I have had a number of people ask me what curvature continuity is. This is a brief explanation.
Curvature continuity is a method in measuring the surface quality. Curvature continuity is measured at curve/surface boundaries. If a curve is curvature continuous, it is regarded as being a C2 curve and a surface regarded as a G2 surface.
Curvature is defined as one over radius therfore C = 1/R. For each curve/surface the curvature discontinuity is measured as the ratio between C1:C2. If C1 does not equal C2, the curve/surface is not curvature continuous. In the real world it is impossible to maintain perfect curvature due to manufacturing limitations therefore a tolerance is typically introduced where any discontinuity inside the tolerance still defines the curve/surface as being curvature continuous.
In brief where the boundaries of two curves/surfaces are curvature continuous, the Radius at that boundary of the curve are equal.