How can I "zero out" velocity in an arbitrary direction?

Question

I'm currently running into an issue with my character controller using physics-based movement of rigidbodies in Unity.

Here's an illustration of the issue I'm facing:

Basically, after a jump, my character sticks to the ground for a split second after landing from a jump. While I have no idea, I just assumed this had something to do with the way Physics were being implemented, given that a portion of the character's velocity is heading downward, it makes sense that there would be some "impact time". I drew a bit of depenetration in the diagram, but that's mostly some creative thinking by me, I don't actually know if that has anything to do with it.

My current solution is to do this during the "landing" frame:

// first frame that the ground is detected
var velocity = rigidbody.velocity;
velocity.y = 0;
rigidbody.velocity = velocity;

This works nicely. However, I've now implemented custom gravity into the project, which allows for completely arbitrary gravity vectors (meaning I can't just set something to 0 and be done with it).

Is it possible to nullify all force in the "gravity" direction upon landing? It's also possible I've got a problem elsewhere if this reads like something that should be happening.

Here's a snippet that has the meat of my movement code:

        var velocity = rigidbody.velocity;
        var normal = CollisionHelper.GetFloorNormal(capsuleCollider, true);

        Vector3 xAxis = ProjectDirectionOnPlane(rightAxis, normal);
        Vector3 zAxis = ProjectDirectionOnPlane(forwardAxis, normal);
        float currentX = Vector3.Dot(velocity, xAxis);
        float currentZ = Vector3.Dot(velocity, zAxis);
        float acceleration = isGrounded ? defaultAcceleration : airAcceleration;
        float maxSpeedChange = acceleration * Time.deltaTime;

        var desiredVelocity = new Vector3(wrapped.input.move_H, 0, wrapped.input.move_V) * defaultSpeed;

        float newX = Mathf.MoveTowards(currentX, desiredVelocity.x, maxSpeedChange);
        float newZ = Mathf.MoveTowards(currentZ, desiredVelocity.z, maxSpeedChange);
        velocity += xAxis * (newX - currentX) + zAxis * (newZ - currentZ);

        rigidbody.velocity = velocity;

Answer 1

This is pretty simple linear algebra. You can make a little helper method for it:

public static class VectorExtensions {

    public static Vector3 RemoveComponent(this Vector3 vector, Vector3 direction) {
        direction = direction.normalized;

        return vector - direction * Vector3.Dot(vector, direction);
    }
}

Then just say:

velocity = velocity.RemoveComponent(Physics.gravity);