Difference between revisions of "3D Math - How accurate should a circle be?"
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SteveBaker (Talk | contribs) (Created page with ' 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 rad…') |
SteveBaker (Talk | contribs) |
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R = 1 / (1 - cos ( PI / numSides )) | R = 1 / (1 - cos ( PI / numSides )) | ||
− | 3 sides 2 radius | + | * 3 sides 2 radius |
− | 4 sides 3 radius | + | * 4 sides 3 radius |
− | 5 sides 5 radius | + | * 5 sides 5 radius |
− | 6 sides 7 radius | + | * 6 sides 7 radius |
− | 7 sides 10 radius | + | * 7 sides 10 radius |
− | 8 sides 13 radius | + | * 8 sides 13 radius |
− | 9 sides 17 radius | + | * 9 sides 17 radius |
− | 10 sides 20 radius | + | * 10 sides 20 radius |
− | 11 sides 25 radius | + | * 11 sides 25 radius |
− | 12 sides 29 radius | + | * 12 sides 29 radius |
− | 13 sides 34 radius | + | * 13 sides 34 radius |
− | 14 sides 40 radius | + | * 14 sides 40 radius |
− | 15 sides 46 radius | + | * 15 sides 46 radius |
− | 16 sides 52 radius | + | * 16 sides 52 radius |
− | 17 sides 59 radius | + | * 17 sides 59 radius |
− | 18 sides 66 radius | + | * 18 sides 66 radius |
− | 19 sides 73 radius | + | * 19 sides 73 radius |
− | 20 sides 81 radius | + | * 20 sides 81 radius |
− | 21 sides 90 radius | + | * 21 sides 90 radius |
− | 22 sides 98 radius | + | * 22 sides 98 radius |
− | 23 sides 107 radius | + | * 23 sides 107 radius |
− | 24 sides 117 radius | + | * 24 sides 117 radius |
− | 25 sides 127 radius | + | * 25 sides 127 radius |
− | 26 sides 137 radius | + | * 26 sides 137 radius |
− | 27 sides 148 radius | + | * 27 sides 148 radius |
− | 28 sides 159 radius | + | * 28 sides 159 radius |
− | 29 sides 171 radius | + | * 29 sides 171 radius |
− | 30 sides 183 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 | |
− | 40 sides 324 radius | + | * 160 sides 5200 radius |
− | 50 sides 507 radius | + | * 180 sides 6600 radius |
− | 60 sides 730 radius | + | * 200 sides 8100 radius |
− | 70 sides 993 radius | + | * 220 sides 9800 radius |
− | 80 sides 1300 radius | + | * 240 sides 11700 radius |
− | 90 sides 1600 radius | + | * 255 sides 13200 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 | + |
Latest revision as of 13:25, 1 September 2010
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