer;

[Serializable]
public class Border
{
    public Mesh borderMesh;
    public BorderProvince[] sharedBetween = new BorderProvince[2];
    public bool isACountryBorder;
}

[SerializeField] private List<Border> _borders;

private List<Vector3> _drawnBorder = new List<Vector3>();

[ContextMenu("Update Border Drawer")]
private void UpdateBorderDrawer()
{
    if (_borders.Count == 0 || _lineRenderer == null) return;

    _drawnBorder = new List<Vector3>();

    Matrix4x4 localToWorld = transform.localToWorldMatrix;

    foreach (Border border in _borders)
    {
        if (border.sharedBetween[0].ID != border.sharedBetween[1].ID)
        {
            border.isACountryBorder = true;
            for (int i = 0; i < border.borderMesh.vertices.Length; i++)
            {
                _drawnBorder.Add(localToWorld.MultiplyPoint3x4(border.borderMesh.vertices[i]));
            }
        }
    }

    _lineRenderer.positionCount = _drawnBorder.Count;
    _lineRenderer.SetPositions(_drawnBorder.ToArray());
}

解决思路及方案 #

Mesh的顶点数组本身是无序的，它的顺序基于三角面索引排列，而非边界的连续路径顺序。要得到正确的边界顶点顺序，需从Mesh的拓扑结构中重建连续路径：

1. 提取边界边并构建连续路径
   遍历Mesh三角面索引，收集仅出现一次的边界边（内部边会被两个三角面共享），再通过邻接关系拼接出连续的顶点路径：

   private List<Vector3> GetOrderedBorderVertices(Mesh mesh, Matrix4x4 localToWorld)
   {
       List<Vector3> orderedVertices = new List<Vector3>();
       if (mesh == null) return orderedVertices;
   
       // 统计所有边的出现次数
       Dictionary<(int, int), int> edgeCount = new Dictionary<(int, int), int>();
       int[] triangles = mesh.triangles;
   
       for (int i = 0; i < triangles.Length; i += 3)
       {
           AddEdge(triangles[i], triangles[i+1], edgeCount);
           AddEdge(triangles[i+1], triangles[i+2], edgeCount);
           AddEdge(triangles[i+2], triangles[i], edgeCount);
       }
   
       // 筛选出仅出现一次的边界边
       List<(int, int)> borderEdges = edgeCount.Where(kv => kv.Value == 1).Select(kv => kv.Key).ToList();
       if (borderEdges.Count == 0) return orderedVertices;
   
       // 构建顶点邻接表
       Dictionary<int, List<int>> adjacency = new Dictionary<int, List<int>>();
       foreach (var edge in borderEdges)
       {
           if (!adjacency.ContainsKey(edge.Item1)) adjacency[edge.Item1] = new List<int>();
           adjacency[edge.Item1].Add(edge.Item2);
           if (!adjacency.ContainsKey(edge.Item2)) adjacency[edge.Item2] = new List<int>();
           adjacency[edge.Item2].Add(edge.Item1);
       }
   
       // 拼接连续路径
       int currentVertex = borderEdges[0].Item1;
       int previousVertex = -1;
       orderedVertices.Add(localToWorld.MultiplyPoint3x4(mesh.vertices[currentVertex]));
   
       while (orderedVertices.Count < borderEdges.Count)
       {
           foreach (int nextVertex in adjacency[currentVertex])
           {
               if (nextVertex != previousVertex)
               {
                   orderedVertices.Add(localToWorld.MultiplyPoint3x4(mesh.vertices[nextVertex]));
                   previousVertex = currentVertex;
                   currentVertex = nextVertex;
                   break;
               }
           }
       }
   
       return orderedVertices;
   }
   
   private void AddEdge(int a, int b, Dictionary<(int, int), int> edgeCount)
   {
       // 按索引大小排序，确保边的唯一性
       var edge = a < b ? (a, b) : (b, a);
       edgeCount[edge] = edgeCount.ContainsKey(edge) ? edgeCount[edge] + 1 : 1;
   }
   

2. 修改原更新方法
   将原代码中直接添加顶点的逻辑替换为上述有序顶点获取方法：

   [ContextMenu("Update Border Drawer")]
   private void UpdateBorderDrawer()
   {
       if (_borders.Count == 0 || _lineRenderer == null) return;
   
       _drawnBorder = new List<Vector3>();
   
       Matrix4x4 localToWorld = transform.localToWorldMatrix;
   
       foreach (Border border in _borders)
       {
           if (border.sharedBetween[0].ID != border.sharedBetween[1].ID)
           {
               border.isACountryBorder = true;
               // 获取有序顶点并添加到列表
               var orderedVertices = GetOrderedBorderVertices(border.borderMesh, localToWorld);
               _drawnBorder.AddRange(orderedVertices);
           }
       }
   
       _lineRenderer.positionCount = _drawnBorder.Count;
       _lineRenderer.SetPositions(_drawnBorder.ToArray());
   }
   

3. 额外注意事项

   • 若Border Mesh包含多个独立边界线段，需拆分处理每个路径
   • 可在编辑器中提前预处理顶点顺序，减少运行时计算开销

内容的提问来源于stack exchange，提问作者Adam Brown