Unity不规则（规则的亦可）物体表面积和体积计算

2024-03-12 20:50| 来源: 网络整理| 查看: 265

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 { /// /// 表面积、体积的计算 /// public static class MeshExtend { /// /// 获取表面积 /// /// 带有MeshFilter的物体 /// 错误回调 /// 表面积 public static float GetArea(this Transform obj, Action callbackError = null) { Mesh mesh = obj.GetComponent().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; } /// /// 计算三角形面积 /// /// 顶点1 /// 顶点2 /// 顶点3 /// 面积 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)); } /// /// 获取体积 /// /// 带有MeshFilter的物体 /// 错误回调 /// public static float GetVolume(this Transform obj, Action callbackError = null) { Mesh mesh = obj.GetComponent().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); } /// /// 获取中心点 /// /// 顶点 /// 中心点 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; } /// /// 计算一个面和中心点组成三棱锥的体积 /// /// 顶点1 /// 顶点2 /// 顶点3 /// 中心点 /// 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; } } }

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