Determining Resting contact between sphere and plane when using external forces

Question

This question has one major question, and one minor question. I believe I am right in either question from my research, but not both.

For my physics loop, the first thing I do is apply a gravitational force to my TotalForce for a rigid body object. I then check for collisions using my TotalForce and my Velocity. My TotalForce is reset to (0, 0, 0) after every physics loop, although I will keep my velocity.

I am familiar with doing a collision check between a moving sphere and a static plane when using only velocity. However, what if I have other forces besides velocity, such as gravity? I put the other forces into TotalForces (right now I only have gravity). To compensate for that, when I determine that the sphere is not currently overlapping the plane, I do

    Vector3 forces = (sphereTotalForces + sphereVelocity);
    Vector3 forcesDT = forces * fElapsedTime;
    float denom = Vec3Dot(&plane->GetNormal(), &forces);

However, this can be problematic for how I thought was suppose to be resting contact. I thought resting contact was computed by

denom * dist == 0.0f

Where dist is

float dist = Vec3Dot(&plane->GetNormal(), &spherePosition) - plane->d;

(For reference, the obvious denom * dist > 0.0f meaning the sphere is moving away from the plane)

However, this can never be true. Even when there appears to be "resting contact". This is due to my forces calculation above always having at least a .y of -9.8 (my gravity). When when moving towards a plane with a normal of (0, 1, 0) will produce a y of denom of -9.8.

My question is

1) Am I calculating resting contact correctly with how I mentioned with my first two code snippets?

If so,

2) How should my "other forces" such as gravity be used? Is my use of TotalForces incorrect?

For reference, my timestep is

  mAcceleration = mTotalForces / mMass;
  mVelocity += mAcceleration * fElapsedTime;
  Vector3 translation = (mVelocity * fElapsedTime);

EDIT

Since it appears that some suggested changes will change my collision code, here is how i detect my collision states

if(fabs(dist) <= sphereRadius)
{ // There already is a collision }
else
{
    Vector3 forces = (sphereTotalForces + sphereVelocity);
    float denom = Vec3Dot(&plane->GetNormal(), &forces);

    // Resting contact
    if(dist == 0) { }
    // Sphere is moving away from plane
    else if(denom * dist > 0.0f) { }
    // There will eventually be a collision
    else
    {
        float fIntersectionTime = (sphereRadius - dist) / denom;
        float r;
        if(dist > 0.0f)
            r = sphereRadius;
        else
            r = -sphereRadius;

        Vector3 collisionPosition = spherePosition + fIntersectionTime * sphereVelocity - r * planeNormal;
    }
}

Answer 1

1. You should use if(fabs(dist) < 0.0001f) { /* collided */ } This is to acocunt for floating point accuracies. You most certainly would not get an exact 0.0f at most angles or contact.

2. the value of dist if negative, is in fact the actual amount you need to shift the body back onto the surface of the plane in case it goes through the plane surface. sphere.position = sphere.position - plane.Normal * fabs(dist);

3. Once you have moved it back to the surface, you can optionally make it bounce in the opposite direction about the plane normal; or just stay on the plane.

   parallel_vec = Vec3.dot(plane.normal, -sphere.velocity);

   perpendicular_vec = sphere.velocity - parallel_vec;

   bounce_velocity = parallel - perpendicular_vec;

4. you cannot blindly do totalforce = external_force + velocity unless everything has unit mass.

EDIT:

1. To fully define a plane in 3D space, you plane structure should store a plane normal vector and a point on the plane. http://en.wikipedia.org/wiki/Plane_(geometry) .

Vector3 planeToSphere = sphere.point - plane.point;

float dist = Vector3.dot(plane.normal, planeToSphere) - plane.radius;

if(dist < 0) { // collided. }

I suggest you study more Maths first if this is the part you do not know.

NB: Sorry, the formatting is messed up... I cannot mark it as code block.

EDIT 2: Based on my understanding on your code, either you are naming your variables badly or as I mentioned earlier, you need to revise your maths and physics theory. This line does not do anything useful.

float denom = Vec3Dot(&plane->GetNormal(), &forces);

A at any instance of time, a force on the sphere can be in any direction at all unrelated to the direction of travel. so denom essentially calculates the amount of force in the direction of the plane surface, but tells you nothing about whether the ball will hit the plane. e.g. gravity is downwards, but a ball can have upward velocity and hit a plane above. With that, you need to Vec3Dot(plane.normal, velocity) instead.

Alternatively, Mark Phariss and Gerhard Powell had already give you the physics equation for linear kinematics, you can use those to directly calculate future positions, velocity and time of impact.

e.g. s = 0.5 * (u + v) * t; gives the displacement after future time t. compare that displacement with distance from plane and you get whether the sphere will hit the plane. So again, I suggest you read up on http://en.wikipedia.org/wiki/Linear_motion and the easy stuff first then http://en.wikipedia.org/wiki/Kinematics .

Yet another method, if you expect or assume no other forces to act on the sphere, then you do a ray / plane collision test to find the time t at which it will hit the plane, in that case, read http://en.wikipedia.org/wiki/Line-plane_intersection .