The term "curvature" ( in NX) is : a definition of "how much a curve or surface bends"
Curvature = 1/radius x Scale factor
i.e the inverse of the radius multiplied with a "suitable" scalefactor.
= when the radius is large, the curvature is small, a small radius has a large curvature, it "bends a lot".
The scale factor is used when , in NX , you are analyzing the curvature, to get a good display.
A line and an arc can be connected ( the endpoints touch) in two ways, either positional or positional and tangent, When tangent the direction vector in the endpoint of the line and the arc is the same.
"tangent".
In cad systems positional connected but non tangent is called G0. ( or C0 depending on how much Math you studied in school...)
connected and tangent is called G1. ( or C1)
But, the curvature in the line and the arc are not the same, they are not curvature continuous. to be curvature continuous G2 ( C2) the curvature ( the radius) in the endpoint-s must be the same.
a line and an arc can never be G2. To go G2 you must involve a transition in some way, imagine shortening the arc slightly and inserting a bridge curve in between, each end having the same radius as the line (=0) and the other end of the spline =r of the arc. then the 2 junctions will be G2. Curvature continuous.
In the same fashion there is G3 (C3) where the G0, G1, G2 are met, but you also match howthe curvature transitions from curve 1 to curve 2.
This can continue in G4 and G5 etc
I doubt that higher continuity than G3 is used any place.
Light reflected in a G1 sheet/solid body with multiple faces will show sharp breaks over the edges.
Light reflected in a G2 sheet/solid body with multiple faces will show smooth bends over the edges, but the bends can be very abrupt and unexpected.
Light reflected in a G3 sheet/solid body with multiple faces will not show where the edges are.
/Tomas