How to calculate position of a moving object on a line

Question

So basically I'm making a pool game (sort of) on c++. I'm still thinking about the theory and how exactly to make it before I start coding and I'm a bit stuck. So the ball starting coordinates are given and also an input is given on how much power is going into the shot and the direction of the shot with coordinates.

Example:

> Ball: (280,70)

Input:
> 2(power) 230(x) 110(y)

Output:
> 180(x) 150(y)

The power means that basically it's going to go X * the distance of the given coordinates. So if it's 1 it would just go to 230 110 but if it's more it will go double, triple, quadruple, etc. times that distance. (external factors should be ignored - friction, etc.)

By now I've managed to create an algorithm to find the line that the ball is going to travel on. But I can't figure out on what point of this line the ball will stop at. Any help will be greatly appreciated!

Also one more thing, I also need to calculate where it would go if it hits the wall of the pool table(pool table is a 2:1 rectangle with given coordinates of edges) and I've also managed to find the line where it would travel on but not the exact point where it will stop.

TL;DR I need to find the point of the line of travel that a billiards ball will stop at.

Answer 1

You probably want to work in terms of orthogonal components, basically thinking of the displacement of the ball in terms of deltaX and deltaY instead of finding a line it will travel. Conveniently, you are already in rectangular coordinates and can compute your changes in x and y followed by scaling them by your power factor. For example, here, deltaX = 2*(280-230) or -100, so the destination will be 280 + -100, which equals 180.

To account for the edges, you bound the movement in any direction to be within the 4 edges. You'll have some extra displacement if it strikes the edge. You might think of a bounce as reversing some of the remainder and then recursively call your moveBall function with power 1 when given the location on the edge the ball strikes plus the excess deltaX and deltaY changed in sign appropriately. If moveBall took std::pair<int, int> startingPosition, std::pair<int, int> displacement, int power, if it hits the wall, you'll return moveBall(locationOnEdge, predictedLocationBasedOnExcess, 1). This setup will recursively call itself as many times as is needed until the ball finally finds its ending position (a ball can bounce off edges multiple times).

For example, if you had an edge at x = 200 and y = 100 (meaning your asserted desired output was different), you'd have a remaining deltaX of -20 and deltaY of 50. Since the ball was traveling up and to the left, it will bounce down and to the left. You'd call moveBall with starting location (200, 100), displacement (-20, -50), and power 1.

I'm doing some guesswork here since you didn't define the expected behavior when the ball bounces off an edge.