REM h8abbc.bas - jackord@kw.igs.net - 3 Nov 07 - BBC Basic v5.50b
      REM distant sphere moving perpendicular to the viewing direction
      REM   at relativistic speeds
      REM the co-ord system has x positive to the right, y positive downward,
      REM   and z positive going away from you
      REM the sphere is transparent with gridlines in blue on the near
      REM   hemisphere (z<=0), and in red on the far hemisphere (z>0)
      
      *FLOAT64
      INSTALL @lib$+"WINLIB5"
      
      REM Initialize Window
      b1% = FN_button("Plot", 90, 5, 50, 20, FN_setproc(PROCp1), 0)
      c1% = FN_combobox("", 5, 5, 80, 100, 0, 3)
      WindowWidth=360
      WindowHeight=280
      VDU 23,22,WindowWidth;WindowHeight;8,15,16,128
      SYS "SetWindowText", @hwnd%, "Relativistic Sphere"
      SYS "SendMessage", c1%, &143, 0, "v/c=0.0"
      SYS "SendMessage", c1%, &143, 1, "v/c=0.2"
      SYS "SendMessage", c1%, &143, 1, "v/c=0.4"
      SYS "SendMessage", c1%, &143, 1, "v/c=0.6"
      SYS "SendMessage", c1%, &143, 1, "v/c=0.8"
      SYS "SendMessage", c1%, &14E, 0, 0
      n=120: r=90: xo=360: yo=300
      OFF: VDU 5
      
      REPEAT
        WAIT 1
      UNTIL FALSE
      QUIT
      
      DEF PROCp1
      SYS "SendMessage", c1%, &147, 0, 0 TO ch1%   : REM Get velocity
      be=.2*ch1%: ga=1/SQR(1-be*be)                : REM Beta and Gamma
      CLS: GCOL 0: MOVE 40, 80
      PRINT "Sphere Moving to the Right at v/c="; be
      FOR i=1 TO 17                                : REM Latitude grid
        th=10*i*PI/180: rr=r*SIN(th)
        x=r*COS(th): y=rr: z=0
        xp=x/ga-be*z                               : REM Find x co-ord
        x1=xo+INT(2*xp): y1=yo-INT(2*y)
        GCOL 9: MOVE x1, y1
        FOR j=1 TO n
          IF j=n/2 THEN GCOL 12
          ph=3*j*PI/180
          y=rr*COS(ph): z=rr*SIN(ph)
          xp=x/ga-be*z                             : REM Find x co-ord
          x2=xo+INT(2*xp): y2=yo-INT(2*y)
          DRAW x2, y2
        NEXT j
      NEXT i
      GCOL 9
      FOR i=1 TO 36                                : REM Longitude grid
        IF i=18 THEN GCOL 12
        ph=10*i*PI/180
        x=-r: y=0: z=0
        xp=x/ga-be*z                               : REM Find x co-ord
        x1=xo+INT(2*xp): y1=yo-INT(2*y)
        MOVE x1, y1
        FOR j=1 TO n/2
          th=3*j*PI/180
          x=-r*COS(th): y=r*SIN(th)*COS(ph): z=r*SIN(th)*SIN(ph)
          xp=x/ga-be*z                             : REM Find x co-ord
          x2=xo+INT(2*xp): y2=yo-INT(2*y)
          DRAW x2, y2
        NEXT j
      NEXT i
      ENDPROC