你需要计算出一个边长

的长方体

边长根据半径(从中心到顶点的距离)计算

apotem(从一条边的中心到中点的距离)是从边长计算出来的。

(more here)

在下面的示例中，bbox位于创建的多边形的中心；您可以根据需要偏移它以匹配您的首选锚定点。在

给定同一个边界框，所有多边形都被计算成内接在同一个圆内——外接圆是多边形边数趋于无穷大时的极限，见下图。在import tkinter as tk

import math

WIDTH, HEIGHT = 500, 500

class Point:

"""convenience for point arithmetic"""

def __init__(self, x, y):

self.x, self.y = x, y

def __add__(self, other):

return Point(self.x + other.x, self.y + other.y)

def __iter__(self):

yield self.x

yield self.y

class RegularPolygon:

def __init__(self, num_sides, bbox_side, x, y): # x, y are bbox center canvas coordinates

self.bbox_side = bbox_side

self.num_sides = num_sides

self.side_length = None

self.apothem = None

self._calc_side_length()

self.points = [Point(x - self.side_length // 2, y - self.apothem)]

self._make_points()

self.lines = []

self._make_lines()

def _calc_side_length(self):

"""Side length given the radius (circumradius):

i/e the distance from the center to a vertex

"""

self.side_length = 2 * (self.bbox_side // 2) * math.sin(math.pi / self.num_sides)

# Apothem, i/e distance from the center of the polygon

# to the midpoint of any side, given the side length

self.apothem = self.side_length / (2 * math.tan(math.pi / self.num_sides))

def _make_points(self):

_angle = 2 * math.pi / self.num_sides

for pdx in range(self.num_sides):

angle = _angle * pdx

_x = math.cos(angle) * self.side_length

_y = math.sin(angle) * self.side_length

self.points.append(self.points[-1] + Point(_x, _y))

def _make_lines(self):

for p0, p1 in zip(self.points[:-1], self.points[1:]):

self.lines.append((*p0, *p1))

def draw(self, canvas):

for line in self.lines:

canvas.create_line(line)

# alternatively, use canvas.create_polygon(points coordinates) instead

root = tk.Tk()

canvas = tk.Canvas(root, width=WIDTH, height=HEIGHT, bg="cyan")

canvas.pack()

CENTER = Point(WIDTH // 2, HEIGHT // 2)

for n_sides in range(3, 12):

p = RegularPolygon(n_sides, 300, *CENTER)

p.draw(canvas)

root.mainloop()

绘制3到12个边的规则多边形(包括)

给定相同的边界框，所有多边形都被计算为内接在同一个圆内，即外接圆。