RogueLike line of sigth(Resolve)

[GameMadeByGamers]

Hello everyone , im making a roguelike game just for exercise myself , i come to a problem when i come to the line of sigth.

Am unable to find a equation/formula for getting the number of purple “square/node” like in this schema:

i think i can resolve this by a exponential equation (y = ab^x) but im not sure on that because i cant get the “b” right when checking it with multiple points.

Thanks for your future responds and help.

[MathiasDG]

You have an arithmetic progression there.

1 → 0
2 → 0 + 2 = 2
3 → 0 + 2 + 4 = 6
4 → 0 + 2 + 4 + 6 = 12
5 → 0 + 2 + 4 + 6 + 8 = 20

[GameMadeByGamers]

yes indeed, the goal would be to have some sort of formula for it to be inside a loop.

[MathiasDG]

I dont get it. Doesnt this formula fit your needs?

Arithmetic progression

It should if all you need is the number of purple squares.

[GameMadeByGamers]

well the number of purple square are base on the range of the line of sight(in red)

[Ryiah]

@MathiasDG

You have an arithmetic progression there.

1 → 0
2 → 0 + 2 = 2
3 → 0 + 2 + 4 = 6
4 → 0 + 2 + 4 + 6 = 12
5 → 0 + 2 + 4 + 6 + 8 = 20

If that’s the pattern this will handle it.

int purpleSquares = lengthOfSight * (lengthOfSight - 1);

[GameMadeByGamers]

thank you