Very Computer

1. Help finding square from diagonal corners

I've worked out an algorithm for calculating the remaining corners of a square
when two diagonal corners are known.  It seems overly complicated to me and I
was hoping if I posted it here someone might be able to advise me on how to
simplify it (or maybe point me to some resources that will aid me).  If it
isn't evident I'm not well-practiced in the areas of geometry or computer
graphics, so be gentle.  After I had some idea of what I needed to do I pretty
much filled out the algorithm through trial and error.

Sorry if it is too hard to read.  I tried my best.

Joel Moore

------------------------
dl = Diagonal Length
sl = Side Length
da = Diagonal Angle
fk = First Known Corner
sk = Second Known Corner
fc = First Calculated Corner
sc = Second Calculated Corner
-------------------------------------------------
dl = SquareRoot((fk.x - sk.x)^2 +
                    (fk.y - sk.y)^2)
sl = Cos(PI/4) * dl

IF (fk.x EQUALS sk.x)
  IF (fk.y IS LESS THAN sk.y)
    da = 0.5*PI (diagonal lies on +Y axis)
  ELSE
    da = 1.5*PI (diagonal lies on -Y axis) (8)
  END IF
ELSE IF (fk.y EQUALS sk.y)
  IF (fk.x IS LESS THAN sk.x)
    da = 0 (diagonal lies on +X axis) (5)
  ELSE
    da = PI (diagonal lies on -X axis) (7)
  END IF
ELSE
  IF (fk.x IS LESS THAN sk.x)
    IF (fk.y IS LESS THAN sk.y)
      da = ArcTan((fk.x - sk.x)/(fk.y - sk.y))
      (diagonal lies in Quadrant 1)
    ELSE
        da = (2 * PI) + ArcTan((fk.x - sk.x) / (fk.y - sk.y))
        (diagonal lies in Quadrant 4)
    END IF
  ELSE
    IF (fk.y IS LESS THAN sk.y)
      da = PI + ArcTan((fk.x - sk.x) / (fk.y - sk.y))
      (diagonal lies in Quadrant 2)
    ELSE
      da = PI + ArcTan((fk.x - sk.x) / (fk.y - sk.y))
      (diagonal lies in Quadrant 3)
    END IF
  END IF
END IF

IF (Diagonal lies in Quadrant 1 or 3) THEN
  fc.x = fk.x - Cos(da + (PI / 4)) * sl
  fc.y = fk.y + Sin(da + (PI / 4)) * sl
  sc.x = fk.x + Cos(da - (PI / 4)) * sl
  sc.y = fk.y - Sin(da - (PI / 4)) * sl
ELSE IF (Diagonal lies in Quadrant 2 or 4) THEN
  fc.x = fk.x + Cos(da + (PI / 4)) * sl
  fc.y = fk.y - Sin(da + (PI / 4)) * sl
  sc.x = fk.x - Cos(da - (PI / 4)) * sl
  sc.y = fk.y + Sin(da - (PI / 4)) * sl
ELSE IF (Diagonal lies on +X, +Y, or -Y axis) THEN
  fc.x = fk.x + Cos(da + (PI / 4)) * sl
  fc.y = fk.y + Sin(da + (PI / 4)) * sl
  sc.x = fk.x + Cos(da - (PI / 4)) * sl
  sc.y = fk.y + Sin(da - (PI / 4)) * sl
ELSE IF (Diagonal lies on -X Axis) THEN
  fc.x = fk.x + Cos(da + (PI / 4)) * sl
  fc.y = fk.y + Sin(da + (PI / 4)) * sl
  sc.x = fk.x + Cos(da - (PI / 4)) * sl
  sc.y = fk.y - Sin(da - (PI / 4)) * sl
END IF

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