如上圖示，我們這里通過讓畫面上一個粒子分裂為X數量的粒子來模擬爆炸效果。粒子會發生“膨脹”，意思是它們會以恒速移動且相互之間的角度相等。這樣就能讓我們以一個向外膨脹的圓圈形式模擬出煙花綻放的畫面。經過一定時間后，粒子會進入“自由落體”階段，也就是由于重力因素它們開始墜落到地面，仿若綻放后熄滅的煙花。

用Python和Tkinter設計煙花：基本知識

這里不再一股腦把數學知識全丟出來，我們邊寫代碼邊說理論。首先，確保你安裝和導入了

Tkinter，它是Python的標準 GUI 庫，廣泛應用于各種各樣的項目和程序開發，在Python中使用 Tkinter 可以快速的創建 GUI 應用程序。

import tkinter as tk

from PIL import Image, ImageTk

from time import time, sleep

from random import choice, uniform, randint

from math import sin, cos, radians

除了Tkinter之外，為了能讓界面有漂亮的背景，我們也導入PIL用于圖像處理，以及導入其它一些包，比如time，random和math。它們能讓我們更容易的控制煙花粒子的運動軌跡。

Tkinter應用的基本設置如下：

root = tk.Tk

為了能初始化Tkinter，我們必須創建一個Tk根部件（root widget），它是一個窗口，帶有標題欄和由窗口管理器提供的其它裝飾物。該根部件必須在我們創建其它小部件之前就創建完畢，而且只能有一個根部件。

w = tk.Label(root, text="Hello Tkinter!")

這一行代碼包含了Label部件。該Label調用中的第一個參數就是父窗口的名字，即我們這里用的“根”。關鍵字參數“text”指明顯示的文字內容。你也可以調用其它小部件：Button，Canvas等等。

w.pack

root.mainloop

接下來的這兩行代碼很重要。這里的打包方法是告訴Tkinter調整窗口大小以適應所用的小部件。窗口直到我們進入Tkinter事件循環，被root.mainloop調用時才會出現。在我們關閉窗口前，腳本會一直在停留在事件循環。

將煙花綻放轉譯成代碼

現在我們設計一個對象，表示煙花事件中的每個粒子。每個粒子都會有一些重要的屬性，支配了它的外觀和移動狀況：大小，顏色，位置，速度等等。

'''

Generic class for particles

particles are emitted almost randomly on the sky, forming a round of circle (a star) before falling and getting removed

from canvas

Attributes:

- id: identifier of a particular particle in a star

- x, y: x,y-coordinate of a star (point of explosion)

- vx, vy: speed of particle in x, y coordinate

- total: total number of particle in a star

- age: how long has the particle last on canvas

- color: self-explantory

- cv: canvas

- lifespan: how long a particle will last on canvas

- intial_speed: speed of particle at explosion

'''

class part:

def __init__(self, cv, idx, total, explosion_speed, x=0., y=0., vx = 0., vy = 0., size=2., color = 'red', lifespan = 2, **kwargs):

self.id = idx

self.x = x

self.y = y

self.initial_speed = explosion_speed

self.vx = vx

self.vy = vy

self.total = total

self.age = 0

self.color = color

self.cv = cv

self.cid = self.cv.create_oval(

x - size, y - size, x + size,

y + size, fill=self.color)

self.lifespan = lifespan

如果我們回過頭想想最開始的想法，就會意識到必須確保每個煙花綻放的所有粒子必須經過3個不同的階段，即“膨脹”“墜落”和“消失”。 所以我們向粒子類中再添加一些運動函數，如下所示：

def update(self, dt):

# 粒子膨脹

if self.alive and self.expand:

move_x = cos(radians(self.id*360/self.total))*self.initial_speed

move_y = sin(radians(self.id*360/self.total))*self.initial_speed

self.vx = move_x/(float(dt)*1000)

self.vy = move_y/(float(dt)*1000)

self.cv.move(self.cid, move_x, move_y)

# 以自由落體墜落

elif self.alive:

self.id*360/self.total))

# we technically don't need to update x, y because move will do the job

self.cv.move(self.cid, self.vx + move_x, self.vy+GRAVITY*dt)

self.vy += GRAVITY*dt

# 如果粒子的生命周期已過，就將其移除

elif self.cid is not None:

cv.delete(self.cid)

self.cid = None

當然，這也意味著我們必須定義每個粒子綻放多久、墜落多久。這部分需要我們多嘗試一些參數，才能達到最佳視覺效果。

# 定義膨脹效果的時間幀

def expand (self):

return self.age <= 1.2

# 檢查粒子是否仍在生命周期內

def alive(self):

return self.age <= self.lifespan

使用Tkinter模擬

現在我們將粒子的移動概念化，不過很明顯，一個煙花不能只有一個粒子，一場煙花秀也不能只有一個煙花。我們下一步就是讓Python和Tkinter以我們可控的方式向天上連續“發射”粒子。

到了這里，我們需要從操作一個粒子升級為在屏幕上展現多個煙花及每個煙花中的多個粒子。

我們的解決思路如下：創建一列列表，每個子列表是一個煙花，其包含一列粒子。每個列表中的例子有相同的x,y坐標、大小、顏色、初始速度。

numb_explode = randint(6,10)

# 為所有模擬煙花綻放的全部粒子創建一列列表

for point in range(numb_explode):

objects =

x_cordi = randint(50,550)

y_cordi = randint(50, 150)

size = uniform (0.5,3)

color = choice(colors)

explosion_speed = uniform(0.2, 1)

total_particles = randint(10,50)

for i in range(1,total_particles):

r = part(cv, idx = i, total = total_particles, explosion_speed = explosion_speed, x = x_cordi, y = y_cordi,

color=color, size = size, lifespan = uniform(0.6,1.75))

objects.append(r)

explode_points.append(objects)

我們下一步就是確保定期更新粒子的屬性。這里我們設置讓粒子每0.01秒更新它們的狀態，在1.8秒之后停止更新（這意味著每個粒子的存在時間為1.6秒，其中1.2秒為“綻放”狀態，0.4秒為“墜落”狀態，0.2秒處于Tkinter將其完全移除前的邊緣狀態）。

total_time = .0

# 在1.8秒時間幀內保持更新

while total_time < 1.8:

sleep(0.01)

tnew = time

t, dt = tnew, tnew - t

for point in explode_points:

for part in point:

part.update(dt)

cv.update

total_time += dt

現在，我們只需將最后兩個gist合并為一個能被Tkinter調用的函數，就叫它simulate吧。該函數會展示所有的數據項，并根據我們設置的時間更新每個數據項的屬性。在我們的主代碼中，我們會用一個alarm處理模塊after調用此函數，after會等待一定的時間，然后再調用函數。

我們這里設置讓Tkinter等待100個單位（1秒鐘）再調取simulate。

if __name__ == '__main__':

root = tk.Tk

cv = tk.Canvas(root, height=600, width=600)

# 繪制一個黑色背景

cv.create_rectangle(0, 0, 600, 600, fill="black")

cv.pack

root.protocol("WM_DELETE_WINDOW", close)

# 在1秒后才開始調用stimulate

root.after(100, simulate, cv)

root.mainloop

好了，這樣我們就用Python代碼放了一場煙花秀：

本文只是基本版本，等你進一步熟悉Tkinter后，還可以添加更多顏色更漂亮的背景照片，讓代碼為你綻放更美的煙花！

本文全部代碼如下：

'''

FIREWORKS SIMULATION WITH TKINTER

*self-containing code

*to run: simply type python simple.py in your console

*compatible with both Python 2 and Python 3

*Dependencies: tkinter, Pillow (only for background image)

*The design is based on high school physics, with some small twists only for aesthetics purpose

'''

import tkinter as tk

#from tkinter import messagebox

#from tkinter import PhotoImage

from PIL import Image, ImageTk

from time import time, sleep

from random import choice, uniform, randint

from math import sin, cos, radians

# gravity, act as our constant g, you can experiment by changing it

GRAVITY = 0.05

# list of color, can choose randomly or use as a queue (FIFO)

colors = ['red', 'blue', 'yellow', 'white', 'green', 'orange', 'purple', 'seagreen', 'indigo', 'cornflowerblue']

'''

Generic class for particles

particles are emitted almost randomly on the sky, forming a round of circle (a star) before falling and getting removed

from canvas

Attributes:

- id: identifier of a particular particle in a star

- x, y: x,y-coordinate of a star (point of explosion)

- vx, vy: speed of particle in x, y coordinate

- total: total number of particle in a star

- age: how long has the particle last on canvas

- color: self-explantory

- cv: canvas

- lifespan: how long a particle will last on canvas

'''

class part:

def __init__(self, cv, idx, total, explosion_speed, x=0., y=0., vx = 0., vy = 0., size=2., color = 'red', lifespan = 2, **kwargs):

self.id = idx

self.x = x

self.y = y

self.initial_speed = explosion_speed

self.vx = vx

self.vy = vy

self.total = total

self.age = 0

self.color = color

self.cv = cv

self.cid = self.cv.create_oval(

x - size, y - size, x + size,

y + size, fill=self.color)

self.lifespan = lifespan

def update(self, dt):

self.age += dt

# particle expansions

if self.alive and self.expand:

move_x = cos(radians(self.id*360/self.total))*self.initial_speed

move_y = sin(radians(self.id*360/self.total))*self.initial_speed

self.cv.move(self.cid, move_x, move_y)

self.vx = move_x/(float(dt)*1000)

# falling down in projectile motion

elif self.alive:

self.id*360/self.total))

# we technically don't need to update x, y because move will do the job

self.cv.move(self.cid, self.vx + move_x, self.vy+GRAVITY*dt)

self.vy += GRAVITY*dt

# remove article if it is over the lifespan

elif self.cid is not None:

cv.delete(self.cid)

self.cid = None

# define time frame for expansion

def expand (self):

return self.age <= 1.2

# check if particle is still alive in lifespan

def alive(self):

return self.age <= self.lifespan

'''

Firework simulation loop:

Recursively call to repeatedly emit new fireworks on canvas

a list of list (list of stars, each of which is a list of particles)

is created and drawn on canvas at every call,

via update protocol inside each 'part' object

'''

def simulate(cv):

t = time

explode_points =

wait_time = randint(10,100)

numb_explode = randint(6,10)

# create list of list of all particles in all simultaneous explosion

for point in range(numb_explode):

objects =

x_cordi = randint(50,550)

y_cordi = randint(50, 150)

speed = uniform (0.5, 1.5)

size = uniform (0.5,3)

color = choice(colors)

explosion_speed = uniform(0.2, 1)

total_particles = randint(10,50)

for i in range(1,total_particles):

r = part(cv, idx = i, total = total_particles, explosion_speed = explosion_speed, x = x_cordi, y = y_cordi,

vx = speed, vy = speed, color=color, size = size, lifespan = uniform(0.6,1.75))

objects.append(r)

explode_points.append(objects)

total_time = .0

# keeps undate within a timeframe of 1.8 second

while total_time < 1.8:

sleep(0.01)

tnew = time

t, dt = tnew, tnew - t

for point in explode_points:

for item in point:

item.update(dt)

cv.update

total_time += dt

# recursive call to continue adding new explosion on canvas

root.after(wait_time, simulate, cv)

def close(*ignore):

"""Stops simulation loop and closes the window."""

global root

root.quit

if __name__ == '__main__':

root = tk.Tk

cv = tk.Canvas(root, height=600, width=600)

# use a nice background image

image = Image.open("image.jpg")

photo = ImageTk.PhotoImage(image)

cv.create_image(0, 0, image=photo, anchor='nw')

cv.pack

root.protocol("WM_DELETE_WINDOW", close)

root.after(100, simulate, cv)

root.mainloop

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