Unity中如何将一些3D点都在同一平面上降维为2D？

Question

我有一个包含四个 3D 点 (Vector3[]) 的数组，它们都在同一平面上。我将 Unity 与 C# 一起使用，目的是将 2D Traingulator 用于这 4 个点。

using UnityEngine;

Vector3[] vertices3D = new Vector3[] {
    new Vector3(0,10,0),
    new Vector3(50,20,0),
    new Vector3(0,10,30),
    new Vector3(50,20,30)
};

由于Triangulator只适用于二维，所有的点都在同一个平面上，所以方法应该是计算基向量或平面的主成分，但我找不到如何.我想将点的维数减少到 2D，以便以生成的三角形位于平面上的方式为它们使用 Triangulator。

所以我想要的输出只有三角形。

Triangulator的源代码在here, and my goal is to create a mesh for the given points, but as you see the following sample code，三角测量仪的输入点应该是二维的：

using UnityEngine;

public class PolygonTester : MonoBehaviour {
    void Start () {
        // Create Vector2 vertices
        Vector2[] vertices2D = new Vector2[] {
            new Vector2(0,0),
            new Vector2(0,50),
            new Vector2(50,50),
            new Vector2(50,100)
        };

        // Use the triangulator to get indices for creating triangles
        Triangulator tr = new Triangulator(vertices2D);
        int[] indices = tr.Triangulate();

        // Create the Vector3 vertices
        Vector3[] vertices = new Vector3[vertices2D.Length];
        for (int i=0; i<vertices.Length; i++) {
            vertices[i] = new Vector3(vertices2D[i].x, vertices2D[i].y, 0);
        }

        // Create the mesh
        Mesh msh = new Mesh();
        msh.vertices = vertices;
        msh.triangles = indices;
        msh.RecalculateNormals();
        msh.RecalculateBounds();

        // Set up game object with mesh;
        gameObject.AddComponent(typeof(MeshRenderer));
        MeshFilter filter = gameObject.AddComponent(typeof(MeshFilter)) as MeshFilter;
        filter.mesh = msh;
    }
}

Answer 1

解决方案 1 - 平凡

如果四边形是凸的并且您知道顶点的顺序，请使用indices = new double[6]{0,1,2,0,2,3};

解决方案 2 - 手动三角测量

如果四边形是凸的，但您不确定顺序，请测试方向并调整索引。

edge1 = vertices3D[1] - vertices3D[0];
edge2 = vertices3D[2] - vertices3D[0];
edge3 = vertices3D[3] - vertices3D[0];
normal12 = Vector3.Cross(edge1, edge2);
normal23 = Vector3.Cross(edge2, edge3);
if (Vector3.Dot(normal12, normal23) > 0)
   indices = new double[6]{0,1,2,0,2,3};
else
   indices = new double[6]{0,1,3,0,3,2};

解决方案 3 - 使用三角测量器

如果四边形不是凸的，或者您确实必须使用库 Triangulator，请变换所有顶点，使它们位于 XY 平面上，第一个顶点位于 (0,0,0)。

edge1 = vertices3D[1] - vertices3D[0];
edge2 = vertices3D[2] - vertices3D[0];
normal = Vector3.Cross(edge1, edge2).normalized;
rotation = Quaternion.FromToRotation(normal, new Vector3(0,0,1));
Vector2[] vertices2D = new Vector2[vertices3D.Length];
for (int i=0; i<vertices3D.Length; i++) {
    rotatedVertex = rotation * (vertices3D[i]-vertices3D[0]);
    vertices2D[i] = new Vector2(rotatedVertex.x, rotatedVertex.y);
}

我不建议只用 4 个点形成一堵墙使用 Triangulator。但是，它对于复杂的多边形和非凸形状应该会很方便。

Unity中如何将一些3D点都在同一平面上降维为2D？

How to reduce the dimensionality of some 3D points, which are all on the same plane, to 2D in Unity?

c#

algorithm

unity3d

geometry

triangulation