What are NURBS.
NURBS stands for Non-Uniform Rational B-Splines.
Now B-Spline's were invented in the 70's for describing visually orders of curve and for modelling curved geometric models. As of yet NURBS are not use much in games due to patching issues especially when animating transformations of an object.(Note even polygon graphics had similar issues years ago)
Using NURBS and topology in order to deduce R-Axial graphics.
To Recap a Right Angle R-Axial represents the surface of a right angle slice of an N-sphere (note a 1-Sphere is a circle ect). (also Note the surface of an N-Sphere above a 1 Sphere is a non-euclidean shape)
The Idea here is to simplify the process of making 3D curved models.So for an object that works around one centre like say an oddly shaped rugby ball our 8 right angle sections will have an oval like distortion to each of the 8, 3D curved triangular sub sections but should still follow the logic of working with 8 R-Axial sub-sections. However an object like a cat would require more centres to describe, The main body, The centres of the feet and toes,a centre for the head,and some centres for the tail.
Using NURBS to calculate non square exponential's, logs and advanced functions of x.
In order to calculate an x position on a non-square function of x or F(x) accurately you will need 2 features. (1) the ability to have infinitive control points which have less or more impact on the curve as it approaches infinity. (2) you will especially for some very advanced non square functions of x require some deep Quantifiable over Infinitesimal algorithmics.