【转帖】Tangent continuous

huangyhg

Tangent continuous is equivalent to G1 continuity. See https://en.wikipedia.org/wiki/Smoothness  subsection "Smoothness of curves and surfaces"
Per Y14.5.1, the local size spine is tangent-continuous and single-valued.
The local size spine was designed to correspond to the local size definition in Y14.5 section 2, not the one in section 5
  Tangent continuous = C0 continuous?
To be fair, the definition in section 5 isn't a bad definition, and the one in section 2 is a terrible definition, but the one in section 2 is the "official one"
  Tangent continuous isn't quite the same thing as C0 continuous
C0 continuous does not require the tangent to be continuous
Tangent continuous is also not the same thing as C1 continuous
  C1 continuous means the derivative is continuous and so it depends on the parametrization. Tangent continuous only depends on the points in the set, not how they are parametrized.
> So the tangent line has the same slope, independent of parameterization.

> Tangent continuous means two things
(1) the tangent direction (in 3D space) everywhere exists
(2) the tangent direction is the same from both directions, everywhere (no kinks in the spine)