Floor(X) modulo X equals X?

Question

quick question. I'm basically working on a program where we have an Entity cross across a grid. Every time it finishes a "step" (ie, goes from (0, 0) to (1, 0)), I need to fire off an event. The entity's movement per frame is calculated by: ``` frameMovement = entitySpeed * (frameDeltaMs / 1000) ``` and then added onto the entity's X co-ordinate. I elected to use world units (1 world unit is 16 pixels) instead of raw pixels for the co-ordinate system simply for separation of concern. The world does not need to know that the distance for one square is 16 pixels - only the drawing system does. So basically, I'm trying to work out how to tell the system that the unit has finished a "step". Obviously, due to the way the frame movement is calculated, you will never be exactly on a new square, so I must "clip" the unit to that square or have a method that will return "true" if we are within a certain distance from the square (which right now I have decided to be 0.05wu - about 0.8 pixels fr…

Accepted Answer

Modulo means we divide and take the remainder (just like in 3rd grade for me).

So ...

```
10 % 9 is 1.
```

And

```
10 % 10 is 0
```

And

```
10.5 % 10.5 is 0. 
```

(Perhaps you could get rounding issues if you had x = ...calculate 10.5.. and then x % x where you would get a number just below 10.5 or just larger than 0.)

So, for all integers,

```
Floor(x) % x is 0.
```

For a non-integer, it works differently.

```
Floor(10.5) => 10 
```

and

```
10 % 10.5 is 10.
```

So barring the effect of rounding errors in the floating point, Floor(x) % x is either 0 (for integers) or Floor(x) for non-integers.

More

Perhaps you could tell if it passed a grid line by comparing the before and after positions:

```
if (Math.Floor(xAfterMoving / gridSize) != Math.floor(xBeforeMoving / gridSize)) {
    fireXGridCrossingEvent();
}
```

Floor(X) modulo X equals X?

Solution

Problem