How can the weight of a NURBS curve/surface be calculated such that corners are exactly circular? It has something to do with the angle of the corner, but that doesn't seem to be displayed anywhere.
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I'm not absolutely certain this pertains, but it may not be possible. NURBS cannot be used to represent a circle exactly, but may only be used to create an approximation, however close. You may want to refer to https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline for more information (especially the note in the section titled: Example: a circle).
Of course, this is a good answer if you are attempting to make a full circle. If your goal, however, is to make an exactly circular join between two perpendicular segments, it may or may not be possible.
Then again, as blender is typically used to generate imagery with a finite sample size (i.e. pixels) it may be possible that the rendering of the NURBS approximation of a circle would be sufficiently accurate so as to be indistinguishable from an actual mathematically precise circle.
Hope this helps.
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$\begingroup$ Well as close as possible is sufficient, perfect circles are finitely impossible because as far as is known π is infinite. NURBS curves can be made very close to circular regardless of the angle between the segments. So based on that angle there must be a formula to calculate what the weight must be of the vertices? $\endgroup$ Commented Oct 2, 2015 at 16:24