Calculating Rotations to change carousel face

Question

I am trying to remember how to do something I believe should be quite simple.

I have a slot machine or a carousel, let's focus on one ring. Each ring has five faces, I calculated that each angle is 72deg.

I made a map of each face to the degree it is on the carousel.

    const slotMap = {
      0: 288,
      1: 216,
      2: 144,
      3: 72,
      4: 360
  }; 

My problem is when I have a first rotation everything works fine. I just rotate it to the face I need. For example, if it's face 3 then I rotate by 72deg.

My issue is trying to find an equation that will turn it to the next face. If I have face 3 and I want it to face 2.

I tried by subtracting the difference in the number of faces from the previous face and the current face and multiplying by 72deg but this did not work.

I believe this has to be either trigonometry or something basic, but it has been bugging me for a long time.

my original equation:

| currentFace - previousFace | * 72deg = nextFace 

has not worked out at all.

I must be forgetting something very basic.

(I am doing this in Javascript but I really want to understand the math before the code)

Answer 1

Your equation works when you try to go from a smaller numbered face to a larger numbered face (from 2 to 3), but not when going from a larger numbered face to a smaller numbered face (from 3 to 2). This is because the equation doesn't distinguish between the two.

For example:

If you want to go from face 2 to face 3: $\mid 3-2\mid \times 72=72$ (the correct degree value for face 3)

But, when you try to go from face 2 to 3: $\mid 3-2\mid=\mid 2-3\mid$, so you will get $72$ again.

If you can reassign the degree values for the faces, such that:

const slotMap = {
      0: 360,
      1: 288,
      2: 216,
      3: 144,
      4: 72
  }; 

You can make the equation: ( currentFace - nextFace ) * 72deg which gives you the degrees you need to rotate.

For example:

To go from face 4 to face 1, you have:

$(4-1) \times 72=216$, which is correct since you need to go $+216^\circ$ from face 4 to get to face 1 ($72^\circ$ to $288^\circ$).

On the other hand, to go from face 1 to 4 you have:

$(1-4) \times 72=-216$, which also holds true.