[dpuch]

I was feeling like making something fun, and this looked like it.

I stole the original code from EMC's wiki but then modified it slightly to run on fanuc controls, and added roughing passes. I only had a stub ball mill, so the roughing lets you specify a max cutter engagement depth for each pass. There are lots more ways to clean it up an add more features.

%
O0070  (BALL IN CUBE)
(CENTER TOP OF CUBE IS XYZ ZERO)
#1=1.5 (SIZE OF BOX AND DIAMETER OF FINISHED BALL)
#2=0.0625 (BALL MILL CUTTER RADIUS)
#3=0.125 (SIZE OF BOX BARS)
#4=5.0 (DEGREES OF STEPOVER RESOLUSION AT THE CORNERS)
#5=#4 (STEPOVER COUNTER)
#6=[[#1/2]+#2] (ACTUAL CUTTER PATH RADIUS OF SPHERE -- CUTTER RADIUS + RADIUS)
(#6 ALSO MINIMUM TOOL FLUTES REQUIRED FOR FULL SPHERE)
#7=5.0 (FEED RATE)
#10=2.0 ( > 1 EQUALS A ROUGH PASS AT #10*#4 STEPOVER)
IF [#10 LT 1.0] THEN #10=1.0 (SAFTEY CHECK - KEEP #10 >= 1.0)
#11=0.05 (ROUGH PASS MATERIAL TO LEAVE IN Z)
#12=0.17 (MAX Z DEPTH PER ROUGH PASS)
#13=FUP[[#6-#11]/#12] (ROUGH PASSES TO TAKE)
#14=[#6-#11]/#13 (Z PER ROUGH PASS)
#15=#11+#14*#13 (SET ROUGHPASS Z OFFSET)

G90 G57 G0 X0 Y0 M3 S4000
(G43 Z1.0 H1)
Z0.1

N0010
   IF [#10 LE 1.0] THEN #15=0 (FINISH Z LEVEL)
   #8 = [[SIN[#5*#10]*#6]*SIN[45]] ( X AND Y ARC START POSISION)
   #9 = [0-[[1-COS[#5*#10]]*#6]]+#15 (ARC Z START HIGHT)
   IF [#8 LT [#1/2-#2-#3]] GOTO 20
   #8 = [#1/2-#2-#3]  (SET LAST PASS AT FINISHED BAR SIZE)
   #9 = 0-[#6 - SQRT[#6*#6 - [#8*#8+#8*#8]]]+#15
   N0020
   IF [#9 GT 0] GOTO 15 (WOULD ONLY CUT AIR, STILL ABOVE Z0)
   G1X[#8]Y[#8] F#7
   Z[#9] F[#7/3]
   G18 G02 X[0-#8]Z[#9]I[0-#8]K[0-[#9+[#6]]] F[#7]
   G19 G03 Y[0-#8]Z[#9]J[0-#8]K[0-[#9+[#6]]]
   G18 G03 X[#8]Z[#9]I[#8]K[0-[#9+[#6]]]
   G19 G02 Y[#8]Z[#9]J[#8]K[0-[#9+[#6]]]
   N0015
   #5=[#5+#4]
IF [#8 LT [#1/2-#2-#3]] GOTO 10

#5=#4 (RESET STEPOVER COUNTER FOR NEXT ROUGH-FINISH PASS) 
G0 Z0.1 
X0 Y0

IF [#10 LE 1.0] GOTO 9000 (DONE)
#13=#13-1.0 (STEP DOWN Z RIOUGHING PASS)
IF [#13 LT 0] GOTO 100 (ROUGHING DONE)
#15=#11+#14*#13 (STARTING ROUGHPASS Z OFFSET)
GOTO 10
N0100
#10=1.0
GOTO 10

N9000
G0 Z1.0
M9
M5
M30
%

I made the mistake of trying to cut the 6th side while just grabbing the sides of the ball :/ It is cut free at least, just not a full sphere.