Basic gravity implementation in OpenGL - c++

Question

I'm trying to implement jumping in my OpenGL game. My left and right 'velocity' and 'friction' is working well, but I'm not able to get my jump working in a nice arc. The player gets stuck in the air:
void keyboard() {
//Move Left
if (GetAsyncKeyState(keyA)) {
playerVelX -= 3;
}
//Move Right
if (GetAsyncKeyState(keyD)) {
playerVelX += 3;
}
//Jump
if (GetAsyncKeyState(keySpace)) {
playerVelY += 3;
}
}
void position() {
//Move on x and y axis
playerX += playerVelX;
playerY += playerVelY;
//Slow down respective axes
playerVelX *= friction;
playerVelY *= gravity;
}
while(gameRunning) {
keyboard();
position();
}
I think I've been looking at it too long. Does anyone have experience implementing gravity like this? Thanks

Answer 1

Your formula for applying gravity is wrong. Remember that F=m.a, v=v_0+ a*t, x=x_0 +v_0*t + 0.5*a*t^2. But the usual approach is to use Euler's method for numerical integration:
gravity=9.81;
velocity+=gravity*deltaT;
position+=velocity*deltaT;
In your code it would look like:
playerVelX *= friction;
playerVelY -= gravity;//If Y point up, so gravity acts against that.
playerX += playerVelX;
playerY += playerVelY;
If you want to have deterministic and stable simulation (which you should) then you need to have deltaTime - how much time passed since last update. See this excellent article Fix Your Timstep! . Also the code above applies the gravity constantly,even when not jumping, so be aware of that.

Answer 2

Summarizing all inaccuracies:
Obvious mistake m * dv/dt = -m * g so dv = -g * dt so playerVelY -= gravity * dt
In the jump, further repulsion is impossible, so
if (GetAsyncKeyState(keySpace) && (playerY <= groundLevel)) {
playerVelY += 3;
}
Gravity should not act if the player is on the surface.
if (playerY < groundLevel)
{
playerY = groundLevel;
playerVelY = 0;
}
More realistic to take into account the reaction force.
Your model playerVelX *= friction; corresponds to viscous friction. The player will never stop. Are you sure you need viscous, not dry friction?
dt should be defined as real time between updates otherwise, the result will depend on the current refresh rate. You need something like
void position() {
static double lastTime = getCurrTime();
double currTime = getCurrTime();
double dt = currTime - lastTime;
playerX += playerVelX * dt;
playerY += playerVelY * dt;
if (playerY < groundLevel)
{
playerY = groundLevel;
playerVelY = 0;
}
//Slow down respective axes
playerVelX *= exp(-friction * dt); // playerVelX *= (1 - friction * dt) for small dt
playerVelY -= gravity * dt;
lastTime = currTime;
}