Timeline for How to determine the center and radius of a circle given some points in 3D?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2012 at 16:28 | history | edited | Mark McClure | CC BY-SA 3.0 |
Added a couple of comments.
|
| Dec 13, 2012 at 15:15 | comment | added | whuber | Just a stray thought--it could be amusing to formulate a Quaternion-based answer. In $\mathbb{R}^3$ that might lead to the most efficient possible computations. | |
| Dec 13, 2012 at 15:11 | comment | added | Mark McClure | @whuber Thanks! My answer is, admittedly, very much three dimensional - but somehow R^3 has a strange way of popping up naturally. :) Later, I'll have to think some on your answer. | |
| Dec 13, 2012 at 15:04 | comment | added | whuber | (+1) Very much better, far more than anyone had a right to expect. At one point you raise an implicit challenge, asking why it is any better to be working in a plane. My answer to that is twofold. First, conceptually this is a plane problem, so the details of the ambient space are just an irrelevant nuisance. (Not much of one in $\mathbb{R}^3$, but how would you generalize your answer to circles in $\mathbb{R}^{17}$, say?) The second is computational and conceptual: methods based on the cross ratio have a deeper connection to projective geometry and may be computationally simpler. | |
| Dec 13, 2012 at 14:25 | history | edited | Mark McClure | CC BY-SA 3.0 |
added 399 characters in body
|
| Dec 13, 2012 at 14:15 | history | edited | Mark McClure | CC BY-SA 3.0 |
added 1050 characters in body
|
| Dec 13, 2012 at 13:56 | history | edited | Mark McClure | CC BY-SA 3.0 |
added 1050 characters in body
|
| Dec 13, 2012 at 13:51 | history | edited | Mark McClure | CC BY-SA 3.0 |
added 1050 characters in body
|
| Dec 13, 2012 at 5:15 | comment | added | Mark McClure | @whuber Is that any better? | |
| Dec 13, 2012 at 5:15 | comment | added | Mark McClure | @RedPotatoe I made some pretty major changes. Does that help? | |
| Dec 13, 2012 at 5:14 | history | edited | Mark McClure | CC BY-SA 3.0 |
added 1050 characters in body
|
| Dec 12, 2012 at 21:22 | comment | added | RedPotatoe | @whuber Is there any way you could help me get my original problem back to a 2D problem? | |
| Dec 12, 2012 at 21:18 | comment | added | whuber | Fair enough: My comment was intended as a (perhaps too subtle) suggestion that your answer would be better for making that point explicit and showing just how the check would be carried out. You will also find that your solution fails in special circumstances, such as where points are coincident or collinear or where coordinates are subject to floating point imprecision. | |
| Dec 12, 2012 at 21:08 | history | edited | Mark McClure | CC BY-SA 3.0 |
added 164 characters in body
|
| Dec 12, 2012 at 21:07 | comment | added | whuber | If you check first three points and next three other points, they could lie on two separate circles. So you have provided necessary but insufficient conditions. | |
| Dec 12, 2012 at 21:02 | history | answered | Mark McClure | CC BY-SA 3.0 |