Spheres , Spherical Coordinates and Circles

[markraz]

Hi, iI need to draw a circle in 3D. Is it possible to calculate the equation of a 3D circle given its radius, center and its normal vector?
If I knew the circle normal (red in pic) based on spherical coordinates, would that be one way to do it?
could I use a nomral and a sphere equation to calculate the circle? or is their a better way to do it?
Thanks in advance

 

[HallsofIvy]

The sphere would be a good start. Then I would use the given center of the circle and the given normal vector to find the equation of the plane it is in. The circle is the intersection of the sphere and the plane.

 

[Steven G]

...Is it possible to calculate the equation of a 3D circle. A 3D circle is a sphere. I think that you meant you mean to say that you want to calculate the equation of a circle in 3D. Personally I would have said I want to calculate the equation of a circle in space.

 

[Romsek]

I would write the unit sphere as a parametric equation and apply translation, scaling, and rotation matrices to get the proper sized sphere placed where you want it with the proper orientation.

https://en.wikipedia.org/wiki/Transformation_matrix

 

[markraz]

Thanks guys, Ok makes sense using a sphere and plane. In my case the plane will always pass through the center of the sphere. So I guess my question now is, how do I find this equation of the circle? and will I be able to find all the points on the circle? is there a standard equation/way to do a sphere plane intersection and get the resulting circle equation?

thanks again