c - find if 4 points on a plane form a rectangle?

Question

Can somebody please show me in C-style pseudocode how to write a function (represent the points however you like) that returns true if 4-points (args to the function) form a rectangle, and false otherwise?

I came up with a solution that first tries to find 2 distinct pairs of points with equal x-value, then does this for the y-axis. But the code is rather long. Just curious to see what others come up with.

Answer 1

• find the center of mass of corner points: cx=(x1+x2+x3+x4)/4, cy=(y1+y2+y3+y4)/4
• test if square of distances from center of mass to all 4 corners are equal

bool isRectangle(double x1, double y1,
                 double x2, double y2,
                 double x3, double y3,
                 double x4, double y4)
{
  double cx,cy;
  double dd1,dd2,dd3,dd4;

  cx=(x1+x2+x3+x4)/4;
  cy=(y1+y2+y3+y4)/4;

  dd1=sqr(cx-x1)+sqr(cy-y1);
  dd2=sqr(cx-x2)+sqr(cy-y2);
  dd3=sqr(cx-x3)+sqr(cy-y3);
  dd4=sqr(cx-x4)+sqr(cy-y4);
  return dd1==dd2 && dd1==dd3 && dd1==dd4;
}

(Of course in practice testing for equality of two floating point numbers a and b should be done with finite accuracy: e.g. abs(a-b) < 1E-6)