circle in 3d space?

2009-04-27 10:14 pm
有冇circle in 3d space equation. 即是他們的坐標是用(x,y,z). 如有, 是否用三點也可找出center. 另外如用十點又能否找出center. 請問如何運算? 可否詳列 一吓!
更新1:

我最想知是能否用三點以上的三維坐標, 找出一個不是平放的圓柱體的圓心. thx!!!!

更新2:

唔知可有人懂用矩陣法以三點以上的坐標求出圓心呢?

回答 (2)

2009-04-28 11:23 pm
✔ 最佳答案
Example of an equation of a circle in 3D:

x^2 + y^2 + z^2 = 81 and
5x - 4y + z + 3 =0

Since it can be transformed to a cicle in a 2D plane, just 3 points on the circle is enough to determine the centre as well as the radius.

e.g.
Given (1, 4, 8), (3, 6, 6), (4, 4, -7) on the above circle, by finding the intersection of the perpendicular bisectors(planes) of any two distinct line segments joining any two points and the plane contains the given 3 points, it can be found that the centre is (-5/14, 2/7, -1/14), and hence the radius is √(15834)/14.
2009-04-28 1:48 am
3點連成一個三角形
任何三角形一定可以形成一個circle
只要用三條邊ge perpendicular bisector 就ok啦
第二條就可能唔得
但我唔識
幫你唔到


收錄日期: 2021-04-29 19:16:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090427000051KK00664

檢視 Wayback Machine 備份