Quantidade de etapas de um campo em uma grade para outra, ortogonally?

Question

Como faço para calcular a quantidade de "etapas" que existe de um campo para outro em uma grade, movendo-se ortogonally?

Estou implementando um sistema de pathfinding A * para um jogo que estou desenvolvendo, e esta simples operação matemática está no meu caminho.

provavelmente deveria reenendar a terceira série.Haha

Answer 1

If I understand correctly, I think you just add up the x,y movements necessary. Given two points (x1,y1) and (x2,y2), then the distance (assuming "moving orthogonally" means moving only horizontally and/or vertically) then it is:

abs(x1-x2) + abs(y1-y2)

For example, moving from position (1,1) to (3,4) means moving 2 spaces to the right and 3 spaces up for a total of 5. abs(1-3)+abs(1-4) = 2 + 3 = 5

Answer 2

I do believe this is a matter of simple math.

Surely, you know your starting x / y values, and your ending x / y values. To get the distance between the two, you do this:

dist = sqrt(dx^2 + dy^2 )

Where dx is the difference between the x-coordinates of the points Where dy is the difference between y-coordinates of the points.

So, for example. Lets say co-ordinate A is A(15,20) and co-ordinate B is B(35,5);

dx = 35 - 15 = 20; dy = 20-5 = 15;

Therefore;

dist between AB = sqrt(20^2 + 15^2) = 25.0 units.

Now for your final answer, this depends how many units a "step" is in your program. If a step is 5 units, (25/5) than there is 5 steps needed to get from point A to B.