What kinds of curve and surface continuity can be achieved in Rhino?

Question

What will be an ideal response?

Answer 1

A way to describe the smoothness at the junction between two contiguous curves or surfaces is called continuity. Rhino 4 uses its proprietary G-Infinity blending technology to provide five kinds of continuity: G0, G1, G2, G3, and G4. G0 continuity is also known as positional continuity. At a G0 (positional) continuity joint, the end points of the curves or the edges of two surfaces simply coincide, having common control points. Their curvature radii and tangent directions at the common joint are different. G1 continuity is also known as tangent continuity. In a G1 continuity joint, the tangent directions of the control points at the end points of the curves or the edges of the surfaces are the same. However, their curvature radii are different. G2 continuity is also called curvature continuity. In a G2 continuity joint, the curvature radii and tangent directions of the control points at the end points of the curves or the edges of contiguous surfaces are the same. At a G3 continuity joint, the change of rate of curvature between contiguous curves/surfaces is constant, providing a much smoother joint than the G2 continuity joint. At a G3 continuity joint, the change of rate of curvature between contiguous curves/surfaces is constant, providing a much smoother joint than the G2 continuity joint. A G4 continuity joint is even smoother because the rate of change of the rate of change of curvature at the common end point/edge of contiguous curves/surfaces is constant. A G4 joint is so smooth that it can hardly be seen as separate curves/surfaces.