How determine if point is within rectangle given all latitude/longitude coordinates?

Question

If given x/y coordinates for all 4 corners of rectangle, and then another x/y, it\'s easy to determine if the point is within the rectangle if top left is 0,0.

But w

Answer 1

Mathematicaly, you could use inequations to determine that.

edit: When doing the example, i've noticed you put the coordinates in the inverse format (y,x) instead of (x,y). In my example I use (x,y) format, so I just inverted the order to easy my explanation.

Let's say A = (-130,10) B = (-100,20) C = (-125,-5) D = (-100,5)

You build an inequation from your rectangle edges :

if( (x,y) < AB && (x,y) > AC && (x,y) > CD && (x,y) < BD) then
    (x,y) belongs to rectangle ABCD
end if

If all inequations are true, then your point belongs to the rectangle

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Concrete example :

AB represent the segment but can be represented by a formula : y = ax + b

to determine a (the slope of the formula, not the point A) you get the difference of

(Ay - By) / (Ax - Bx) 

Ay means Y component of point A wich is 10 in that case

That formula gives us

(10 - 20) / (-130 - -100) = -10 / -30 = 1/3

Now we have

y = x/3 + b

We now determine b. We now that both point A and B belongs to that formula. So we take any of them to replace the x,y values in the formula. Let's take point B :

20 = -100/3 + b

We isolate b giving us :

b = -100 / 60 = -10/6

We have now

y = x/3 - (6/10)

So if we want to determine if Point Z (10, 15) belongs to your retangle, you check firstly if

y > x/3 - (10/6)

Then in the case of Z(10, 15) :

15 > 10/3 - (10/6)

15 > 10/6

15 > 1.66 is true

So condition is met for this edge. You need to this same logic for each edges.

Note that to determine if you use > or <, you need to tell if at a certain x value, our point has a bigger y or smaller y value than our rectangle edge.

You can use < and > if you want a point to be strictly inside the rectangle; <= and >= if a point on the rectangle's edge belongs to the rectangle too. You decide.

I hope that my explanation is clear. Feel free to ask more if some points are unclear.