计算 3D 网格的体积

我厌倦了计算 3D 物体（立方体、圆柱体...）的体积，有人可以帮忙吗

有这个问题吗？问题是，如何计算物体的体积

基于三角形的坐标。我的班级做得不好，有人能帮我吗

提高班级水平 ?

thanks

public class Algorithm
{
    private  Mesh _mesh { get; set; }

    public Algorithm(Mesh mesh)
    {
        _mesh = mesh;
    }

    private double SignedVolumeOfTriangle(Vector3 p1, Vector3 p2, Vector3 p3)
    {
        var v321 = p3.X * p2.Y * p1.Z;
        var v231 = p2.X * p3.Y * p1.Z;
        var v312 = p3.X * p1.Y * p2.Z;
        var v132 = p1.X * p3.Y * p2.Z;
        var v213 = p2.X * p1.Y * p3.Z;
        var v123 = p1.X * p2.Y * p3.Z;
        return (1.0 / 6.0) * (-v321 + v231 + v312 - v132 - v213 + v123);
    }

    public double VolumeOfMesh()
    {
        double volume = 0.0;

        Vector3[] vertices = _mesh.Vertices;
        int[] triangles = _mesh.Triangles;

        for (int i = 0; i < _mesh.Triangles.Length; i += 3)
        {
            Vector3 p1 = vertices[triangles[i + 0]];
            Vector3 p2 = vertices[triangles[i + 1]];
            Vector3 p3 = vertices[triangles[i + 2]];

            volume += SignedVolumeOfTriangle(p1, p2, p3);
        }

        return Math.Abs(volume);
    }
}



public  class Mesh
{
    public Mesh(Vector3[] _vertices,int[] _triangles)
    {
        Vertices = _vertices;
        Triangles = _triangles;
    }

    public Vector3[] Vertices { get; set; }

    public int[] Triangles { get; set; }
}


public class Vector3
{
    public Vector3()
    {

    }

    public Vector3(double x,double y,double z)
    {
        X = x;
        Y = y;
        Z = z;
    }

    public double X { get; set; }

    public double Y { get; set; }

    public double Z { get; set; }
}



private void button1_Click(object sender, EventArgs e)
{
        Vector3[] vers = new Vector3[8] {
                                    new Vector3 {X = 5,Y = 5,Z =5},
                                    new Vector3 {X = 15,Y = 5,Z =5},
                                    new Vector3 {X = 15,Y = 15,Z =5},
                                    new Vector3 {X = 5,Y = 15,Z =5},
                                    new Vector3 {X = 5,Y = 5,Z =15},
                                    new Vector3 {X = 15,Y = 5,Z =15},
                                    new Vector3 {X = 15,Y = 15,Z =15},
                                    new Vector3 {X = 5,Y = 15,Z =15},
        };

        int[] trs = new int[36] { 0, 1, 2, 0, 2, 3, 4, 5, 6, 4, 6, 7, 
                                  1, 6, 2, 1, 5, 6, 0, 4, 7, 0, 7, 3,
                                  0, 1, 5, 0, 5, 4, 3, 2, 6,3, 6, 7 };


        Mesh mesh = new Mesh(vers, trs);
        Algorithm algo = new Algorithm(mesh);
        var vol = algo.VolumeOfMesh();

        MessageBox.Show(vol.ToString());
}

我的测试结果是vol = 666,666，但它应该是1000。

线路

double v132 = (p3.X - basePoint.X) * (p3.Y - basePoint.Y) * (p2.Z - basePoint.Z);

根据不正确如何计算表面由三角形组成的 3D 网格对象的体积 https://stackoverflow.com/questions/1406029/how-to-calculate-the-volume-of-a-3d-mesh-object-the-surface-of-which-is-made-up-t它应该是（注意 p1.X 而不是 p3.X）：

var v132 = p1.X*p3.Y*p2.Z;

EDIT

尽管您将此答案标记为正确，但我测试了代码并发现了更多错误。

通过调整三角形索引，三角形并不全部朝外（或朝内）：

0, 1, 2,
0, 2, 3,
4, 6, 5,
4, 7, 6,// adjusted
1, 6, 2,
1, 5, 6,
0, 7, 4,// adjusted
0, 3, 7,// adjusted
0, 5, 1,// adjusted
0, 4, 5,// adjusted
3, 2, 6,
3, 6, 7

所有法线均朝外。然后计算返回 -1000 负值，具体取决于基本偏移量。