最近專案需要對不規則物體的體積與面積進行計算，查閱了很多資料都沒有進展，有的說用微積分的也有用VTK的感覺這些都很麻煩而且沒有具體明確的思路，今天看到一篇相關資料感覺很簡單易懂而切也很實用。

    程式碼如下：

using System.Collections;
using System.Collections.Generic;
using UnityEngine;[RequireComponent(typeof(MeshFilter))]
public class MeshCalculator : MonoBehaviour
{
    private MeshFilter mf = null;
    private Vector3 scale;
    private float sum;
    private string sum1;
    // Use this for initialization
    void Start()
    {
        this.mf = this.GetComponent<MeshFilter>();
        //有損縮放
        this.scale = this.transform.lossyScale;        this.CalculateSumArea();
        this.CalculateSumVolume();
    }    private void CalculateSumVolume()
    {
        Vector3[] arrVertices = this.mf.mesh.vertices;
        int[] arrTriangles = this.mf.mesh.triangles;
        float sum = 0.0f;        for (int i = 0; i < this.mf.mesh.subMeshCount; i++)
        {
            int[] arrIndices = this.mf.mesh.GetTriangles(i);
            for (int j = 0; j < arrIndices.Length; j += 3)
                sum += this.CalculateVolume(arrVertices[arrIndices[j]]
                                        , arrVertices[arrIndices[j + 1]]
                                        , arrVertices[arrIndices[j + 2]]);
        }
               
        Debug.Log("Volume= " + Mathf.Abs(sum));
    }    private void CalculateSumArea()
    {
        Vector3[] arrVertices = this.mf.mesh.vertices;
        int[] arrTriangles = this.mf.mesh.triangles;
        float sum1 = 0.0f;        for (int i = 0; i < this.mf.mesh.subMeshCount; i++)
        {
            int[] arrIndices = this.mf.mesh.GetTriangles(i);
            for (int j = 0; j < arrIndices.Length; j += 3)
                sum1 += this.CalculateArea(arrVertices[arrIndices[j]]
                                        , arrVertices[arrIndices[j + 1]]
                                        , arrVertices[arrIndices[j + 2]]);
        }
             Debug.Log("Area = " + sum1);
    }    private float CalculateVolume(Vector3 pt0, Vector3 pt1, Vector3 pt2)
    {
        pt0 = new Vector3(pt0.x * this.scale.x, pt0.y * this.scale.y, pt0.z * this.scale.z);
        pt1 = new Vector3(pt1.x * this.scale.x, pt1.y * this.scale.y, pt1.z * this.scale.z);
        pt2 = new Vector3(pt2.x * this.scale.x, pt2.y * this.scale.y, pt2.z * this.scale.z);        float v321 = pt2.x * pt1.y * pt0.z;
        float v231 = pt1.x * pt2.y * pt0.z;
        float v312 = pt2.x * pt0.y * pt1.z;
        float v132 = pt0.x * pt2.y * pt1.z;
        float v213 = pt1.x * pt0.y * pt2.z;
        float v123 = pt0.x * pt1.y * pt2.z;        return (1.0f / 6.0f) * (-v321 + v231 + v312 - v132 - v213 + v123);
    }    private float CalculateArea(Vector3 pt0, Vector3 pt1, Vector3 pt2)
    {
        pt0 = new Vector3(pt0.x * this.scale.x, pt0.y * this.scale.y, pt0.z * this.scale.z);
        pt1 = new Vector3(pt1.x * this.scale.x, pt1.y * this.scale.y, pt1.z * this.scale.z);
        pt2 = new Vector3(pt2.x * this.scale.x, pt2.y * this.scale.y, pt2.z * this.scale.z);        float a = (pt1 - pt0).magnitude;
        float b = (pt2 - pt1).magnitude;
        float c = (pt0 - pt2).magnitude;
        float p = (a + b + c) * 0.5f;        return Mathf.Sqrt(p * (p - a) * (p - b) * (p - c));
    }   /* private void OnGUI()
    {
        GUILayout.Label("體積：" + Mathf.Abs(sum));
        GUILayout.Label("面積：" +sum1);
    }*/}

經測試符合對不規則物體的體積表面積的求解

有篇國外的論文提到了一種計算方式。有興趣的童學可以看看，演算法非常簡單，程式碼量也少。
專案是在Unity平臺做的，我用的是C#程式碼，你們還可以參考這個unity帖子。

他通過對每個三角面片求其面積然後進行總的相加就可以了，但是對於那篇論文上講解的對三角面片的買諾記求解那塊不是很理解，希望有懂得的人指導一下。

轉自：https://blog.csdn.net/zhang_hui_cs/article/details/77618329