圆与圆的碰撞（物理），但是当很多圆堆积起来时就会出问题

Question

我正在尝试制作一个尽可能真实的球物理模拟器。目前，我已经计算出了球之间的所有碰撞，当球很少时效果非常好。但一旦你创建了大约 400-500 个球，事情就开始变得奇怪：底部的球被压扁，彼此重叠。一旦你添加更多的球，事情就会变得更加疯狂，球几乎开始在底部传送。

一些截图： 100 个球： 拥有超过 600 个球：

有谁知道发生了什么以及造成这种情况的原因是什么？如何改进代码来防止这种情况发生？

（为了便于测试，使用滚轮快速连续创建大量球）

这是代码，它不太长：

import pygame
from pygame.locals import *
from random import *
from math import *

WIDTH = 1200
HEIGHT = 800
FPS = 144
VEC = pygame.math.Vector2

pygame.init()
screen = pygame.display.set_mode((WIDTH, HEIGHT), HWSURFACE | DOUBLEBUF)
pygame.display.set_caption("Bouncy balls with physics")
clock = pygame.time.Clock()

gravity = 3200
colors = range(50, 255, 10)
sizes = (15, 25)

absvec = lambda v: VEC(abs(v.x), abs(v.y))
inttup = lambda tup: tuple((int(tup[0]), int(tup[1])))

class Ball:
    instances = []
    regions = {}

    def __init__(self, pos):
        __class__.instances.append(self)
        self.pos = VEC(pos)
        self.region = inttup(self.pos // (sizes[1] * 2) + VEC(1, 1))
        if self.region in __class__.regions:
            __class__.regions[self.region].append(self)
        else:
            __class__.regions[self.region] = [self]
        self.vel = VEC(0, 0)
        self.radius = randint(*sizes)
        self.mass = self.radius ** 2 * pi
        self.color = (choice(colors), choice(colors), choice(colors))
        self.moving = True

    def update_position(self):
        self.vel.y += gravity * dt
        self.vel -= self.vel.normalize() * 160 * dt
        if -6 < self.vel.x < 6:
            self.vel.x = 0
        if -6 < self.vel.y < 6:
            self.vel.y = 0
        self.pos += self.vel * dt

        new_region = inttup(self.pos // (sizes[1] * 2) + VEC(1, 1))
        if self.region != new_region:
            if new_region in __class__.regions:
                __class__.regions[new_region].append(self)
            else:
                __class__.regions[new_region] = [self]
            __class__.regions[self.region].remove(self)
            self.region = new_region

    def update_pushout(self):
        self.collisions = []
        for x in range(self.region[0] - 1, self.region[0] + 2):
            for y in range(self.region[1] - 1, self.region[1] + 2):
                if (x, y) in __class__.regions:
                    for ball in __class__.regions[(x, y)]:
                        dist = self.pos.distance_to(ball.pos)
                        if dist < self.radius + ball.radius and ball != self:
                            self.collisions.append(ball)
                            overlap = -(dist - self.radius - ball.radius) * 0.5
                            self.pos += overlap * (self.pos - ball.pos).normalize()
                            ball.pos -= overlap * (self.pos - ball.pos).normalize()
    
    def update_collision(self):
        for ball in self.collisions:
            self.vel *= 0.85
            n = (ball.pos - self.pos).normalize()
            k = self.vel - ball.vel
            p = 2 * (n * k) / (self.mass + ball.mass)
            self.vel -= p * ball.mass * n
            ball.vel += p * self.mass * n

        if self.pos.x < self.radius:
            self.vel.x *= -0.8
            self.pos.x = self.radius
        elif self.pos.x > WIDTH - self.radius:
            self.vel.x *= -0.8
            self.pos.x = WIDTH - self.radius
        if self.pos.y < self.radius:
            self.vel.y *= -0.8
            self.pos.y = self.radius
        elif self.pos.y > HEIGHT - self.radius:
            if self.vel.y <= gravity * dt:
                self.vel.y = 0
            else:
                self.vel.y *= -0.8
            self.pos.y = HEIGHT - self.radius

    def draw(self, screen):
        pygame.draw.circle(screen, self.color, self.pos, self.radius)

    def kill(self):
        __class__.instances.remove(self)
        __class__.regions[self.region].remove(self)
        del self

running = True
while running:
    dt = clock.tick_busy_loop(FPS) / 1000
    screen.fill((30, 30, 30))
    pygame.display.set_caption(f"Bouncy balls with physics | FPS: {str(int(clock.get_fps()))} | Ball count: {len(Ball.instances)}")

    for event in pygame.event.get():
        if event.type == QUIT:
            running = False
        if event.type == MOUSEBUTTONDOWN:
            mpos = VEC(pygame.mouse.get_pos())
            if sum([len(balls) for balls in Ball.regions.values()]) <= 1000:
                Ball(mpos)
        if event.type == KEYDOWN:
            if event.key == K_c:
                for ball in Ball.instances.copy():
                    ball.kill()

    for ball in Ball.instances:
        ball.update_position()
        ball.update_pushout()
        ball.update_collision()
        ball.draw(screen)

    pygame.display.flip()

pygame.quit()
quit()

这是两个球碰撞时执行的代码：

self.vel *= 0.85
n = (ball.pos - self.pos).normalize()
k = self.vel - ball.vel
p = 2 * (n * k) / (self.mass + ball.mass)
self.vel -= p * ball.mass * n
ball.vel += p * self.mass * n

从此维基百科页面获取：https://en.wikipedia.org/wiki/Elastic_collision

提前致谢！

Answer 1

这是由于您添加的重力因子，这会导致圆环“下降”并在它们应该处于平衡时挤压它们下方的圆环

我现在无法测试它，但我的猜测是将 g 应用于您的 k 因子而不是主速度（我也不是100%确定）

告诉我是否是这样