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)。
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,计算出其所在平行六面体的体积,四面体的体积就是其1/6
详细代码如下:
/*******************************************************************************
* 版本声明:v1.0.0
* 类 名 称:AreaCalculation
* 创建日期:2021-03-31 17:08:28
* 作者名称:末零
* 功能描述:根据网格获取表面积和体积
* 修改记录:
*
******************************************************************************/
using System;
using UnityEngine;
namespace LastZero.Utility
{
/// <summary>
/// 表面积、体积的计算
/// </summary>
public static class MeshExtend
{
/// <summary>
/// 获取表面积
/// </summary>
/// <param name="obj">带有MeshFilter的物体</param>
/// <param name="callbackError">错误回调</param>
/// <returns>表面积</returns>
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;
}
/// <summary>
/// 计算三角形面积
/// </summary>
/// <param name="point1">顶点1</param>
/// <param name="point2">顶点2</param>
/// <param name="point3">顶点3</param>
/// <returns>面积</returns>
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));
}
/// <summary>
/// 获取体积
/// </summary>
/// <param name="obj">带有MeshFilter的物体</param>
/// <param name="callbackError">错误回调</param>
/// <returns></returns>
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);
}
/// <summary>
/// 获取中心点
/// </summary>
/// <param name="points">顶点</param>
/// <returns>中心点</returns>
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;
}
/// <summary>
/// 计算一个面和中心点组成三棱锥的体积
/// </summary>
/// <param name="point1">顶点1</param>
/// <param name="point2">顶点2</param>
/// <param name="point3">顶点3</param>
/// <param name="center">中心点</param>
/// <returns></returns>
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;
}
}
}