To detect whether two balls collide, just check whether the distance between their centers is less than two times the radius. To do a perfectly elastic collision between the balls, you only need to worry about the component of the velocity that is in the direction of the collision. The other component (tangent to the collision) will stay the same for both balls. You can get the collision components by creating a unit vector pointing in the direction from one ball to the other, then taking the dot product with the velocity vectors of the balls. You can then plug these components into a 1D perfectly elastic collision equation.

维基百科对整个过程有一个很好的总结。对于任何质量的球，新的速度可以用以下公式计算(其中v1和v2是碰撞后的速度，u1和u2是碰撞前的速度):

如果两个球质量相同，那么速度只是互换。下面是我写的一些类似的代码:

void Simulation::collide(Storage::Iterator a, Storage::Iterator b)
{
    // Check whether there actually was a collision
    if (a == b)
        return;

    Vector collision = a.position() - b.position();
    double distance = collision.length();
    if (distance == 0.0) {              // hack to avoid div by zero
        collision = Vector(1.0, 0.0);
        distance = 1.0;
    }
    if (distance > 1.0)
        return;

    // Get the components of the velocity vectors which are parallel to the collision.
    // The perpendicular component remains the same for both fish
    collision = collision / distance;
    double aci = a.velocity().dot(collision);
    double bci = b.velocity().dot(collision);

    // Solve for the new velocities using the 1-dimensional elastic collision equations.
    // Turns out it's really simple when the masses are the same.
    double acf = bci;
    double bcf = aci;

    // Replace the collision velocity components with the new ones
    a.velocity() += (acf - aci) * collision;
    b.velocity() += (bcf - bci) * collision;
}

至于效率，Ryan Fox是对的，您应该考虑将区域划分为部分，然后在每个部分中进行碰撞检测。请记住，球可以在一个部分的边界上与其他球碰撞，所以这可能会使您的代码更加复杂。不过，在你有几百个球之前，效率可能并不重要。为了获得额外的奖励，你可以在不同的核心上运行每个部分，或者在每个部分中拆分碰撞处理。

有两种简单的方法。杰伊已经介绍了从球的中心起跳的准确方法。

更简单的方法是使用矩形包围框，将框的大小设置为球的80%，这样就可以很好地模拟碰撞。

给你的球类添加一个方法:

public Rectangle getBoundingRect()
{
   int ballHeight = (int)Ball.Height * 0.80f;
   int ballWidth = (int)Ball.Width * 0.80f;
   int x = Ball.X - ballWidth / 2;
   int y = Ball.Y - ballHeight / 2;

   return new Rectangle(x,y,ballHeight,ballWidth);
}

然后，在循环中:

// Checks every ball against every other ball. 
// For best results, split it into quadrants like Ryan suggested. 
// I didn't do that for simplicity here.
for (int i = 0; i < balls.count; i++)
{
    Rectangle r1 = balls[i].getBoundingRect();

    for (int k = 0; k < balls.count; k++)
    {

        if (balls[i] != balls[k])
        {
            Rectangle r2 = balls[k].getBoundingRect();

            if (r1.Intersects(r2))
            {
                 // balls[i] collided with balls[k]
            }
        }
    }
}

如果你有很多球，我会考虑使用四叉树。为了确定弹跳的方向，只需使用基于碰撞法向的简单能量守恒公式。弹性，重量和速度会让它更真实一些。

减少碰撞检查数量的一个好方法是将屏幕分割成不同的部分。然后只将每个球与同一区域的球进行比较。

改进问题中给出的圆碰撞检测检测圆的解决方案:

float dx = circle1.x - circle2.x,
      dy = circle1.y - circle2.y,
       r = circle1.r + circle2.r;
return (dx * dx + dy * dy <= r * r);

它避免了不必要的“如果有两个返回”和使用不必要的变量。

我找到了一个很棒的页面，上面有关于2D碰撞检测和响应的信息。

http://www.metanetsoftware.com/technique.html (web.archive.org)

他们试图从学术的角度解释这是如何做到的。他们从简单的对象对对象碰撞检测开始，然后转向碰撞响应以及如何扩展它。

编辑:更新链接