Unity不规则（规则的亦可）物体表面积和体积计算

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这两个计算，首先想到的是从mesh入手（当然，包围盒可能更简单，但是实在太不精确，如果只是想得到大概的值，可以采取包围盒的方式计算）。

那接下来，从Mesh入手：

首先看一下Unity Mesh API：

这里呢，我们需要的主要是vertices，也就是Mesh的顶点

每三个点是一个面，通过面积公式，计算出每个面的面积S=√[p(p-l1)(p-l2)(p-l3)]（p为半周长）

而体积的思路，依然是通过顶点，每个三角面和中心点组成一个三棱锥，首先我们求以这三个向量为邻棱的平行六面体的面积，那就是（a×b）·c的绝对值，然后四面体的体积是平行六面体的六分之一，因为四面体的底是平行六面体的一半,而且要多乘一个三分之一。

详细代码如下：

using System;
using UnityEngine;

public static class MeshExtend
{
    public static float GetArea(this Transform obj, Action callbackError = null)
    {
        Mesh mesh = obj.GetComponent<MeshFilter>().mesh;
        if (mesh == null)
        {
            Debug.LogWarning("There is no 'MeshFilter' component!");
            callbackError?.Invoke();
            return -1;
        }

        Vector3[] vertices = mesh.vertices;
        Vector3 lossyScale = obj.lossyScale;

        float area = 0;
        for (int i = 0; i < mesh.subMeshCount; i++)
        {
            int[] triangles = mesh.GetTriangles(i);
            for (int j = 0; j < triangles.Length; j += 3)
            {
                area += CalculateTriangleArea(vertices[triangles[j]], vertices[triangles[j + 1]], vertices[triangles[j + 2]], lossyScale);
            }
        }

        return area;
    }

    private static float CalculateTriangleArea(Vector3 point1, Vector3 point2, Vector3 point3, Vector3 lossyScale)
    {
        //计算缩放
        point1 = new Vector3(point1.x * lossyScale.x, point1.y * lossyScale.y, point1.z * lossyScale.z);
        point2 = new Vector3(point2.x * lossyScale.x, point2.y * lossyScale.y, point2.z * lossyScale.z);
        point3 = new Vector3(point3.x * lossyScale.x, point3.y * lossyScale.y, point3.z * lossyScale.z);

        //计算边长
        float l1 = (point2 - point1).magnitude;
        float l2 = (point3 - point2).magnitude;
        float l3 = (point1 - point3).magnitude;
        float p = (l1 + l2 + l3) * 0.5f;

        //计算面积  S=√[p(p-l1)(p-l2)(p-l3)]（p为半周长）
        return Mathf.Sqrt(p * (p - l1) * (p - l2) * (p - l3));
    }

    public static float GetVolume(this Transform obj, Action callbackError = null)
    {
        Mesh mesh = obj.GetComponent<MeshFilter>().mesh;
        if (mesh == null)
        {
            Debug.LogWarning("There is no 'MeshFilter' component!");
            callbackError?.Invoke();
            return -1;
        }

        Vector3[] vertices = mesh.vertices;
        Vector3 lossyScale = obj.lossyScale;
        Vector3 o = GetCenter(vertices);

        float volume = 0;
        for (int i = 0; i < mesh.subMeshCount; i++)
        {
            int[] triangles = mesh.GetTriangles(i);
            for (int j = 0; j < triangles.Length; j += 3)
            {
                volume += CalculateVolumeOfTriangle(vertices[triangles[j]], vertices[triangles[j + 1]], vertices[triangles[j + 2]], o, lossyScale);
            }
        }

        return Mathf.Abs(volume);
    }

    private static Vector3 GetCenter(Vector3[] points)
    {
        Vector3 center = Vector3.zero;
        for (int i = 0; i < points.Length; i++)
        {
            center += points[i];
        }
        center = center / points.Length;
        return center;
    }

    private static float CalculateVolumeOfTriangle(Vector3 point1, Vector3 point2, Vector3 point3, Vector3 center, Vector3 lossyScale)
    {
        //计算缩放
        point1 = new Vector3(point1.x * lossyScale.x, point1.y * lossyScale.y, point1.z * lossyScale.z);
        point2 = new Vector3(point2.x * lossyScale.x, point2.y * lossyScale.y, point2.z * lossyScale.z);
        point3 = new Vector3(point3.x * lossyScale.x, point3.y * lossyScale.y, point3.z * lossyScale.z);

        //向量
        Vector3 v1 = point1 - center;
        Vector3 v2 = point2 - center;
        Vector3 v3 = point3 - center;

        //计算体积
        //首先我们求以这三个向量为邻棱的平行六面体的面积
        //那就是（a×b）·c的绝对值
        //然后四面体的体积是平行六面体的六分之一
        //因为四面体的底是平行六面体的一半,而且要多乘一个三分之一
        float v = Vector3.Dot(Vector3.Cross(v1, v2), v3) / 6f;
        return v;
    }
}