Geometric continuity
Part 1 Curve continuity
<Quote: Rhinoceros Help>
Position (G0)
The end points of curves share the xyz coordinate.the curves are position continuous (G0) at the ends.
Tangent (G1)
Tangency measures position and curve direction at the ends. The direction is determined by the first and second point on each curve. If these all fall on a line then two curves are tangent (G1) at the ends. Curves and surfaces with G1 continuity are also G0 continuous.
Curvature (G2)
Curvature continuity between two curves measures position, direction, and radius of curvature at the ends. If the radius of curvature is the same at the common end point, curves are curvature continuous (G2). This condition is not easy to determine by just looking at where the points are located. Curves and surfaces with G2 continuity are also G1 and therefore G0 continuous.
Tools for testing continuity
GCon: You can use ‘Gcon’ command to analyzes the geometric continuity between two curves.
Curve Analysis(Curvature Graph On):This can be used to analyzes the continuity of polycurve.
The curvature graph changes from one value to a different value. (G1/Tangent)
No jumps in the curvature graph.The curvature graph of the first segment connects end-to-end with the curvature graph of the second segment. (G2/curvature continuous)
(Perhaps it can be used to manually adjust the geometric continuity between two curves)
Part 2 Surface continuity
1) Surfaces share a common edge but the adjoining faces are not smooth or continuous(G0 continuous).
2) Share a common edge and the adjoining faces are tangent(G1 continuous).
3) Surfaces share a common edge and the adjoining faces are curvature continuous(G2 continuous).
Tools for testing continuity
Zebra: You can use ‘Zebra’ command to analyzes the geometric continuity.
Position Only (G0)
If the stripes have kinks or jump sideways as they cross the connection from one surface to the next, the surfaces touch, but have a kink or crease at the point where the zebra stripes jag. This indicates G0 (position only) continuity between the surfaces.
Tangent matches; curvature does not match (G1)
If the stripes line up as they cross the connection but turn sharply at the connection, the position and tangency between the surfaces match. This indicates G1 (position + tangency) continuity between the surfaces. Surfaces that are connected with the FilletSrf command display this behavior.
Position, curvature, and tangency match (G2)
If the stripes match and continue smoothly over the connection, this means that the position, tangency, and curvature between the surfaces match. This matching indicates G2 (position + tangency + curvature) continuity between the surfaces. Surfaces connected with the BlendSrf, MatchSrf, or NetworkSrf commands display this behavior. When you use surface edges as part of the curve network, the NetworkSrf options allow any of these connections.