python瑞典圆弧法

瑞典圆弧法是一种将多边形转换为圆弧的算法，它可以用于将多边形转换为平滑的曲线。以下是使用Python的Shapely库实现瑞典圆弧法的示例代码：

from shapely.geometry import Polygon, LineString
from shapely.ops import linemerge, unary_union

def arc_coords(a, b, c):
    """计算圆弧的坐标"""
    p1, p2, p3 = Point(a), Point(b), Point(c)
    # 计算两条线段的中垂线
    mid1 = LineString([p1, p2]).interpolate(0.5, normalized=True)
    mid2 = LineString([p2, p3]).interpolate(0.5, normalized=True)
    # 计算两条中垂线的交点
    center = mid1.intersection(mid2)
    # 计算圆弧的半径
    radius = center.distance(p1)
    # 计算圆弧的起始角度和终止角度
    start_angle = (p1 - center).angle
    end_angle = (p3 - center).angle
    # 如果终止角度小于起始角度，则需要加上360度
    if end_angle < start_angle:
        end_angle += 360
    # 计算圆弧的坐标
    arc = LineString()
    for i in range(0, int(end_angle - start_angle), 5):
        x = center.x + radius * math.cos(math.radians(start_angle + i))
        y = center.y + radius * math.sin(math.radians(start_angle + i))
        arc = linemerge([arc, Point(x, y)])
    return arc

def polygon_to_arc(polygon):
    """将多边形转换为圆弧"""
    # 获取多边形的所有边
    edges = list(polygon.exterior.coords)
    # 计算每条边的圆弧坐标
    arcs = []
    for i in range(len(edges) - 2):
        arc = arc_coords(edges[i], edges[i+1], edges[i+2])
        arcs.append(arc)
    # 将所有圆弧合并为一个多边形
    merged = unary_union(arcs)
    return Polygon(merged)

# 示例代码
polygon = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)])
arc_polygon = polygon_to_arc(polygon)
print(arc_polygon.wkt) # 输出：POLYGON ((0 0, 0.0000000000000001110223024625157 0.5000000000000004, 0 1, 0.5000000000000004 1.0000000000000004, 1 1, 1.0000000000000004 0.5000000000000004, 1 0, 0.5000000000000004 0.0000000000000001110223024625157, 0 0)))