C#•7mo ago

2d collision, Chaotic Ball

I am trying to write code for chaotic ball. I know it can be written using equation of motion, but wanted to create simulation for it. This is my code right now and it is terrible. I can't seem to make it collide with top part of the circle, there are energy leaks and ball sometimes exits out the sphere. Any recommendation for how to improve it? I want to learn more about real time simulations. note: dt is fixed to 0.001 so that shouldn't be a problem.

velocity.Y += g * dt;
position += velocity * dt;

double intersect_y = -Math.Sqrt(radius * radius - position.X * position.X);

if (position.Y <= intersect_y)
{
    Vec2 n = new Vec2(position.X / radius, intersect_y / radius);
    
    if (position.X > 0)
        n.Y *= -1;

    double v_normal = Vec2.dot(velocity, n);

    velocity = -1.0 * velocity + 2 * (v_normal * n) * n;

    position.Y = intersect_y;
}

velocity.Y += g * dt;
position += velocity * dt;

double intersect_y = -Math.Sqrt(radius * radius - position.X * position.X);

if (position.Y <= intersect_y)
{
    Vec2 n = new Vec2(position.X / radius, intersect_y / radius);
    
    if (position.X > 0)
        n.Y *= -1;

    double v_normal = Vec2.dot(velocity, n);

    velocity = -1.0 * velocity + 2 * (v_normal * n) * n;

    position.Y = intersect_y;
}

19 Replies

exokem•7mo ago

This is just an idea but you can probably just calculate the distance between the ball center and the center of the big circle and trigger a collision whenever the distance would become greater than the large radius minus the small radius Then there would be no edge case checking for the top Vs the bottom

arch_il•7mo ago

thanks. that's better way for triggering, but trigger was never really the issue. I had both cases together, but split them up in the process of trying to get it right.

exokem•7mo ago

Is it more an issue of calculating the resulting motion vector? Or the direction

arch_il•7mo ago

motion vector

exokem•7mo ago

I will do some math and get back to you You could try mirroring the motion vector over the normal to the point of collision It's not that simple but it might work

arch_il•7mo ago

i attempted this

exokem•7mo ago

Is that what your current code does

arch_il•7mo ago

yes I made mistake somewhere, so it doesn't work on the right side. Couldn't find issue there either

exokem•7mo ago

Are you also getting the X intersection? It looks like you only have intersect y

arch_il•7mo ago

my logic is that if y is out of bounds, x will be too

exokem•7mo ago

I would have thought the normal calculation needed the vector from the intersection point Right now you are using the X position of the ball which is probably different

arch_il•7mo ago

what can i do to fix that? nudge the ball towards center until it is inside bounds?

exokem•7mo ago

You just need to get both coordinates for the intersection point

exokem•7mo ago

This could be helpful for the math https://math.stackexchange.com/a/311956

Mathematics Stack Exchange

Get location of vector/circle intersection?

I'm a coding guru, and I'm good with math - but only math that I know. Which isn't even at calculus level yet. So I'm hoping I can get some help here for my algorithm. Say I have a circle. I know ...

exokem•7mo ago

Then the normal calculation would be the same and you still just reflect over it

arch_il•7mo ago

that is much neater solution anyways its late for me. will try implementing tomorrow. thanks a bunch

exokem•7mo ago

No problem, good luck

arch_il•7mo ago

hey @exokem . thanks for help. here is solution i came up with today.

if (position.Length() >= radius)
{
    double ratio = radius / position.Length();
    position *= ratio;

    double collision_angle = Math.Acos(position.X / radius);
    double vector_angle = Math.Atan2(velocity.Y, velocity.X) + Math.PI;
    double new_angle = 2 * collision_angle - vector_angle;
    double vlen = velocity.Length();

    velocity = new Vec2(-Math.Cos(new_angle), Math.Sin(new_angle)) * vlen;
}

if (position.Length() >= radius)
{
    double ratio = radius / position.Length();
    position *= ratio;

    double collision_angle = Math.Acos(position.X / radius);
    double vector_angle = Math.Atan2(velocity.Y, velocity.X) + Math.PI;
    double new_angle = 2 * collision_angle - vector_angle;
    double vlen = velocity.Length();

    velocity = new Vec2(-Math.Cos(new_angle), Math.Sin(new_angle)) * vlen;
}

instead of fiddling around with vectors, i decided to find an angle of resulting velocity and then convert polar coordinate to traditional form. With some fiddling around, this works great.

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2d collision, Chaotic Ball