'* fxy.bas - graphs f(x,y)
'*
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'* Qbasic Developer
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DEFSNG A-Z

CONST xmin = -2
CONST xmax = 2

CONST ymin = -2
CONST ymax = 2

CONST xres = 10
CONST yres = 10

CONST u = 640
CONST v = 480

COMMON SHARED zx, zy

DECLARE FUNCTION f! (x AS SINGLE, y AS SINGLE)
DECLARE SUB Axis ()
DECLARE SUB Graph ()
DECLARE SUB Zvector (x!, y!)

SCREEN 12

   WINDOW (xmin, ymin)-(xmax, ymax)
   Axis
   Graph

END

SUB Axis

LINE (-1 / SQR(2), -1 / SQR(2))-(1 / SQR(2), 1 / SQR(2)), 1
LINE (1, 0)-(-1, 0), 1
LINE (0, 1)-(0, 0), 1

END SUB

FUNCTION f (x AS SINGLE, y AS SINGLE)

   IF (1 - x ^ 2 - y ^ 2) < 0 THEN
      f = 0
   ELSE
      f = SQR(1 - x ^ 2 - y ^ 2)
   END IF

END FUNCTION

SUB Graph

DEFSNG A-Z

   dx = (xmax - xmin) / u * xres
   dy = (ymax - ymin) / v * yres

   x = xmin
   DO WHILE x < xmax
      y = ymin
      DO WHILE y < ymax
         Zvector x, y
         CIRCLE (zx, zy), .001, 2    'plot point
         y = y + dy
      LOOP
      x = x + dx
   LOOP

END SUB

SUB Zvector (x, y)

   z = f(x, y)
  
   IF z <> 999 THEN              ' map 3-d vector into 2-d if it exists
      zx = x * -1 / SQR(2) + y
      zy = x * -1 / SQR(2) + z
   ELSE
      zx = 999
      zy = 999
   END IF

END SUB