How do I create a pentagon and hexagon using create_line in python tkinter canvas?

问题

Here is the code I have for drawing a triangle and square in python tkinter canvas using create_lines, how would I use create_lines to create a pentagon and hexagon?

Note: For the pentagon and hexagon, the length and width refer to the total square shaped area the shape is contained within, not the width and length of the sides.

    self.x, self.y = 50, 50

def triangle(self):
    width = self.width.get()
    length = self.length.get()
    color = self.color_select.get()

    self.canvas.create_line(self.x, self.y, (self.x + (int(length) / 2)), (self.y + int(length)), fill = color)

    self.canvas.create_line(self.x, self.y, (self.x - (int(length) / 2)), (self.y + int(length)), fill = color)

    self.canvas.create_line((self.x - (int(length) / 2)), (self.y + int(length)), (self.x + (int(length) / 2)), (self.y + int(length)), fill = color)

    self.x += 50

def square(self):
    width = self.width.get()
    length = self.length.get()
    color = self.color_select.get()

    self.canvas.create_line(self.x, self.y, self.x + int(width), self.y, fill = color)

    self.canvas.create_line(self.x, self.y, self.x, self.y + int(length), fill = color)
    self.y += int(length)

    self.canvas.create_line(self.x, self.y, self.x + int(width), self.y, fill = color)
    self.x += int(width)

    self.canvas.create_line(self.x, self.y, self.x, self.y - int(length), fill = color)
    self.y -= int(length)

    self.x += 50

def pentagon(self):
    width = self.width.get()
    length = self.length.get()
    color = self.color_select.get()

def hexagon(self):
    width = self.width.get()
    length = self.length.get()
    color = self.color_select.get()

回答1:

To create a regular polygon from a bounding box, you need to calculate the side length, and the apothem.
The side length is calculated from the radius (the distance from the center to a vertex)
The Apothem (the distance from the center to the mid-point of a side), is calculated from the side length.
(more here)

in the following example, the bbox is centered on the center of the polygon created; you can offset it as you please to match your preferred anchoring point.

Given the same bounding box, all polygons are calculated to be inscribed in the same circle - the circumcircle, which is the limit of a polygon when the number of sides tends to infinity, see image below.

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()  

Drawing regular polygons from 3 to 12 sides (incl)

Given the same bounding box, all polygons are calculated to be inscribed in the same circle, the circumcircle.

来源：https://stackoverflow.com/questions/55842453/how-do-i-create-a-pentagon-and-hexagon-using-create-line-in-python-tkinter-canva