Check if point belongs to square

Question

I want to check if a point P(x1,y1) belongs , is inside , a square with center C(x,y) and horizontal diagonal r.

• Square with the above characteristics:

• Function that calculates the distance between two points

  float calculate_distance (float x1,float y1,float x2 ,float y2)
  {
    float distance;
    float distance_x = x1-x2;
    float distance_y = y1- y2;
    distance = sqrt( (distance_x * distance_x) + (distance_y * distance_y));
    return distance;
  } 
  

Answer 1

You don't need the Euclidian distance between points here.

Just as for a circle (at the origin) you know that x²+y² is some constant (r²), here you know that |x|+|y| is some constant (r again), which is even simpler. Actually you can interpolate between these shapes by using exponents between 1 and 2.

So to check whether a point (x,y) is inside the diamond (which without loss of generality can be assumed to be centered on the origin), just test

fabsf(x)+fabsf(y) <= r