Pygame球碰撞

Question

我正在尝试模拟两个球之间的弹性碰撞。问题是，这些球有时不会遵循适当的行为，有时会“振动”或“粘在”彼此之间，或者当发生碰撞时它们甚至只是彼此之间。我不知道这是否与我使用的方程式有关（应该是标准的，但我真的不知道）。这是我的代码：

import pygame
import random
import math

def checkcirclecollide(x1, y1, r1, x2, y2, r2):
    return (x1 - x2)**2 + (y1 - y2)**2 == (r1 + r2)**2

def ballcollision(m1, m2, v1, v2):
    v2f = (2*m1*v1+m2*v2-m1*v2)/(m1+m2)
    v1f = (m1*v1+m2*v2-m2*v2f)/m1
    return v1f, v2f

class Ball:
    def __init__(self, x, y, vx, vy, r, m):
        self.x = x
        self.y = y
        self.vx = vx
        self.vy = vy
        self.r = r
        self.m = m
    def change_attribute(self, x=None, y=None, vx=None, vy=None, r=None, m=None):
        if x!=None: self.x = x
        if y!=None: self.y = y
        if vx!=None: self.vx = vx
        if vy!=None: self.vy = vy
        if r!=None: self.r = r
        if m!=None: self.m = m

pygame.init()
screen = pygame.display.set_mode((500, 500))
x, y = random.randint(11, 489), random.randint(11, 489)
vx, vy = random.randint(-5, 5), random.randint(-5, 5)
animationTimer = pygame.time.Clock()
balls = []
num_balls = 2
for x in range(num_balls):
    balls.append(Ball(random.randint(11, 489), random.randint(11, 489), random.randint(-5, 5), random.randint(-5, 5), random.randint(30, 50), random.randint(1, 4)*5))
while True:
    for e in pygame.event.get():   
        if e.type == pygame.QUIT:
            break
    for ball in balls:
        pygame.draw.circle(screen, (200, 0, 0), (ball.x, ball.y), ball.r)
        if ball.x-ball.r<=0 or ball.x+ball.r>=500:
            ball.change_attribute(vx = -ball.vx)
        if ball.y-ball.r<=0 or ball.y+ball.r>=500:
            ball.change_attribute(vy = -ball.vy)
        for other in balls:
            if other != ball and checkcirclecollide(ball.x, ball.y, ball.r, other.x, other.y, other.r):
                new_v1x, new_v2x = ballcollision(ball.m, other.m, ball.vx, other.vx)
                new_v1y, new_v2y = ballcollision(ball.m, other.m, ball.vy, other.vy)
                ball.change_attribute(vx = new_v1x, vy = new_v1y)
                other.change_attribute(vx = new_v2x, vy = new_v2y)
        ball.change_attribute(x = ball.x+ball.vx, y = ball.y+ball.vy)
    animationTimer.tick(100)
    pygame.display.update()
    screen.fill((0, 0, 0))

Answer 1

我对您的脚本进行了一些修改。我所做的修改在脚本本身上进行了解释。由于动能不在我的专业领域，因此我不知道它是否真的有效，也许仍然需要一些修改。但是，至少球不再融合或粘在墙壁上。

另外，我为每个球添加了自定义颜色。它们在测试中要好得多，并查看它们彼此相撞的位置以及如何相撞。

import pygame
import random
import math

# From: http://www.jeffreythompson.org/collision-detection/circle-circle.php
def checkcirclecollide(x1, y1, r1, x2, y2, r2):
    distX = x1 - x2
    distY = y1 - y2
    distance = math.sqrt( (distX * distX) + (distY * distY) )

    return (distance <= (r1 + r2))

# Kinectic Energy.. I'm sorry, I have no idea what this does..
def ballcollision(m1, m2, v1, v2):
    v2f = (2*m1*v1 + m2*v2 - m1*v2) / (m1+m2)
    v1f = (m1*v1 + m2*v2 - m2*v2f)/m1
    return v1f, v2f

# When two balls collide, there's no guarantee they are touching
# by their extremities.
#
# As they have different speeds, they might enter into one's
# space when they collide. So before/after applying the kinetic energy,
# we must firstly separate the balls so they do not merge to
# each other.
#
# Basically this happens:
#   __  __
#  /  /\  \
#  \__\/__/
#
# What does it do? It separates each ball once they merge:
#   ___   ___
#  /   \ /   \
#  \___/ \___/
#
# This function should only be called when both balls are
# colliding to each other.
def separate_balls(ball, other):
    # Get the Opposite direction
    angle = - math.atan2(ball.y - other.y, ball.x - other.x)

    # Calculate distance between both balls
    distX = ball.x - other.x
    distY = ball.y - other.y
    distance = math.sqrt( (distX * distX) + (distY * distY) )
    diffR = ball.r + other.r - distance

    diffR *= 0.5

    # Separate each ball by half of distance
    ball.x += math.cos(angle) * diffR
    ball.y += math.sin(angle) * diffR

    other.x -= math.cos(angle) * diffR
    other.y -= math.sin(angle) * diffR

class Ball:
    def __init__(self, x, y, vx, vy, r, m, color):
        self.x = x
        self.y = y
        self.vx = vx
        self.vy = vy
        self.r = r
        self.m = m

        # This is better for testing
        self.color = color

    def change_attribute(self, x=None, y=None, vx=None, vy=None, r=None, m=None):
        if x!=None: self.x = x
        if y!=None: self.y = y
        if vx!=None: self.vx = vx
        if vy!=None: self.vy = vy
        if r!=None: self.r = r
        if m!=None: self.m = m

pygame.init()
screen = pygame.display.set_mode((500, 500))

x, y = random.randint(11, 489), random.randint(11, 489)
vx, vy = random.randint(-5, 5), random.randint(-5, 5)

animationTimer = pygame.time.Clock()
balls = []
num_balls = 2

# Now I added random colors!
for x in range(num_balls):
    balls.append(Ball(random.randint(11, 489), random.randint(11, 489), random.randint(-5, 5), random.randint(-5, 5), random.randint(30, 50), random.randint(1, 4)*5, (random.randint(0, 255), random.randint(0, 255), random.randint(0, 255))))

while True:
    for e in pygame.event.get():   
        if e.type == pygame.QUIT:
            break
    
    for ball in balls:
        pygame.draw.circle(screen, ball.color, (ball.x, ball.y), ball.r)
        
        if ball.x-ball.r-ball.vx<=0 or ball.x+ball.r+ball.vx>=500:

            # Avoid sticking at walls
            if (ball.x<=ball.r):
                ball.x-=(ball.vx-1)
            elif (ball.x>=500-ball.r):
                ball.x+=(ball.vx-1)

            ball.change_attribute(vx = -ball.vx)
        
        if ball.y-ball.r-ball.vy<=0 or ball.y+ball.r+ball.vy>=500:

            # Avoid sticking at walls
            if (ball.y<=ball.r):
                ball.y-=(ball.vy-1)
            elif (ball.y>=500-ball.r):
                ball.y+=(ball.vy-1)

            ball.change_attribute(vy = -ball.vy)
        
        for other in balls:
            if other != ball and checkcirclecollide(ball.x, ball.y, ball.r, other.x, other.y, other.r):
                new_v1x, new_v2x = ballcollision(ball.m, other.m, ball.vx, other.vx)
                new_v1y, new_v2y = ballcollision(ball.m, other.m, ball.vy, other.vy)



                # Save current position
                originalX = ball.x
                originalY = ball.y

                # Calculate a hint of next position
                lookAheadX = ball.x + ball.vx
                lookAheadY = ball.y + ball.vy

                # Push hint position
                ball.change_attribute(x = lookAheadX, y = lookAheadY)

                # Separate both balls from each other
                separate_balls(ball, other)

                # Pop hint position to original one
                ball.change_attribute(x = originalX, y = originalY)



                ball.change_attribute(vx = new_v1x, vy = new_v1y)
                other.change_attribute(vx = new_v2x, vy = new_v2y)
        
        ball.change_attribute(x = ball.x+ball.vx, y = ball.y+ball.vy)
    
    animationTimer.tick(100)
    pygame.display.update()
    screen.fill((0, 0, 0))

另外，这是我在 andy_balls（）上使用的想法。我的油漆不是很好，但是我们去了：

x 在脚本上为 diffr 。我使用此值将每个球融合后将每个球彼此移开。