How to implement throw curve with virtual height in a 2D side-view game

Question

I am working on a 2d side-view soccer game that looks like this image:

But now I stuck on how to implement parabola pass ball. I have found many questions corresponding to my problem:

• Calculating velocity needed to hit target in parabolic arc
• Throw object towards predefined place?
• http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

But they all just tell how to draw parabola in simple 2d space. In my game, except for the normal x,y there is also a virtual height coordinate, so the final viewing position of the ball is:

world position + current_height * Calc_Scale. (Calc_Scale is 0.3f)

Currently I did it the following way: I calculate the pass time(T) and distance(D) from point A to B

the pct = current_time / T
current_height = D * (4* pct - 4 * pct* pct)

Unfortunately, it looks bad...

UPDATE: @ashes999 I tried quadratic equation like current_height = D * (4* pct - 4 * pct* pct), it is not good(I am continuing to try different factors).I am pretty sure sin/cos can not work here, for example, player A is in(300, 200), B is(300, 800), the ball will make a direct line beyond B's head then drop to B's feet(or head), and this can not be done by cos/sin way, And I am thinking can this be done by some sort of projection, I just calculate the x,y,z then project z value into y axis?

void RSSoccerBall::Pass(const vector2d& target, double force)
{
vector2d DistVec(target - m_vPosition);
m_PassDistance = DistVec.getLength();
if(m_PassDistance > MaxShortPassDistance)
{
m_CurrentPassTime = 0.f;
m_PassTime = TimeToCoverDistance(target, m_vPosition, force, true);
}
}

void RSSoccerBall::update(float dt)
{
//for parabola calc
if(m_CurrentPassTime < m_PassTime)
{
m_CurrentPassTime += dt;
float pct = m_CurrentPassTime / m_PassTime;

m_Height = m_PassDistance * 0.7 *  (4 * pct - 4 * pct * pct);
}
vector2d    exactViewPos = m_vPosition; //m_vPosition is the 2d world position
exactViewPos.y += m_Height;
//render football at exactViewPos;
...
}

@Mario, These are my code ,I have used an extra variable to store height. - Determing an object's position along a curve over time this is where the equation from

I do not want the top of the arc always to be at 50% distance traveled, because player A and B probably not in same Y value, if B's Y value is higher than A's Y, the top of the arc will be exceed 50%. I found a wiki link: - http://en.wikipedia.org/wiki/Range_of_a_projectile describe Ideal projectile motion on uneven ground, but the formulas are complicated for me to convert into current situation(we have start point, end point, start velocity, travel time)

Can anyone give me some pointers how to accomplish that?

Answer 1

Your actual view of the ball or playing field shouldn't really matter in this.

• First of all, you'd mostly want a constant/fixed horizontal velocity for the ball. You can add air resistance to this, but it wouldn't really change anything, as you'll just have to add it to the equation.
• Ignore the actual height of the shot for now.
• Having a target distance as well as a velocity, it's rather trivial to calculate the travel time of the ball: t = d / v
• Now for making a nice arc you'll just have to set your initial vertical velocity right. You'll want the top of the arc to be at 50% distance travelled.
• To achieve this you'll need your gravity to completely negate that velocity once you arrive at half the distance. So for this you'll have to apply the max velocity the ball may achieve when falling down for the time it needs to travel there: vy = -g * 0.5 * t

Here's a simple jsFiddle showing you the overall idea. Note that the height of the arc depends on the time the ball needs to reach its target. Click anywhere in the playing field to kick the ball at that position. For a bit more accurate model (with friction), click here.

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In case I haven't been clear enough:

• Behind the scenes your playing field should be a real 3D representation of the playing field.
• Only for drawing you collapse everything to the 2D representation that is shown on screen.
• This way you won't have to worry about any weird side effects, like doing complicated math, and you won't have to worry any fake height for your ball.
• Since the ball is the only element that can go into third dimension, you can simplify the whole game to be 2D (top-down playing field; only behind the scenes) and store your ball height in an extra variable.