How can we write a circle equation (in 3D) with the know values of circle radius, center position in 3D, and the normal vector that is perpendicular to the plane that circle is lying on? Thanks in advance.
Asked
Active
Viewed 49 times
1 Answers
0
$$((\vec p-\vec c)^2-r^2)^2+(\vec n(\vec p-\vec c))^2=0$$
or
$$\vec p=\vec a\cos\theta+\vec b\sin\theta+\vec c$$
where
$$\vec a=r\frac{\vec n\times\vec m}{\|\vec n\times\vec m\|},\vec b=r\frac{\vec a\times\vec n}{\|\vec a\times\vec n\|}$$ and $\vec m$ is an arbitrary vector not parallel to $\vec n$.