from math import sin, cos, pi
import matplotlib.pyplot as plt
from matplotlib.patches import Circle, RegularPolygon
from matplotlib.animation import FuncAnimation
from matplotlib import colormaps as cm
import matplotlib.colors as mplcolors


RADIUS_C = 1

num_sides = [i for i in range(3, 11)]
num_sides_min = min(num_sides)
num_sides_max = max(num_sides)
num_frames = len(num_sides)

cmap = cm.get_cmap("winter")
colors = [mplcolors.to_hex(cmap(i)) for i in range(num_frames)]

polygon_areas = []
polygon_prims = []
for n_side in num_sides:
    polygon_areas.append(n_side * RADIUS_C**2 * sin(pi /n_side) * cos(pi / n_side))
    polygon_prims.append(2 * n_side * RADIUS_C * sin(pi / n_side))

fig, ax = plt.subplots(figsize=(6, 6))


def create_circle():
    shape_1 = Circle((1.5, 1.5),
                     radius=RADIUS_C,
                     fill=False,
                     linewidth=0.2,
                     edgecolor="red")
    ax.add_patch(shape_1)


def animate(frame):
    ax.clear()
    ax.axis([0, 3, 0, 3])
    create_circle()
    n_sides = frame + 3
    for i in range(frame + 1):
        ax.add_patch(polygons[i])
    ax.text(.1, .25,
            f"Sides: {n_sides}",
            fontsize=12,
            color='black',
            ha='left',
            va='top')
    ax.text(1, .25,
            f"A: {polygon_areas[frame]:.6f}",
            fontsize=12,
            color='black',
            ha='left',
            va='top')
    ax.text(2, .25,
            f"C: {polygon_prims[frame]:.6f}",
            fontsize=12,
            color='black',
            ha='left',
            va='top')


polygons = []
for polygon in range(num_sides_min, num_sides_max+1):
    shape_2 = RegularPolygon((1.5, 1.5),
                             numVertices=polygon,
                             radius=1,
                             facecolor="None",
                             linewidth=0.2,
                             edgecolor=colors[polygon-3])
    polygons.append(shape_2)

anim = FuncAnimation(fig,
                     animate,
                     frames=num_frames,
                     interval=200,
                     repeat=True)

plt.show()