How do you know if a point is in a square?

Question

JavaScript

How to understand whether a given point of coordinates (x, y) is included in the square (each point is floating)?

Answer 1

const point = (x, y) => ({ x, y });

const A = point(-1, 1);
const B = point(1, 1);
const C = point(1, -1);
const D = point(-1, -1);
const E = point(0, 0);

const side = (a, b, p) =>  Math.sign((b.x - a.x) * (p.y - a.y) - (b.y - a.y) * (p.x - a.x));

const inArea = side(A, B, E) === -1 &&
               side(B, C, E) === -1 &&
               side(C, D, E) === -1 &&
               side(D, A, E) === -1;

console.log(inArea); // true

On Lua

function point(x, y)
    return { ["x"] = x, ["y"] = y }
end

function sign(number)
    if (number < 0) then
        return -1
    elseif (number > 0) then
        return 1
    else 
        return number
    end
end

function side(a, b, p)
    return sign((b.x - a.x) * (p.y - a.y) - (b.y - a.y) * (p.x - a.x))
end

A = point(-1, 1)
B = point(1, 1)
C = point(1, -1)
D = point(-1, -1)
E = point(0, 0)

inArea = side(A, B, E) == -1 and
         side(B, C, E) == -1 and
         side(C, D, E) == -1 and
         side(D, A, E) == -1;

print(inArea) -- true

Answer 2

If this is an even square, then x1=x4, and the other parameters are also equal in pairs. In this case, write normally.
For an even square - you need to make sure that the X-coordinate of the point is between the X-coordinates of the left and right borders; and similarly for the Y-coordinate.
And you can calculate the middle point. And then make sure that the deviation of the X and Y coordinates differ from the midpoint by no more than half the side of the square - in absolute value. This is good because you can not be afraid to confuse the right and left sides of the square.
Or maybe a square. rotated - then it must be set a little differently, there are several options.
Here the calculations are a little more complicated.

Answer 3

function aabbPoint(x, y, rx, ry, rw, rh)
  return x >= rx and x <= rx + rw and y >= ry and y <= ry + rh
end