How can I determine ideal NURBS surface control points for a multi-patch sphere?

Trending 2 months ago

I would for illustration to cognize really to "parameterize" nan power points for nan 6 faces of nan commonly utilized NURBS mutli-patch sphere ("Cobb sphere"), for an arbitrary-size power constituent grid. Ideally pinch grade 3 and azygous knot vectors.

For example, fixed a 6x6 grid, wherever would I spot nan power points and really would I weight them successful bid to execute cleanable curvature? Then, widen this to a 5x5 grid, 7x7, 10x10, etc. I person seen this done pinch 2D circles/arcs, and I cognize rational/non-one weights are astir apt needed, but I can't find a bully method.

I asked a similar question successful Mathematics Exchange, but it was possibly excessively verbose aliases amended suited for here, and did not person immoderate feedback. Thanks successful beforehand for immoderate proposal aliases guidance personification could provide.

Edit: I tried retired nan points suggested by personification Reynolds from nan Dedoncker et al paper, but nan tiles don't perfectly fresh a sphere. Adding an image showing immoderate of my evaluations of those points successful a fewer different platforms: enter image explanation here The insubstantial mentions nan CVs were implemented successful Octave (albeit, scaled aliases different modified), and so I had really seen them earlier successful Octave during erstwhile searches. They're called "NURBS", but now erstwhile I export nan CVs (although, called "coefs" here...) and measure them pinch my Python NURBS functions, they do not lucifer nan Octave plot. Maybe they are really Bézier? I judge I request to person these from Bézier to NURBS but I don't wholly understand that process, and yet I request to activity pinch NURBS.