I implemented the code from the question "Ball to Ball Collision - Detection and Handling" in Objective-C. However, whenever the balls collide at an angle their velocity increases dramatically. All of the vector math is done using cocos2d-iphone, with the header CGPointExtension.h. What is the cause of this undesired acceleration?
The following is an example of this increase in speed:
Input:
mass == 12.56637
velocity.x == 1.73199439
velocity.y == -10.5695238
ball.mass == 12.56637
ball.velocity.x == 6.04341078
ball.velocity.y == 14.2686739
Output:
mass == 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));
}