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()
===================================================
第二个版本 version.1.1： Edit by Hongten 2013-09-28 17:40
===================================================
修改记录：
1.调整画布大小
2.调整了小球的半径,以及小球的速度初始值，小球初始圆心坐标
3.游标的范围修改为：[-200, 200]
这些修改主要是针对上面的缺陷而进行的。
优点：
1.小球移动的过程更直观
2.小球的移动速度变小，但是可以根据游标来修改小球移动速度
3.界面比之前更加友好
运行效果：
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。
修改记录：
1.调整画布大小
2.调整了小球的半径,以及小球的速度初始值，小球初始圆心坐标
3.游标的范围修改为：[-200, 200]
这些修改主要是针对上面的缺陷而进行的。
优点：
1.小球移动的过程更直观
2.小球的移动速度变小，但是可以根据游标来修改小球移动速度
3.界面比之前更加友好
'''
__author__ = {'author' : 'Hongten',
'Email' : 'hongtenzone@foxmail.com',
'Blog' : 'http://www.cnblogs.com/hongten/',
'Created' : '2013-09-28',
'Version' : '1.1'}
class Pong(Frame):
def createWidgets(self):
#放缩率
self.scaling = 100.0
#画布比例
self.canvas_width = 10
self.canvas_height = 5.6
## 画布
self.draw = Canvas(self, width=(self.canvas_width * self.scaling),
height=(self.canvas_height * self.scaling),
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_=-200, to=200)
self.speed.pack(side=BOTTOM, fill=X)
#小球直径
self.ball_d = 1.0
#小球碰撞墙壁的范围
self.scaling_left = round(self.ball_d / 2, 1)
self.scaling_right = self.canvas_width - self.scaling_left
self.scaling_bottom = self.canvas_height - self.scaling_left
self.scaling_top = self.scaling_left
#游标度数
self.scale_value = self.speed.get() * 0.1
#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("0.60i", "0.60i", "1.60i", "1.60i",
fill="red")
self.second_ball = self.draw.create_oval("2.0i", "2.0i", "3.0i", "3.0i",
fill='black')
self.three_ball = self.draw.create_oval("4.0i", "4.0i", "5.0i", "5.0i",
fill='brown')
self.four_ball = self.draw.create_oval("6.0i", "2.0i", "7.0i", "3.0i",
fill='green')
self.five_ball = self.draw.create_oval("8.0i", "3.0i", "9.0i", "4.0i",
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 = 1.1
self.y = 1.1
#第一个小球的速度方向
self.velocity_x = -0.2
self.velocity_y = 0.1
self.second_ball_x = 2.5
self.second_ball_y = 2.5
self.second_ball_v_x = 0.1
self.second_ball_v_y = -0.2
self.three_ball_x = 4.5
self.three_ball_y = 4.5
self.three_ball_v_x = -0.1
self.three_ball_v_y = -0.2
self.four_ball_x = 6.5
self.four_ball_y = 2.5
self.four_ball_v_x = 0.1
self.four_ball_v_y = -0.2
self.five_ball_x = 8.5
self.five_ball_y = 3.5
self.five_ball_v_x = 0.1
self.five_ball_v_y = 0.2
#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() * 0.1
#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_bottom) or (self.ball_y[index] < self.scaling_top):
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()
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