It seems to me that this might be done by finding the position at which the disc will intersect the line on which the AI character stands--that presumably being then the position that the AI character should aim to move towards.

If your playing field is aligned such that the AI character's line lies along one of the axes (e.g. if it's at y = -5, with only the x-coordinate varying), then finding that point should be just a matter of entering the static coordinate (i.e. “-5” in the previous example) into a line-equation that corresponds to the disc's velocity, and using the point that results.

If not, then you can likely find the desired point by calculating the general (2D) intersection of the AI character's line with the disc's velocity.

Jvdicator said:
Let's see if I got this right: I needto find the intersection between the disc velocity vector and the one that lies on the character's right's? And then add it to the character's location?

Hmm… Not quite. If you add that intersection-point to the character's current position then you'll end up with the character being placed incorrectly, I would expect!

Put it this way:

Let's say that your AI character is standing at the point x = 0, y = 5, and that the character moves along the x-axis. That is, that the line on which the character stands and moves is the line y = 5.

Then, let's say that we calculate that the disc will intersect the AI character's line at the point x = 7, y = 5.

If we then add that intersection-point to the AI character's position we get a new position of x = 0+7 = 7, y = 5+5 = 10--which results in moving the AI character away from their line.

Instead, I would imagine that the thing to do would be to treat the intersection-point as a target, and to move the AI character towards it. To do this, I would suggest finding the vector that lies between the AI character's current point and the intersection-point, and moving the character along this new vector.

Jvdicator said:
Like in the picture? (Was masterfully handcrafted by me).

That is the intersection that I have in mind, yes.

I hadn't realised that you also have walls against which your discs might bounce--that introduces a complication, but one that can be dealt with, I do think.

Jvdicator said:
The velocity01 vector vill ever intersect the green one?

That depends on whether the green line is a line segment, or an infinite line. If it's a line-segment, then there will be no intersection; if it's an infinite line, then there will be an intersection, I believe.

(To be more accurate, the maths is more or less the same for both an infinite line and a segment, but in the case of a segment one discards results that lie beyond the ends of the segment, if I'm not much mistaken.)

Remember: If the line that your character moves along is aligned with an axis, then you likely don't need the full line-line intersection maths: you should be able to substitute the character's location on the other axis into an equation for the disc's movement-vector, and from that then get the intercept position on the aligned axis.

To explain by example, if I'm not much mistaken:

Let's say that your character moves along the x-axis, and is located at a y-coordinate of 5. Note that, since it only moves on the x-axis, its y-coordinate should not change.

Now, let's assume that the disc has a movement-vector of, let's say, (2, 3), and is at position (1, 2). From that we can say that it has the following two equations:

x = 1 + 2*t
y = 2 + 3*t

That is, it starts at an x-position of 1, and moves along the x-axis at a rate of 2, and starts at a y-position of 2 and moves along the y-axis at a rate of 3. The variable “t” is “time”--i.e. after 1 unit of time it will have moved 2 units along the x-axis and 3 units along the y-axis.

Now, we're not currently interested in time, but that's okay--that will disappear presently, I think that we'll find.

So, we know that the AI character is standing at a y-coordinate of 5. Thus the intercept will presumably also happen at a y-coordinate of 5. Thus we can substitute that value into the equation for the y-axis, and get this:

5 = 2 + 3*t
5 - 2 = 3*t
3 = 3*t
t = 1

And since we now have a value for “t”, we can put that into the equation for the x-axis, and thus get an x-value:

x = 1 + 2*t
x = 1 + 2*1
x = 1 + 2 = 3

Thus we find that the disc will intercept the AI character's line at a location of (3, 5)!

Jvdicator said:
So I could just replace the character's X value with the disc's one and call it a day, apparently?

As long as you don't mind the character perfectly matching the disc's position, with no mistakes and never being too slow to reach the disc, then indeed, that should work.

Jvdicator said:
That would not work in case I had to change the rotation of the platforms, then I would have to go for the scary math, right?

I believe so, yes.

Good luck, and strength to you for it! I hope that you do succeed in getting it working! ^_^