我正在尝试在pygame中编写粒子模拟的代码，但是在编码粒子之间的碰撞时遇到了麻烦。所有碰撞都是弹性的，因此应保持动能。但是，我遇到两个主要问题：
我非常感谢能帮助解决这些问题的见识。
我使用此文档（http://www.vobarian.com/collisions/2dcollisions2.pdf）帮助计算了碰撞后粒子的新速度。所有粒子的质量相同，因此在计算中我忽略了它们的质量。 到目前为止，这是我的代码：
import pygame
pygame.init()
import random
import numpy
HEIGHT = 500
WIDTH = 500
NUM_BALLS = 2
#setup
win = pygame.display.set_mode((WIDTH,HEIGHT))
pygame.display.set_caption("Simulation")
class Particle(object):
def __init__(self, x, y , radius):
self.x = x
self.y = y
self.radius = radius
self.xvel = random.randint(1,5)
self.yvel = random.randint(1,5)
def Draw_circle(self):
pygame.draw.circle(win, (255,0,0), (self.x, self.y), self.radius)
def redrawGameWindow():
win.fill((0,0,0))
for ball in balls:
ball.Draw_circle()
pygame.display.update()
balls = []
for turn in range(NUM_BALLS):
balls.append(Particle(random.randint(20,WIDTH-20),random.randint(20,HEIGHT-20),20))
run = True
while run:
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
for ball in balls:
if (ball.x + ball.radius) <= WIDTH or (ball.x - ball.radius) >= 0:
ball.x += ball.xvel
if (ball.x + ball.radius) > WIDTH or (ball.x - ball.radius) < 0:
ball.xvel *= -1
ball.x += ball.xvel
if (ball.y + ball.radius) <= HEIGHT or (ball.y - ball.radius) >= 0:
ball.y += ball.yvel
if (ball.y + ball.radius) > HEIGHT or (ball.y - ball.radius) < 0:
ball.yvel *= -1
ball.y += ball.yvel
#code for collision between balls
for ball in balls:
for i in range(len(balls)):
for j in range (i+1, len(balls)):
d = (balls[j].x-balls[i].x)**2 + (balls[j].y-balls[i].y)**2
if d < (balls[j].radius + balls[i].radius)**2:
print("collision")
n = (balls[i].x-balls[j].x, balls[i].y-balls[j].y) #normal vector
un = n/ numpy.sqrt((balls[i].x-balls[j].x)**2 + (balls[i].y-balls[j].y)**2) #unit normal vector
ut = numpy.array((-un[1],un[0])) #unit tangent vector
u1n = numpy.vdot(un, (balls[j].xvel, balls[j].yvel)) #initial velocity in normal direction for first ball
v1t = numpy.vdot(ut, (balls[j].xvel, balls[j].yvel)) #initial velocity in tangent direction (remains unchanged)
u2n = numpy.vdot(un, (balls[i].xvel, balls[i].yvel)) #second ball
v2t = numpy.vdot(ut, (balls[i].xvel, balls[i].yvel))
v1n = u2n
v2n = u1n
v1n *= un
v2n *= un
v1t *= ut
v2t *= ut
v1 = v1n + v1t #ball 1 final velocity
v2 = v2n + v2t #ball 2 final velocity
balls[j].xvel = int(numpy.vdot(v1, (1,0))) #splitting final velocities into x and y components again
balls[j].yvel = int(numpy.vdot(v1, (0,1)))
balls[i].xvel = int(numpy.vdot(v2, (1,0)))
balls[i].yvel = int(numpy.vdot(v2, (0,1)))
redrawGameWindow()
pygame.time.delay(20)
pygame.quit()
答案 0 :(得分：1)
在v1 = v1n + v1t中，v1n是向量，而v1t是标量。
因此，值v1t被添加到v1n向量的两个分量中，从而导致错误。
您想将切线速度添加为矢量，因此应该像对法向速度那样进行操作：
v1n *= un
v2n *= un
v1t *= ut
v2t *= ut
请注意，对于两个截然不同的事物（向量及其范数）使用相同的变量，会使您的代码更难以理解，并且可能导致错误-就像刚才那样。您可能应该以更一致的方式重命名变量，以使差异更清晰。
此外，ut必须是一个numpy数组，但是您将其设为元组。考虑区别：
带有元组
>>> t = (3, 4)
>>> 3*t
(3, 4, 3, 4, 3, 4)
使用np.array：
>>> t = np.array((3, 4))
>>> 3*t
array([ 9, 12])
所以，您必须更改
ut = (-un[1],un[0])
进入
ut = numpy.array((-un[1],un[0]))
答案 1 :(得分：0)
即使您始终检查是否存在碰撞，物体粘在一起的问题还是很简单的，它真正能够识别出的时间就是圆圈已经过去但彼此稍微接触了。圆圈现在反弹并移动了一点。但是，它们还没有完全移动到完全不会碰到的地方，这意味着弹跳再次出现，并且循环播放。我编写了可解决此问题的代码，但是您必须更改bounce函数并使用您的代码，因为我的代码不是那么完美，但可以起作用。
import pygame
pygame.init()
import random
import numpy
HEIGHT = 500
WIDTH = 500
NUM_BALLS = 2
#setup
win = pygame.display.set_mode((WIDTH,HEIGHT))
pygame.display.set_caption("Simulation")
class Particle(object):
def __init__(self, x, y , radius):
self.x = x
self.y = y
self.radius = radius
self.xvel = random.randint(1,5)
self.yvel = random.randint(1,5)
self.colideCheck = []
def Draw_circle(self):
pygame.draw.circle(win, (255,0,0), (int(self.x), int(self.y)), self.radius)
def redrawGameWindow():
win.fill((0,0,0))
for ball in balls:
ball.Draw_circle()
pygame.display.update()
def bounce(v1,v2, mass1 = 1, mass2 = 1):
#i Tried my own bouncing mechanism, but doesn't work completly well, add yours here
multi1 = mass1/(mass1+mass2)
multi2 = mass2/(mass1+mass2)
deltaV2 = (multi1*v1[0]-multi2*v2[0],multi1*v1[1]-multi2*v2[1])
deltaV1 = (multi2*v2[0]-multi1*v1[0],multi2*v2[1]-multi1*v1[1])
print("preVelocities:",v1,v2)
return deltaV1,deltaV2
def checkCollide(circ1Cord,circ1Rad,circ2Cord,circ2Rad):
tryDist = circ1Rad+circ2Rad
actualDist = dist(circ1Cord,circ2Cord)
if dist(circ1Cord,circ2Cord) <= tryDist:
return True
return False
def dist(pt1,pt2):
dX = pt1[0]-pt2[0]
dY = pt1[1]-pt2[1]
return (dX**2 + dY**2)**0.5
balls = []
for turn in range(NUM_BALLS):
balls.append(Particle(random.randint(60,WIDTH-60),random.randint(60,HEIGHT-60),60))
run = True
while run:
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
for ball in balls:
if (ball.x + ball.radius) <= WIDTH and (ball.x - ball.radius) >= 0:
ball.x += ball.xvel
else:
ball.xvel *= -1
ball.x += ball.xvel
if (ball.y + ball.radius) <= HEIGHT and (ball.y - ball.radius) >= 0:
ball.y += ball.yvel
else:
ball.yvel *= -1
ball.y += ball.yvel
for ball in balls:
for secBallCheck in balls:
if secBallCheck not in ball.colideCheck and ball!= secBallCheck and checkCollide((ball.x,ball.y),ball.radius,(secBallCheck.x,secBallCheck.y),secBallCheck.radius):
print("COLLIDE")
vel1,vel2 = bounce((ball.xvel,ball.yvel),(secBallCheck.xvel,secBallCheck.yvel))
print(vel1,vel2)
ball.xvel = vel1[0]
ball.yvel = vel1[1]
ball.colideCheck.append(secBallCheck)
secBallCheck.xvel = vel2[0]
secBallCheck.yvel = vel2[1]
secBallCheck.colideCheck.append(ball)
elif not checkCollide((ball.x,ball.y),ball.radius,(secBallCheck.x,secBallCheck.y),secBallCheck.radius):
if ball in secBallCheck.colideCheck:
secBallCheck.colideCheck.remove(ball)
ball.colideCheck.remove(secBallCheck)
redrawGameWindow()
pygame.time.delay(20)
pygame.quit()