Calculating the 2D turn movement required given an incoming and outgoing direction - kotlin

Question

Consider a 2D square tiled grid (chess board like) which contains conveyor belt like structures that can curve and move game pieces around.
I need to calculate the turn movement (TURN_LEFT, TURN_RIGHT or STAY), depending on
the direction from which a piece moves onto the field
the direction from which the underlying belt exits the field
Example:
1 2
1 |>X>|>v |
2 | | v |
The belt makes a RIGHT turn. As such, the result of calcTurn(LEFT, DOWN) should be TURN_RIGHT. Meaning the X game piece will be rotated 90° right when it moves over the curve at (1,2).
I already implemented a function but it only works on some of my test cases.
enum class Direction {
NONE,
UP,
RIGHT,
DOWN,
LEFT;
fun isOpposite(other: Direction) = this == UP && other == DOWN
|| this == DOWN && other == UP
|| this == LEFT && other == RIGHT
|| this == RIGHT && other == LEFT
}
data class Vec2(val x: Float, val y: Float)
fun Direction.toVec2() = when (this) {
Direction.NONE -> Vec2(0f, 0f)
Direction.UP -> Vec2(0f, 1f)
Direction.RIGHT -> Vec2(1f, 0f)
Direction.DOWN -> Vec2(0f, -1f)
Direction.LEFT -> Vec2(-1f, 0f)
}
fun getTurnMovement(incomingDirection: Direction, outgoingDirection: Direction): Movement {
if (incomingDirection.isOpposite(outgoingDirection) || incomingDirection == outgoingDirection) {
return Movement.STAY
}
val incVec = incomingDirection.toVec2()
val outVec = outgoingDirection.toVec2()
val angle = atan2(
incVec.x * outVec.x - incVec.y * outVec.y,
incVec.x * outVec.x + incVec.y * outVec.y
)
return when {
angle < 0 -> Movement.TURN_RIGHT
angle > 0 -> Movement.TURN_LEFT
else -> Movement.STAY
}
}
I can't quite figure out what's going wrong here, especially not because some test cases work (like DOWN+LEFT=TURN_LEFT) but others don't (like DOWN+RIGHT=STAY instead of TURN_LEFT)

Answer 1

You're trying to calculate the angle between two two-dimensional vectors, but are doing so incorrectly.
Mathematically, given two vectors (x1,y1) and (x2,y2), the angle between them is the angle of the second to the x-axis minus the angle of the first to the x-axis. In equation form: arctan(y2/x2) - arctan(y1/x1).
Translating that to Kotlin, you should instead use:
val angle = atan2(outVec.y, outVec.x) - atan2(incVec.y, incVec.x)
I'd note that you could achieve also your overall goal by just delineating the cases in a when statement as you only have a small number of possible directions, but perhaps you want a more general solution.

Answer 2

It's not answering your question of why your code isn't working, but here's another general approach you could use for wrapping ordered data like this:
enum class Direction {
UP, RIGHT, DOWN, LEFT;
companion object {
// storing thing means you only need to generate the array once
private val directions = values()
private fun getPositionWrapped(pos: Int) = directions[(pos).mod(directions.size)]
}
// using getters here as a general example
val toLeft get() = getPositionWrapped(ordinal - 1)
val toRight get() = getPositionWrapped(ordinal + 1)
val opposite get() = getPositionWrapped(ordinal + 2)
}
It's taking advantage of the fact enums are ordered, with an ordinal property to pull out the position of a particular constant. It also uses the (x).mod(y) trick where if x is negative, putting it in parentheses makes it wrap around
x| 6 5 4 3 2 1 0 -1 -2 -3 -4 -5
mod 4| 2 1 0 3 2 1 0 3 2 1 0 3
which makes it easy to grab the next or previous (or however far you want to jump) index, acting like a circular array.
Since you have a NONE value in your example (which obviously doesn't fit into this pattern) I'd probably represent that with a null Direction? instead, since it's more of a lack of a value than an actual type of direction. Depends what you're doing of course!