While a 2D circle is parameterized by only three numbers (two for the center and one for the radius), in 3D six are needed. One set of parametric equations for the circle in 2D is given by
for a circle of radius and center .
In 3D, a parametric equation is
for a circle of radius , center , and normal vector ( is the cross product). Here, is any unit vector perpendicular to . Since there are an infinite number of vectors perpendicular to , using a parametrized is helpful. If the orientation is specified by a zenith angle and azimuth , then , , and can have simple forms:
The above notation follows a variable naming convention used in physics. Another convention labels the zenith angle and azimuth .