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Copy pathcircle-inscribed-with-pentagram-v2.py
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circle-inscribed-with-pentagram-v2.py
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import matplotlib.pyplot as plt
import numpy as np
def find_intersection_point(p1, p2, p3, p4):
# 寻找线段p1p2和线段p3p4的交点
x_num = (p1[0] * p2[1] - p1[1] * p2[0]) * (p3[0] - p4[0]) - (p1[0] - p2[0]) * (p3[0] * p4[1] - p3[1] * p4[0])
x_denom = (p1[0] - p2[0]) * (p3[1] - p4[1]) - (p1[1] - p2[1]) * (p3[0] - p4[0])
y_num = (p1[0] * p2[1] - p1[1] * p2[0]) * (p3[1] - p4[1]) - (p1[1] - p2[1]) * (p3[0] * p4[1] - p3[1] * p4[0])
y_denom = (p1[0] - p2[0]) * (p3[1] - p4[1]) - (p1[1] - p2[1]) * (p3[0] - p4[0])
if x_denom == 0 or y_denom == 0:
raise ValueError("Lines are parallel and do not intersect.")
intersection_x = x_num / x_denom
intersection_y = y_num / y_denom
return intersection_x, intersection_y
star_points = []
focus_points = []
distance = 0
radius1 = 4.2
intersections = []
edges = [('B', 'D'), ('B', 'E'), ('C', 'A'), ('C', 'E'), ('A', 'D')]
intersection_points = []
def draw_star(center, radius):
angle_offset = np.radians(54)
# 计算五角星的五个顶点坐标，并让一个顶点朝上
angles = (np.linspace(0, 2 * np.pi, 6)[:-1] + np.pi / 10 ) + angle_offset
star_points = [(center[0] + radius * np.cos(angle), center[1] + radius * np.sin(angle)) for angle in angles]
# 绘制圆
circle = plt.Circle(center, radius, fill=False, color='blue')
circle1 = plt.Circle(center, radius1, fill=False, color='blue')
plt.gca().add_patch(circle)
plt.gca().add_patch(circle1)
# 绘制五角星
star = plt.Polygon(star_points, fill=False, color='red')
# 绘制五角星的五个顶点到圆心的连线
plt.gca().add_patch(star)
focus_pointss = []
# 存储焦点坐标和外圆的顶点
points_dict = {'C': center, 'F': (0, 0)}
for i in range(5):
point_label = chr(65 + i) # 使用字母标记点，A对应索引0，B对应索引1，以此类推
points_dict[point_label] = star_points[i]
plt.plot([center[0], star_points[i][0]], [center[1], star_points[i][1]], color='green')
# 绘制相隔一个点的连线
next_index = (i + 2) % 5
plt.plot([star_points[i][0], star_points[next_index][0]], [star_points[i][1], star_points[next_index][1]],color='green')
# 计算焦点坐标并添加到列表中
focus_x = (star_points[i][0] + star_points[next_index][0]) / 2
focus_y = (star_points[i][1] + star_points[next_index][1]) / 2
focus_points.append((focus_x, focus_y))
# 设置画布大小和坐标轴范围
plt.axis('equal')
plt.xlim(center[0] - radius, center[0] + radius)
plt.ylim(center[1] - radius, center[1] + radius)
# 绘制内切圆
for i, focus_point in enumerate(focus_points):
# 计算焦点与圆心的距离
distance = np.sqrt(focus_point[0] ** 2 + focus_point[1] ** 2)
# 绘制内切圆
tangent_circle = plt.Circle(center, distance, fill=False, color='orange', linestyle='dashed')
plt.gca().add_patch(tangent_circle)
# 计算新的焦点坐标（顺时针旋转36°）
new_x = focus_point[0] * np.cos(np.radians(36)) - focus_point[1] * np.sin(np.radians(36))
new_y = focus_point[0] * np.sin(np.radians(36)) + focus_point[1] * np.cos(np.radians(36))
# 绘制新坐标的标记点
plt.scatter(new_x, new_y, color='orange')
# 将新焦点坐标追加到focus_points列表中
focus_pointss.append((new_x, new_y))
print("distance is:", distance)
# 标注焦点坐标
focus_points.extend(focus_pointss)
for i, focus_point in enumerate(focus_points):
plt.text(focus_point[0], focus_point[1], f'F{i + 1}', color='black', fontsize=12)
print(focus_points)
# 标注点的字母标记
for label, point in points_dict.items():
plt.text(point[0], point[1], label, ha='center', va='center', fontsize=12)
print(points_dict)
# 计算内切圆与线段的交点
def circle_line_intersection(circle_radius, point1, point2):
x1, y1 = point1
x2, y2 = point2
dx = x2 - x1
dy = y2 - y1
dr = np.sqrt(dx ** 2 + dy ** 2)
D = x1 * y2 - x2 * y1
discriminant = circle_radius ** 2 * dr ** 2 - D ** 2
if discriminant >= 0:
x_intersection1 = (D * dy + np.sign(dy) * dx * np.sqrt(discriminant)) / dr ** 2
y_intersection1 = (-D * dx + np.abs(dy) * np.sqrt(discriminant)) / dr ** 2
x_intersection2 = (D * dy - np.sign(dy) * dx * np.sqrt(discriminant)) / dr ** 2
y_intersection2 = (-D * dx - np.abs(dy) * np.sqrt(discriminant)) / dr ** 2
return [(x_intersection1, y_intersection1), (x_intersection2, y_intersection2)]
else:
return []
# 计算circle1（内切圆）与线段BD、BE、CA、CE、AD的交点，并存在列表中
line_segments = [(points_dict['B'], points_dict['D']), (points_dict['B'], points_dict['E']),
(points_dict['C'], points_dict['A']), (points_dict['C'], points_dict['E']),
(points_dict['A'], points_dict['D'])]
for segment in line_segments:
points = circle_line_intersection(radius1, segment[0], segment[1])
intersections.extend(points)
# 线段BE与线段AC的交点
intersection_point_BE_AC = find_intersection_point(points_dict['B'], points_dict['E'], points_dict['A'],points_dict['C'])
plt.scatter(*intersection_point_BE_AC, color='purple', marker='x')
intersection_points.append(intersection_point_BE_AC)
# 线段BE与线段AD的交点
intersection_point_BE_AD = find_intersection_point(points_dict['B'], points_dict['E'], points_dict['A'],points_dict['D'])
plt.scatter(*intersection_point_BE_AD, color='purple', marker='x')
intersection_points.append(intersection_point_BE_AD)
# 线段CE与线段DB的交点
intersection_point_CE_DB = find_intersection_point(points_dict['C'], points_dict['E'], points_dict['D'],points_dict['B'])
plt.scatter(*intersection_point_CE_DB, color='purple', marker='x')
intersection_points.append(intersection_point_CE_DB)
# 线段CE与线段DA的交点
intersection_point_CE_DA = find_intersection_point(points_dict['C'], points_dict['E'], points_dict['D'],points_dict['A'])
plt.scatter(*intersection_point_CE_DA, color='purple', marker='x')
intersection_points.append(intersection_point_CE_DA)
# 线段DB与线段AC的交点
intersection_point_DB_AC = find_intersection_point(points_dict['D'], points_dict['B'], points_dict['A'],points_dict['C'])
plt.scatter(*intersection_point_DB_AC, color='purple', marker='x')
intersection_points.append(intersection_point_DB_AC)
# 标注交点坐标
for i, intersection_point in enumerate(intersection_points):
plt.text(intersection_point[0], intersection_point[1], f'P{i + 1}', color='purple', fontsize=12)
print(f"P{i+1}:({intersection_point[0],intersection_point[1]})")
# 计算EF的延长线的终点坐标
F_x, F_y = points_dict["F"]
EF_extension_x = 3 * focus_points[5][0] - F_x
EF_extension_y = 3 * focus_points[5][1] - F_y
# 绘制EF延长线
plt.plot([F_y, EF_extension_x], [F_x, EF_extension_y], color='purple', linestyle='dashed')
rotation_angle = np.radians(-90)
rotated_EF_extension_x = EF_extension_x * np.cos(rotation_angle) - EF_extension_y * np.sin(rotation_angle)
rotated_EF_extension_y = EF_extension_x * np.sin(rotation_angle) + EF_extension_y * np.cos(rotation_angle)
plt.plot([-rotated_EF_extension_x, rotated_EF_extension_x], [-rotated_EF_extension_y, rotated_EF_extension_y],color='black', linestyle='dashed')
# 输入点的坐标
B = points_dict["B"]
new_Bx = B[0]
new_By = B[1]
# 添加双曲线
a = 1.55
k = round(new_By / new_Bx, 1)
b = round(a * k, 2)
x_hyperbola = np.linspace(-a * 5, a * 5, 1000)
y_hyperbola = np.sqrt((x_hyperbola ** 2 / a ** 2 - 1) * b ** 2)
plt.plot(x_hyperbola, y_hyperbola, color='purple', linestyle='--', label='Hyperbola: x^2/1.55^2 - y^2/0.93^2 = 1')
plt.plot(x_hyperbola, -y_hyperbola, color='purple', linestyle='--')
plt.show()
def main():
center = (0, 0) # 圆心坐标
radius = 5 # 圆的半径
draw_star(center, radius)
if __name__ == '__main__':
main()