计算三维网格的体积

本文关键字：维网格 三维 计算 | 更新日期: 2023-09-27 17:50:36

我累了计算三维物体(立方体，圆柱体…)的体积，有谁可以帮助

这个问题?问题是，如何从他的

计算出物体的体积基于三角形的

坐标。我们班的功课做得不好，谁来帮我一下?

改进类?

感谢
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

计算三维网格的体积

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

是不正确的，根据如何计算一个三维网格对象的体积，其表面是由三角形组成的，它应该是(注意p1。(3):

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

编辑

虽然你把这个答案标记为正确，但我测试了代码，发现了更多的错误。

通过调整三角形索引并不是所有的三角形都向外(或向内):

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

所有法线向外。然后，根据基本偏移量，计算返回-1000。

相关文章：