如何确定正方形与多边形相交的内边界顶点？Python实现求助

我正尝试编写Python脚本，获取正方形瓦片与n顶点闭合多边形之间相交内边缘的所有顶点坐标(x,y)。目前已完成如下代码，但得到的内边界顶点存在错误，请问是否有专门算法可用于确定内边缘，以明确搜索方向？

from shapely.geometry import Polygon, LineString, MultiLineString
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon as MplPolygon

square_coords = [
    (53906250, 35456250),     # lt
    (54296875, 35456250),   # rt
    (54296875, 35546875),  # rb
    (53906250, 35546785)     # lb
]

polygon_coords = [
    (54340742, 35518900),
    (53997222, 35518800),
    (53997298, 35183478),
    (54340666, 35183478),
    (54340742, 35518890)
]

square = Polygon(square_coords)
polygon = Polygon(polygon_coords)

intersection = square.intersection(polygon)

fig, ax = plt.subplots()
ax.set_aspect('equal')

square_patch = MplPolygon(list(square.exterior.coords), color='blue', alpha=0.4, label='Square')
ax.add_patch(square_patch)

polygon_patch = MplPolygon(list(polygon.exterior.coords), color='green', alpha=0.4, label='Polygon')
ax.add_patch(polygon_patch)

if not intersection.is_empty:
    if intersection.geom_type == 'Polygon':
        inter_coords = list(intersection.exterior.coords)
        inter_patch = MplPolygon(inter_coords, color='red', alpha=0.6, label='Intersection')
        ax.add_patch(inter_patch)
    elif intersection.geom_type == 'MultiPolygon':
        for part in intersection.geoms:
            inter_coords = list(part.exterior.coords)
            inter_patch = MplPolygon(inter_coords, color='red', alpha=0.6, label='Intersection')
            ax.add_patch(inter_patch)

polygon_boundary = polygon.boundary
intersection_boundary = intersection.boundary

inner_border = polygon_boundary.intersection(intersection_boundary)

if not inner_border.is_empty:
    if isinstance(inner_border, (LineString, MultiLineString)):
        if isinstance(inner_border, LineString):
            lines = [inner_border]
        else:
            lines = list(inner_border.geoms)

        for line in lines:
            x, y = line.xy
            ax.plot(x, y, color='black', linewidth=2, label='Inner Border')
            ax.scatter([x[0], x[-1]], [y[0], y[-1]], color='purple', s=40, zorder=10)
            ax.text(x[0], y[0], f"({x[0]:.5f}, {y[0]:.5f})", fontsize=7, color='purple')
            ax.text(x[-1], y[-1], f"({x[-1]:.5f}, {y[-1]:.5f})", fontsize=7, color='purple')

ax.set_title("Polygon-Square Intersection & Inner Border")
ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.grid(True)
ax.legend()
plt.tight_layout()
plt.show()

我的目标是获取示例图中黄色边界上的所有相交顶点坐标(x,y)：

内容的提问来源于stack exchange，提问作者tomazj