3D Rigid body sphere collision response (C++) - c++

Question

I am currently programming a 3D physics engine in C++ and have two spheres in my scene. I can detect when said spheres are colliding and they have some basic collision as a response but the spheres go inside each other a lot and act minimally upon each other so I'm looking to change this to be a RigidBody collision. I've looked online and many tutorials are on 2D collisions and use Elastic collision which is already hard enough to translate into 2D. Any advice on where to look for Rigidbody sphere collision would be a huge help and I'll put below the code I am currently using for my collision. Thanks in advance!
for (size_t i = 0; i < pool.size(); i++)
{
if (pool.at(i) == this)
{
continue;
}
DynamicObjects* other = pool.at(i);
SScollision = PFG::SphereToSphereCollision(pos, other->GetPosition(), rad, other->GetRadious(), contactPoint);
if (SScollision)
{
glm::vec3 relativeVel = this->GetVelocity() - other->GetVelocity();
float eCof = -(1.0f + 1.0f) * glm::dot(relativeVel, contactPoint);
float jLin = eCof / (1.0f / this->GetMass() + 1.0f / other->GetMass());
glm::vec3 collision_impulse_force = jLin * contactPoint / deltaTs;
//ClearForces();
AddForce(1.0f / this->GetMass() * collision_impulse_force);
//pool.at(otherI)->ClearForces();
other->AddForce(-(1.0f / other->GetMass() * collision_impulse_force));
}
}

Answer 1

When dealing with forces (as opposed to pressure, stress, or potentials), you will need to use a mass-spring-damper model. You can look into the discrete particle method for a technique that is used in many fields.
To learn for yourself, try to understand your state variables and your system. Take the acceleration you are seeing and divide the sphere's velocity (or velocity difference) by that acceleration. This will give you an idea of the time scale that the sphere needs to slow down on impact. Multiply by the velocity and you get a displacement, you can get an idea of how far that sphere will travel before slowing down.
Also, take a look at your time step. If the velocity multiplied by the time step allows the sphere to travel further than your threshold for detecting contact, then the sphere's will pass through each other. The same is true if your contact force doesn't increase as the sphere's begin to intersect.
If you want to take a deeper look at collision mechanics, look for topics under "dynamic behavior of materials". There you will see concepts for wave mechanics and elastic behavior. Most numerical methods transition to energy potential models rather than mass-spring-damper models, you can check out methods such as molecular dynamics, smoothed particle hydrodynamics, and peri-dynamics.
The main point is that these numerical methods operate on governing equations that don't allow particles (or your spheres) to pass through each other. The spring models, or potentials often have very (very) stiff responses when objects begin to intersect, as compared to the normal contact between objects.
A couple of points to take away:
Your integrator (i.e. time step) is likely too coarse or your collision detection is too fine, allowing the spheres to intersect.
Look up the discrete particle method (sometimes called the discrete element method), it is very popular and has many, many people using, studying, and publishing. You will find code, mass-spring-damper models, parameters, and other methods to help you reach your goal.