Getting the velocity vector from position vectors - c++

Question

I looked at a bunch of similar questions, and I cannot seem to find one that particularly answers my question. I am coding a simple 3d game, and I am trying to allow the player to pick up and move entities around my map. I essentially want to get a velocity vector that will "push" the physics object a distance from the player's eyes, wherever they are looking. Here's an example of this being done in another game (the player is holding a chair entity in front of his eyes).
To do this, I find out the player's eye angles, then get the forward vector from the angles, then calculate the velocity of the object. Here is my working code:
void Player::PickupOtherEntity( Entity& HoldingEntity )
{
QAngle eyeAngles = this->GetPlayerEyeAngles();
Vector3 vecPos = this->GetEyePosition();
Vector3 vecDir = eyeAngles.Forward();
Vector3 holdingEntPos = HoldingEntity.GetLocation();
// update object by holding it a distance away
vecPos.x += vecDir.x * DISTANCE_TO_HOLD;
vecPos.y += vecDir.y * DISTANCE_TO_HOLD;
vecPos.z += vecDir.z * DISTANCE_TO_HOLD;
Vector3 vecVel = vecPos - holdingEntPos;
vecVel = vecVel.Scale(OBJECT_SPEED_TO_MOVE);
// set the entity's velocity as to "push" it to be in front of the player's eyes
// at a distance of DISTANCE_TO_HOLD away
HoldingEntity.SetVelocity(vecVel);
}
All that is great, but I want to convert my math so that I can apply an impulse. Instead of setting a completely new velocity to the object, I want to "add" some velocity to its existing velocity. So supposing I have its current velocity, what kind of math do I need to "add" velocity? This is essentially a game physics question. Thank you!

Answer 1

A very simple implementation could be like this:
velocity(t+delta) = velocity(t) + delta * acceleration(t)
acceleration(t) = force(t) / mass of the object
velocity, acceleration and force are vectors. t, delta and mass scalars.
This only works reasonably well for small and equally spaced deltas. What you are essentially trying to achieve with this is a simulation of bodies using classical mechanics.

Answer 2

An Impulse is technically F∆t for a constant F. Here we might want to assume a∆t instead because mass is irrelevant. If you want to animate an impulse you have to decide what the change in velocity should be and how long it needs to take. It gets complicated real fast.
To be honest an impulse isn't the correct thing to do. Instead it would be preferable to set a constant pick_up_velocity (people don't tend to pick things up using an impulse), and refresh the position each time the object rises up velocity.y, until it reaches the correct level:
while(entPos.y < holdingEntPos.y)
{
entPos.y += pickupVel.y;
//some sort of short delay
}
And as for floating in front of the player's eyes, set an EyeMovementEvent of some sort that also sends the correct change in position to any entity the player is holding.
And if I missed something and that's what you are already doing, remember that when humans apply an impulse, it is generally really high acceleration for a really short time, much less than a frame. You wouldn't see it in-game anyways.

Answer 3

basic Newtonian/D'Alembert physics dictate:
derivate(position)=velocity
derivate(velocity)=acceleration
and also backwards:
integrate(acceleration)=velocity
integrate(velocity)=position
so for your engine you can use:
rectangle summation instead of integration (numerical solution of integral). Define time constant dt [seconds] which is the interval between updates (timer or 1/fps). So the update code (must be periodically called every dt:
vx+=ax*dt;
vy+=ay*dt;
vz+=az*dt;
x+=vx*dt;
y+=vy*dt;
z+=vz*dt;
where:
a{x,y,z} [m/s^2] is actual acceleration (in your case direction vector scaled to a=Force/mass)
v{x,y,z} [m/s] is actual velocity
x,y,z [m] is actual position
These values have to be initialized a,v to zero and x,y,z to init position
all objects/players... have their own variables
full stop is done by v=0; a=0;
driving of objects is done only by change of a
in case of collision mirror v vector by collision normal
and maybe multiply by some k<1.0 (0.95 for example) to account energy loss on impact
You can add gravity or any other force field by adding g vector:
vx+=ax*dt+gx*dt;
vy+=ay*dt+gy*dt;
vz+=az*dt+gz*dt;
also You can add friction and anything else you need
PS. the same goes for angles just use angle/omega/epsilon/I instead of x/a/v/m
to be clear by angles I mean rotation (pitch,yaw,roll) around mass center