环境：

Open3D

1.1 凸包法介绍：

用于找到包围给定点集的最小凸多边形或凸多面体

常用的凸包算法：
Grabam扫描法（适用三维层面）
Jarvis卷包裹法（不适用三维层面）
Clarkson-Shor
QuickHull

2.1 python代码

import open3d as o3d
import numpy as np


def draw_point_cloud(result):
    for geometry in result:
        o3d.visualization.draw_geometries([geometry], "result", 800, 600,
                                          50, 50, False, False, True)


def main():
    np.random.seed(42)  # 设置随机种子以确保可重复性

    # 随机生成点云数据
    num_points = 1000
    points = np.random.rand(num_points, 3) * 10  # 在[0, 10)范围内生成点
    pc = o3d.geometry.PointCloud()
    pc.points = o3d.utility.Vector3dVector(points)

    result = [pc]

    # 凸包算法
    tm, tm_ls = o3d.geometry.TriangleMesh(), o3d.geometry.LineSet()
    res = pc.compute_convex_hull()
    tm, _ = res
    tm.compute_vertex_normals(True)
    tm_ls = o3d.geometry.LineSet.create_from_triangle_mesh(tm)
    color = np.random.rand(3)

    # 将tm_ls.lines转换为NumPy数组
    lines_np = np.asarray(tm_ls.lines)
    colors = np.tile(color, (lines_np.shape[0], 1))
    tm_ls.colors = o3d.utility.Vector3dVector(colors)

    print(f"凸包表面积为: {tm.get_surface_area()}")
    print(f"凸包体积为: {tm.get_volume()}")

    convex_hull_index = res[1]
    convex_hull_point = pc.select_by_index(convex_hull_index)
    convex_hull_point.paint_uniform_color([1, 0, 0])

    result.extend([convex_hull_point, tm_ls, tm])
    draw_point_cloud(result)

if __name__ == "__main__":
    main()

3.1 可视化

4.1 体积/表面积Calculation

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