使用python和pygame绘制繁花曲线的方法

# -*- coding: utf-8 -*-

import math

'''
功能：
  已知圆的圆心和半径，获取某弧度对应的圆上点的坐标
入参：
  center：圆心
  radius：半径
  radian：弧度
'''
def get_point_in_circle(center, radius, radian):
  return (center[0] + radius * math.cos(radian), center[1] - radius * math.sin(radian))

'''
功能：
  内外圆A和B，内圆A沿着外圆B的内圈滚动，已知外圆圆心、半径，已知内圆半径，已知公转弧度和绕点半径，计算绕点坐标
入参：
  center_A：外圆圆心
  radius_A：外圆半径
  radius_B：内圆半径
  radius_C：绕点半径
  radian：公转弧度
'''
def get_point_in_child_circle(center_A, radius_A, radius_B, radius_C, radian):
  # 计算内圆圆心坐标
  center_B = get_point_in_circle(center_A, radius_A - radius_B, radian)
  # 计算绕点弧度（公转为逆时针，则自转为顺时针）
  radian_C = 2.0*math.pi - ((radius_A / radius_B * radian) % (2.0*math.pi))
  # 计算绕点坐标
  return get_point_in_circle(center_B, radius_C, radian_C)

''' 计算两点距离（平方和） '''
def get_instance(p1, p2):
  return (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1])
  
'''
功能：
  获取绕点路径的所有点的坐标
入参：
  center：外圆圆心
  radius_A：外圆半径
  radius_B：内圆半径
  radius_C：绕点半径
  shift_radian：每次偏移的弧度，默认0.01，值越小，精度越高，计算量越大
'''
def get_points(center, radius_A, radius_B, radius_C, shift_radian=0.01):
  # 转为实数
  radius_A *= 1.0
  radius_B *= 1.0
  radius_C *= 1.0
  
  P2 = 2*math.pi # 一圈的弧度为 2PI
  R_PER_ROUND = int(P2/shift_radian/4) + 1 # 一圈需要走多少步（弧度偏移多少次）
  
  # 第一圈的起点坐标
  start_point = get_point_in_child_circle(center, radius_A, radius_B, radius_C, 0)
  points = [start_point]
  # 第一圈的路径坐标
  for r in range(1, R_PER_ROUND):
    points.append(get_point_in_child_circle(center, radius_A, radius_B, radius_C, shift_radian*r))
  
  # 以圈为单位，每圈的起始弧度为 2PI*round，某圈的起点坐标与第一圈的起点坐标距离在一定范围内，认为路径结束
  for round in range(1, 100):
    s_radian = round*P2
    s_point = get_point_in_child_circle(center, radius_A, radius_B, radius_C, s_radian)
    if get_instance(s_point, start_point) < 0.1:
      break
    points.append(s_point)
    for r in range(1, R_PER_ROUND):
      points.append(get_point_in_child_circle(center, radius_A, radius_B, radius_C, s_radian + shift_radian*r))
    
  return points

# -*- coding: utf-8 -*-
import math
import random

'''
功能：
  已知圆的圆心和半径，获取某弧度对应的圆上点的坐标
入参：
  center：圆心
  radius：半径
  radian：弧度
'''
def get_point_in_circle(center, radius, radian):
  return (center[0] + radius * math.cos(radian), center[1] - radius * math.sin(radian))

'''
功能：
  内外圆A和B，内圆A沿着外圆B的内圈滚动，已知外圆圆心、半径，已知内圆半径、公转弧度，已知绕点半径，计算绕点坐标
入参：
  center_A：外圆圆心
  radius_A：外圆半径
  radius_B：内圆半径
  radius_C：绕点半径
  radian：公转弧度
'''
def get_point_in_child_circle(center_A, radius_A, radius_B, radius_C, radian):
  # 计算内圆圆心坐标
  center_B = get_point_in_circle(center_A, radius_A - radius_B, radian)
  # 计算绕点弧度（公转为逆时针，则自转为顺时针）
  radian_C = 2.0*math.pi - ((radius_A / radius_B * radian) % (2.0*math.pi))
  # 计算绕点坐标
  center_C = get_point_in_circle(center_B, radius_C, radian_C)
  center_B_Int = (int(center_B[0]), int(center_B[1]))
  return center_B_Int, center_C

''' 计算两点距离（平方和） '''
def get_instance(p1, p2):
  return (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1])
  
'''
功能：
  获取绕点路径的所有点的坐标
入参：
  center：外圆圆心
  radius_A：外圆半径
  radius_B：内圆半径
  radius_C：绕点半径
  shift_radian：每次偏移的弧度，默认0.01，值越小，精度越高，计算量越大
'''
def get_points(center_A, radius_A, radius_B, radius_C, shift_radian=0.01):
  # 转为实数
  radius_A *= 1.0
  radius_B *= 1.0
  radius_C *= 1.0
  
  P2 = 2*math.pi # 一圈的弧度为 2PI
  R_PER_ROUND = int(P2/shift_radian) + 1 # 一圈需要走多少步（弧度偏移多少次）
  
  # 第一圈的起点坐标
  start_center, start_point = get_point_in_child_circle(center_A, radius_A, radius_B, radius_C, 0)
  points = [start_point]
  centers = [start_center]
  # 第一圈的路径坐标
  for r in range(1, R_PER_ROUND):
    center, point = get_point_in_child_circle(center_A, radius_A, radius_B, radius_C, shift_radian*r)
    points.append(point)
    centers.append(center)
  
  # 以圈为单位，每圈的起始弧度为 2PI*round，某圈的起点坐标与第一圈的起点坐标距离在一定范围内，认为路径结束
  for round in range(1, 100):
    s_radian = round*P2
    s_center, s_point = get_point_in_child_circle(center_A, radius_A, radius_B, radius_C, s_radian)
    if get_instance(s_point, start_point) < 0.1:
      break
    points.append(s_point)
    centers.append(s_center)
    for r in range(1, R_PER_ROUND):
      center, point = get_point_in_child_circle(center_A, radius_A, radius_B, radius_C, s_radian + shift_radian*r)
      points.append(point)
      centers.append(center)  
  print(len(points)/R_PER_ROUND)    
  return centers, points

import pygame
from pygame.locals import *

pygame.init()
screen = pygame.display.set_mode((600, 400))
clock = pygame.time.Clock()

color_black = (0, 0, 0)
color_white = (255, 255, 255)
color_red = (255, 0, 0)
color_yello = (255, 255, 0)

center = (300, 200)
radius_A = 150
radius_B = 110
radius_C = 50

test_centers, test_points = get_points(center, radius_A, radius_B, radius_C)
test_idx = 2
draw_point_num_per_tti = 5

while True:
  for event in pygame.event.get():
    if event.type==pygame.QUIT:
      pygame.quit() 
      exit(0)
  
  screen.fill(color_white)
  
  pygame.draw.circle(screen, color_black, center, int(radius_A), 2)
  
  if test_idx <= len(test_points):
    pygame.draw.aalines(screen, (0, 0, 255), False, test_points[:test_idx], 1)
    if test_idx < len(test_centers):
      pygame.draw.circle(screen, color_black, test_centers[test_idx], int(radius_B), 1)
      pygame.draw.aaline(screen, color_black, test_centers[test_idx], test_points[test_idx], 1)
    test_idx = min(test_idx + draw_point_num_per_tti, len(test_points))
  
  clock.tick(50)
  pygame.display.flip()