完成这个小球的完全弹性碰撞游戏灵感来自于：

下面是我花了一周下班时间所编写的一个小球完全弹性碰撞游戏：

游戏初始化状态：

最下面的游标和修改小球的移动速度

源码部分：

复制代码 代码如下:

python tkinter

python version 3.3.2

from tkinter import *

'''
判断
两个小球
{
圆心：A(x1,y1) 半径：r X轴速度：Vax Y轴速度：Vay
圆心：B(x2,y2) 半径：R X轴速度：Vbx Y轴速度：Vby
}
碰撞的条件是：
1.两个小球的圆心距离不大于两小球半径之和(r+R)，即：
{
(x2 - x1)^2 + (y2 - y1)^2 <= (r + R)^2
}
2.小球碰撞后，两小球的数度交换，即：
{
tempVax = Vax
tempVay = Vay
Vax = Vbx
Vay = Vby
Vbx = tempVax
Vby = tempVay
或：
Vax = Vax + Vbx
Vbx = Vax - Vbx
Vax = Vax - Vbx
Vay = Vay + Vby
Vby = Vay - Vby
Vay = Vay - Vby
}

游戏规则：  
五小球在画布中移动，他们之间会产生碰撞，当然小球和上下左右都会产生碰撞  
碰撞后，小球会改变方向返回  
而最下面的游标则用于调节小球的移动速度，游标的范围是[-100, 100]  

缺陷或BUG：  
1.在修改游标数据从而改变小球移动速度的时候，小球移动的距离得不到及时的更新  
导致小球可能会逃离画布  
2.小球在运动的过程中，有时候也有可能逃离画布

总结：  
完成这个游戏，花了一个星期的下班时间。在这个过程中不仅回去学习了高中的数学知识，  
物理知识，很多东西都忘得差不多了，不过很快又学返回来了。  
游戏其实很多就是数学问题。  

游戏中还存在缺陷或BUG，希望志同道合者可以共同完善。  

'''

author = {'author' : 'Hongten',
'Email' : 'hongtenzone@foxmail.com',
'Blog' : 'http://www.cnblogs.com/hongten/',
'Created' : '2013-09-28',
'Version' : '1.0'}

class Pong(Frame):
def createWidgets(self):

画布

    self.draw = Canvas(self, width="5i", height="5i", bg='white')

    ## 游标(控制小球移动速度，范围：[-100, 100])  
    self.speed = Scale(self, orient=HORIZONTAL, label="ball speed",  
                       from_=-100, to=100)

    self.speed.pack(side=BOTTOM, fill=X)

    #小球碰撞墙壁的范围  
    self.scaling_right = 4.8  
    self.scaling_left = 0.2  
    #小球直径  
    self.ball_d = 0.4  
    #游标度数  
    self.scale_value = self.speed.get()  
    #放缩率  
    self.scaling = 100.0

    #存放小球数组  
    self.balls = []  
    #存放小球x坐标数组  
    self.ball_x = []  
    #存放小球y坐标数组  
    self.ball_y = []  
    #存放小球x轴方向速度数组  
    self.ball_v_x = []  
    #存放小球y轴方向速度数组  
    self.ball_v_y = []

    # 五个小球  
    self.ball = self.draw.create_oval("0.10i", "0.10i", "0.50i", "0.50i",  
                                      fill="red")  
    self.second_ball = self.draw.create_oval("0.70i", "0.70i", "1.10i", "1.10i",  
                                             fill='black')  
    self.three_ball = self.draw.create_oval("1.30i", "1.30i", "1.70i", "1.70i",  
                                             fill='brown')  
    self.four_ball = self.draw.create_oval("2.0i", "2.0i", "2.40i", "2.40i",  
                                             fill='green')  
    self.five_ball = self.draw.create_oval("3.0i", "3.0i", "3.40i", "3.40i",  
                                             fill='gray')

    #把五个小球放入数组  
    self.balls.append(self.ball)  
    self.balls.append(self.second_ball)  
    self.balls.append(self.three_ball)  
    self.balls.append(self.four_ball)  
    self.balls.append(self.five_ball)

    #第一个小球，即self.ball的圆心坐标(self.x, self.y),这里进行了放缩,目的是为了  
    #在小球移动的过程中更加流畅  
    self.x = 0.3          
    self.y = 0.3  
    #第一个小球的速度方向  
    self.velocity_x = -0.2  
    self.velocity_y = 0.5

    self.second_ball_x = 0.9  
    self.second_ball_y = 0.9  
    self.second_ball_v_x = 0.4  
    self.second_ball_v_y = -0.5

    self.three_ball_x = 1.5  
    self.three_ball_y = 1.5  
    self.three_ball_v_x = -0.3  
    self.three_ball_v_y = -0.5

    self.four_ball_x = 2.2  
    self.four_ball_y = 2.2  
    self.four_ball_v_x = 0.1  
    self.four_ball_v_y = -0.5

    self.five_ball_x = 3.2  
    self.five_ball_y = 3.2  
    self.five_ball_v_x = 0.3  
    self.five_ball_v_y = 0.5


    #更新小球的坐标  
    self.update_ball_x_y()  
    self.draw.pack(side=LEFT)

def update_ball_x_y(self, *args):  
    '''更新小球的坐标，即把各个小球的圆心坐标信息以及速度信息存放到数组中，  
       便于在后面循环遍历的时候使用。'''  
    #第一个小球信息  
    self.ball_x.append(self.x)  
    self.ball_y.append(self.y)  
    self.ball_v_x.append(self.velocity_x)  
    self.ball_v_y.append(self.velocity_y)

    self.ball_x.append(self.second_ball_x)  
    self.ball_y.append(self.second_ball_y)  
    self.ball_v_x.append(self.second_ball_v_x)  
    self.ball_v_y.append(self.second_ball_v_y)

    self.ball_x.append(self.three_ball_x)  
    self.ball_y.append(self.three_ball_y)  
    self.ball_v_x.append(self.three_ball_v_x)  
    self.ball_v_y.append(self.three_ball_v_y)

    self.ball_x.append(self.four_ball_x)  
    self.ball_y.append(self.four_ball_y)  
    self.ball_v_x.append(self.four_ball_v_x)  
    self.ball_v_y.append(self.four_ball_v_y)

    self.ball_x.append(self.five_ball_x)  
    self.ball_y.append(self.five_ball_y)  
    self.ball_v_x.append(self.five_ball_v_x)  
    self.ball_v_y.append(self.five_ball_v_y)  

def update_ball_velocity(self, index, *args):  
    '''更新各个小球速度信息，即小球碰撞到四周和另外的小球索要更新的速度信息'''  
    #游标值  
    self.scale_value = self.speed.get()  
    #碰撞墙壁  
    if (self.ball_x[index] > self.scaling_right) or (self.ball_x[index] < self.scaling_left):  
        self.ball_v_x[index] = -1.0 * self.ball_v_x[index]  
    if (self.ball_y[index] > self.scaling_right) or (self.ball_y[index] < self.scaling_left):  
        self.ball_v_y[index] = -1.0 *  self.ball_v_y[index]

    '''  
    #TEST:  
    for n in range(len(self.balls)):  
        #print((self.ball_x[index] - self.ball_x[n])**2)  
        #print(round((self.ball_x[index] - self.ball_x[n])**2 + (self.ball_y[index] - self.ball_y[n])**2, 2))  
        print(round((self.ball_x[index] - self.ball_x[n])**2 + (self.ball_y[index] - self.ball_y[n])**2, 2) <= round(self.ball_d**2, 2))  
    '''  
    for n in range(len(self.balls)):  
        #小球碰撞条件，即：(x2 - x1)^2 + (y2 - y1)^2 <= (r + R)^2  
        if (round((self.ball_x[index] - self.ball_x[n])**2 + (self.ball_y[index] - self.ball_y[n])**2, 2) <= round(self.ball_d**2, 2)):  
            #两小球速度交换  
            temp_vx = self.ball_v_x[index]  
            temp_vy = self.ball_v_y[index]  
            self.ball_v_x[index] = self.ball_v_x[n]  
            self.ball_v_y[index] = self.ball_v_y[n]  
            self.ball_v_x[n] = temp_vx  
            self.ball_v_y[n] = temp_vy  
    #print(self.ball_v_x, self.ball_v_y)  

    '''  
    #WRONG:  
    for n in range(len(self.balls)):              
        if (((self.ball_x[index] - self.ball_x[n])**2 + (self.ball_y[index] - self.ball_y[n])**2) <= self.ball_d**2):  
            #两小球速度交换  
            self.ball_v_x[index] = self.ball_v_x[index] + self.ball_v_x[n]  
            self.ball_v_x[n] = self.ball_v_x[0] - self.ball_v_x[n]  
            self.ball_v_x[index] = self.ball_v_x[index] - self.ball_v_x[n]  
            self.ball_v_y[index] = self.ball_v_y[index] + self.ball_v_y[n]  
            self.ball_v_y[n] = self.ball_v_y[index] - self.ball_v_y[n]  
            self.ball_v_y[index] = self.ball_v_y[index] - self.ball_v_y[n]  
    print(self.ball_v_x, self.ball_v_y)  
    '''  

def get_ball_deltax(self, index, *args):  
    '''获取小球X轴坐标移动距离并且更新小球的圆心X坐标，返回X轴所需移动距离'''  
    deltax = (self.ball_v_x[index] * self.scale_value / self.scaling)  
    self.ball_x[index] = self.ball_x[index] + deltax  
    return deltax

def get_ball_deltay(self, index, *args):  
    '''获取小球Y轴坐标移动距离并且更新小球的圆心Y坐标，返回Y轴所需移动距离'''  
    deltay = (self.ball_v_y[index] * self.scale_value / self.scaling)  
    self.ball_y[index] = self.ball_y[index] + deltay  
    return deltay  

def moveBall(self, *args):  
    '''移动第一个小球，编号为：0,这是根据数组：self.balls确定的。'''  
    self.update_ball_velocity(0)         
    deltax = self.get_ball_deltax(0)  
    deltay = self.get_ball_deltay(0)  
    #小球移动  
    self.draw.move(self.ball,  "%ri" % deltax, "%ri" % deltay)  
    self.after(10, self.moveBall)

def move_second_ball(self, *args):  
    self.update_ball_velocity(1)         
    deltax = self.get_ball_deltax(1)  
    deltay = self.get_ball_deltay(1)          
    self.draw.move(self.second_ball,  "%ri" % deltax, "%ri" % deltay)  
    self.after(10, self.move_second_ball)


def move_three_ball(self, *args):  
    self.update_ball_velocity(2)         
    deltax = self.get_ball_deltax(2)  
    deltay = self.get_ball_deltay(2)  
    self.draw.move(self.three_ball,  "%ri" % deltax, "%ri" % deltay)  
    self.after(10, self.move_three_ball)

def move_four_ball(self, *args):  
    self.update_ball_velocity(3)         
    deltax = self.get_ball_deltax(3)  
    deltay = self.get_ball_deltay(3)  
    self.draw.move(self.four_ball,  "%ri" % deltax, "%ri" % deltay)  
    self.after(10, self.move_four_ball)

def move_five_ball(self, *args):  
    self.update_ball_velocity(4)         
    deltax = self.get_ball_deltax(4)  
    deltay = self.get_ball_deltay(4)  
    self.draw.move(self.five_ball,  "%ri" % deltax, "%ri" % deltay)  
    self.after(10, self.move_five_ball)


def __init__(self, master=None):  
    '''初始化函数'''  
    Frame.__init__(self, master)  
    Pack.config(self)  
    self.createWidgets()  
    self.after(10, self.moveBall)  
    self.after(10, self.move_three_ball)  
    self.after(10, self.move_four_ball)  
    self.after(10, self.move_five_ball)  
    self.after(10, self.move_second_ball)  

game = Pong()

game.mainloop()