[Algorithms] C1 vs G1 (Was: "N-Patches")

[Tony C. <to...@mi...>]

>As for G1 vs. C1, G1 means that the tangents of the two connecting
>patches are identical.  C1 means that the parametric velocities of
>the two connecting patches are identical.  eg. if you had a particle
>flying along a bezier curve at a constant speed in parametric
>coordinates, then it would keep going the same direction at a G1
>joint, but it would suddenly change speed (which it wouldn't do with
>C1).  G1 or G2 is really what we care about for graphics, C1 and C2
>are unecessarily strong constraints.

So, if I have this right:

Define g(x) = f(x)/|f(x)| for all |f(x)| != 0

Then g C0 continuous at y => f is G0 at y?

What would you call that property, i.e. if C0 == "continuous", what is G0?

Tony Cox - DirectX Luminary
Windows Gaming Developer Relations Group
http://msdn.microsoft.com/directx