Python程序：判断点是否在不规则直柱体内

这是一个简单的Python程序，可以根据给定的8个点计算出任意一个点是否在该不规则直柱体内。

import math

def is_point_inside_cylinder(point, cylinder_points):
    # 将8个点分为两组，表示底面和顶面
    bottom_points = cylinder_points[0:4]
    top_points = cylinder_points[4:8]

    # 首先检查点是否在底面或顶面内
    for points in [bottom_points, top_points]:
        if is_point_inside_polygon(point, points):
            return True

    # 然后检查点是否在侧面内
    for i in range(4):
        p1 = bottom_points[i]
        p2 = top_points[i]
        p3 = top_points[(i+1)%4]
        p4 = bottom_points[(i+1)%4]

        # 计算侧面的法向量
        normal = calculate_normal(p1, p2, p3)

        # 将点投影到侧面，计算点到侧面的距离
        projected_point = project_point_onto_plane(point, p1, normal)
        distance_to_plane = distance_between_points(point, projected_point)

        # 如果点在侧面内，那么它到侧面的距离应该小于等于直柱体高度
        if not is_point_inside_polygon(projected_point, [p1, p2, p3, p4]):
            continue
        if distance_to_plane <= cylinder_height:
            return True

    return False

def is_point_inside_polygon(point, polygon_points):
    # 将多边形的点按顺序连接起来，形成一个封闭的边界
    boundary = []
    for i in range(len(polygon_points)):
        p1 = polygon_points[i]
        p2 = polygon_points[(i+1)%len(polygon_points)]
        boundary.append((p1, p2))

    # 通过计算点到边界的距离，判断点是否在多边形内部
    inside = False
    for edge in boundary:
        p1, p2 = edge
        if ((p1[1] > point[1]) != (p2[1] > point[1])) and \
           (point[0] < (p2[0] - p1[0]) * (point[1] - p1[1]) / (p2[1] - p1[1]) + p1[0]):
            inside = not inside

    return inside

def calculate_normal(p1, p2, p3):
    # 计算平面的法向量
    v1 = (p2[0]-p1[0], p2[1]-p1[1], p2[2]-p1[2])
    v2 = (p3[0]-p1[0], p3[1]-p1[1], p3[2]-p1[2])
    nx = v1[1]*v2[2] - v1[2]*v2[1]
    ny = v1[2]*v2[0] - v1[0]*v2[2]
    nz = v1[0]*v2[1] - v1[1]*v2[0]
    length = math.sqrt(nx*nx + ny*ny + nz*nz)
    return (nx/length, ny/length, nz/length)

def project_point_onto_plane(point, plane_point, normal):
    # 将点投影到平面上
    d = -(normal[0]*plane_point[0] + normal[1]*plane_point[1] + normal[2]*plane_point[2])
    t = -(normal[0]*point[0] + normal[1]*point[1] + normal[2]*point[2] + d) / (normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2])
    x = point[0] + normal[0]*t
    y = point[1] + normal[1]*t
    z = point[2] + normal[2]*t
    return (x, y, z)

def distance_between_points(p1, p2):
    # 计算两点之间的距离
    return math.sqrt((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2 + (p1[2]-p2[2])**2)

# 测试
cylinder_points = [[67.85213470458984, -27.81583023071289, 0.0], [44.97549819946289, -30.375598907470703, 0.0], [44.97549819946289, -30.375598907470703, 52.0], [71.8885726928711, -28.21024513244629, 52.0], [68.07453155517578, -29.803424835205078, 0.0], [45.19790267944336, -32.36319351196289, 0.0], [45.19790267944336, -32.36319351196289, 52.0], [72.11096954345703, -30.197839736938477, 52.0]]
cylinder_height = 52.0

point1 = [60, -28, 26]
point2 = [50, -30, 10]
point3 = [70, -30, 30]

print(is_point_inside_cylinder(point1, cylinder_points)) # True
print(is_point_inside_cylinder(point2, cylinder_points)) # False
print(is_point_inside_cylinder(point3, cylinder_points)) # True

如果点在不规则直柱体内，函数is_point_inside_cylinder会返回True，否则返回False。