Difference between revisions of "3D Math - How accurate should a circle be?"

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(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…')
 
 
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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
31 sides 195 radius
+
* 40 sides 324 radius
32 sides 208 radius
+
* 50 sides 507 radius
33 sides 221 radius
+
* 60 sides 730 radius
34 sides 234 radius
+
* 70 sides 993 radius
35 sides 248 radius
+
* 80 sides 1300 radius
36 sides 263 radius
+
* 90 sides 1600 radius
37 sides 278 radius
+
* 100 sides 2000 radius
38 sides 293 radius
+
* 120 sides 2900 radius
39 sides 308 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 12:25, 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