objective-c - Ball to Ball Collision - 碰撞时获得显着速度

Question

我在 Objective-C 中实现了问题“Ball to Ball Collision - Detection and Handling”中的代码。然而，只要球以一定角度碰撞，它们的速度就会急剧增加。所有矢量数学都是使用 cocos2d-iphone 完成的，标题为 CGPointExtension.h。这种意外加速的原因是什么？

下面是速度提升的例子:

输入:
质量 == 12.56637
velocity.x == 1.73199439
velocity.y == -10.5695238

ball.mass == 12.56637
ball.velocity.x == 6.04341078
ball.velocity.y == 14.2686739

输出:
质量 == 12.56637
velocity.x == 110.004326
velocity.y == -10.5695238

ball.mass == 12.56637
ball.velocity.x == -102.22892
ball.velocity.y == -72.4030228

#import "CGPointExtension.h"
#define RESTITUTION_CONSTANT (0.75) //elasticity of the system

- (void) resolveCollision:(Ball*) ball
{
    // get the mtd (minimum translation distance)
    CGPoint delta = ccpSub(position, ball.position);
    float d = ccpLength(delta);
    // minimum translation distance to push balls apart after intersecting
    CGPoint mtd = ccpMult(delta, (((radius + ball.radius)-d)/d)); 


    // resolve intersection --
    // inverse mass quantities
    float im1 = 1 / [self mass]; 
    float im2 = 1 / [ball mass];

    // push-pull them apart based off their mass
    position = ccpAdd(position, ccpMult(mtd, (im1 / (im1 + im2))));
    ball.position = ccpSub(ball.position, ccpMult(mtd, (im2 / (im1 + im2))));

    // impact speed
    CGPoint v = ccpSub(velocity, ball.velocity);
    float vn = ccpDot(v,ccpNormalize(mtd));

    // sphere intersecting but moving away from each other already
    if (vn > 0.0f) return;

    // collision impulse
    float i = (-(1.0f + RESTITUTION_CONSTANT) * vn) / ([self mass] + [ball mass]);
    CGPoint impulse = ccpMult(mtd, i);


    // change in momentum
    velocity = ccpAdd(velocity, ccpMult(impulse, im1));
    ball.velocity = ccpSub(ball.velocity, ccpMult(impulse, im2));

}

Answer 1

查看原始代码和原始发帖人的评论后，代码似乎是一样的，所以如果原始代码是正确的实现，我会怀疑是错误的矢量库或某种未初始化的变量。

为什么要将 1.0 添加到恢复系数？

发件人:http://en.wikipedia.org/wiki/Coefficient_of_restitution

COR 通常是 [0,1] 范围内的数字。定性地，1 代表完全弹性碰撞，而 0 代表完全非弹性碰撞。 COR大于1在理论上是可能的，代表产生动能的碰撞，例如地雷被扔在一起爆炸。

另一个问题是:

/ (im1 + im2)

您除以质量的倒数之和以获得沿接触向量的冲量 - 您可能应该除以质量本身的总和。这是在放大你的冲动(“她就是这么说的”)。