3D Math - How accurate should a circle be?

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If you want to draw an accurate circle using straight lines - how many do you need?

Assuming you'd like your line to lie within one pixel of the true edge, then the largest radius you can draw with an N-sided polygon is:

 R = 1 / (1 - cos ( PI / numSides ))
  • 3 sides 2 radius
  • 4 sides 3 radius
  • 5 sides 5 radius
  • 6 sides 7 radius
  • 7 sides 10 radius
  • 8 sides 13 radius
  • 9 sides 17 radius
  • 10 sides 20 radius
  • 11 sides 25 radius
  • 12 sides 29 radius
  • 13 sides 34 radius
  • 14 sides 40 radius
  • 15 sides 46 radius
  • 16 sides 52 radius
  • 17 sides 59 radius
  • 18 sides 66 radius
  • 19 sides 73 radius
  • 20 sides 81 radius
  • 21 sides 90 radius
  • 22 sides 98 radius
  • 23 sides 107 radius
  • 24 sides 117 radius
  • 25 sides 127 radius
  • 26 sides 137 radius
  • 27 sides 148 radius
  • 28 sides 159 radius
  • 29 sides 171 radius
  • 30 sides 183 radius
  • 40 sides 324 radius
  • 50 sides 507 radius
  • 60 sides 730 radius
  • 70 sides 993 radius
  • 80 sides 1300 radius
  • 90 sides 1600 radius
  • 100 sides 2000 radius
  • 120 sides 2900 radius
  • 140 sides 4000 radius
  • 160 sides 5200 radius
  • 180 sides 6600 radius
  • 200 sides 8100 radius
  • 220 sides 9800 radius
  • 240 sides 11700 radius
  • 255 sides 13200 radius