cartesian coordinate system, calc change in position

[BubikolRamios]

Need to know if an object moved, from x1 to x2, for how much and in which direction
For our case say that y = 0.

examples

x1   x2     expected  result
1    -1              -2
1     2                1 
-1   -2              -1
-1   -3              -2
6     7                1
7     6               -1
etc

The simplest way to calc that ?

[BWiz]

Well if y is always zero, then the distance traveled will always be x_final - x_initial. The sign of the answer will tell you whether your moved in the +x direction or the -x direction.

If your y changes, however, you'll have to use the distance formula to calculate the MAGNITUDE of the distance. To get the direction and magnitude, I would use vectors, and their respective operations.

[bobleny]

If both your Y and X coordinates change, you can just use the Pythagorean theorem (a2 + b2 = c2) where the difference in X is your a and the difference in Y is your b. Then solve for c and you have your distance between the two points.

Point 1 (-1, 0)
Point 2 (2, 4)

|-1 - 2| = a = 3
|0 - 4| = b = 4

a squared = 9
b squared = 16

9 + 16 = c = 25

The square root of 25 = 5

The distance between Point 1 and Point 2 is 5.

[bullant]

Originally Posted by BubikolRamios

Need to know if an object moved, from x1 to x2, for how much and in which direction
For our case say that y = 0.

examples

x1   x2     expected  result
1    -1              -2
1     2                1 
-1   -2              -1
-1   -3              -2
6     7                1
7     6               -1
etc

The simplest way to calc that ?

deltaX = x2 - x1 where deltaX is the distance moved on the x axis.

Bear in mind that subtracting a negative number is the same as adding the absolute value of that number.

If you take the highlighted xample:

deltaX = x2 - x1 = -3 - (-1) = -3 + 1 = -2

If deltaX is negative (less than 0), the object moved in the negative direction on the x axis. If deltaX is positive, the object moved in the positive direction on the x axis.

If the object moves on the y axis as well, then as bobleny described, you can use Pythagoras' Theorem to solve for the straight line distance between 2 points.

distance = sqrt(deltaX^2 + deltaY^2)

In bobleny's example there needs to be a minor correction

9 + 16 = c^2 = 25