Question

How would I write a function to move from point1 to point2 given some time?

For example:

Point move(Point point1, Point point2, long timeInMilliseconds, int speedPerSecond)
{
  // basic stuff
  int pointsMoved = speedPerSecond * 1000 / timeInMilliseconds;
  if (point1.x == point2.x && point1.y > point2.y)
    return (new Point(point1.x, Math.min(point2.y, point1.y + pointsMoved)));
  ...
}

Yes, that’s where my sad math skills end.
How do I move if the movement is not diagonal or vertical? if there’s an angle?

BTW, I plan to recalculate the current point based on point1 and point2, I will not be updating point1 nor point2 from the caller, so caller would look like this:

Point currentPoint = move(originalPoint, finalPoint, getCurrentTime() - originalTime, 10);

The signature of the function doesn’t have to be what I mentioned. It could very well use degrees, but that’s going to be another thing to figure out, if I have to use degrees.

Answer 1

Here’s the general motion formula:

p = k⟨p₂ – p₁⟩ + p₁

p₁ is the initial position. p₂ is the final position. p is the current location. k is a ratio, usually between 0 and 1, that determines how much of the distance to p₂ we’ve covered.

Your function receives t_n, the current time, and v, the speed from the p₁ to p₂. Therefore we need one additional piece to calculate k: the distance from p₁ to p₂. t_n is in time units (t), the distance |p₂ – p₁| is in distance units (d), and the speed is in distance per time units (d / t). k is unitless, so we have to neutralize the units in the three values.

d / (d / t) / t
= d / d · t / t
= 1

and our units are neutralized.

So we have:

k = |p₂ – p₁| / v / t_n

The distance is easily determined via the Pythagorean Theorem, giving us k. From there we decompose the general formula into its components:

p_x = k(x₂ – x₁) + x₁
p_y = k(y₂ – y₁) + y₁

k, being unitless despite containing elements with components, does not get decomposed.