To extend to the next level of motional complexity above the isotropic cone models, an anisotropic cone can be modelled. This cone is defined via the ball and socket joint pivoted mechanics with an angular restriction in all three angles. The simplest anisotropic distribution would be to create an ellipse using the standard quadric surface formula for an elliptic cone
+  = 0.  (16.38) 
Let the two cone opening halfangles of the ellipse be θ_{x} and θ_{y}. For a sphere of radius z = 1 and using the tilt angles θ and φ, a boundary polar angle θ_{max} can be modelled as
As the quadric constants a, b and c are angles rather than axis lengths, this is not a true ellipse. It will therefore instead be called a pseudoellipse. The form of this pseudoelliptic cone is shown in figure 16.13.

The model consists of the average domain position, a single pivot point, the full motional eigenframe, and the maximum cone opening and torsion halfangles
where P_{i} are the average domain position translations and rotations, E_{i} are the Euler angles defining the motional eigenframe, p_{i} are the coordinates of the pivot point, θ_{x} and θ_{y} are the maximum cone opening halfangles, and σ_{max} is the torsion halfangle.
The relax user manual (PDF), created 20190308.