G0, G1, G2, and G3 are continuous ways of describing curved surfaces and curves, and the degree of smoothness is generally used to judge the surface quality when repairing a curved surface.
G0-point continuous: refers to the continuous point of the curved surface or curve. The curve has no breakpoints, and there is no crack at the junction of the curved surfaces.
Judgment method: the curve is continuous, but there are corners; the curved surface has no holes or cracks, but there are lumps.
Mathematical explanation: The intersection of a curve or any plane with the surface is continuous.
G1-Tangent continuous: refers to the continuous surface or curve points, and all connected line segments and surface pieces are in a tangent relationship.
Judgment method: the curve is continuous, smooth and without sharp corners; the curved surface is continuous, and there is no corner.
Mathematical explanation: The intersection of a curve or any plane and the surface is continuous, and the first derivative is continuous.
G2-Curvature continuity: It means that the curved surface or the point of the curve is continuous, and the result of the curvature analysis is continuous change.
Judgment method: analyze the curvature of the curve, and the curvature curve is continuous without breakpoints. Perform zebra crossing analysis on the plane, all zebra crossings are smooth and have no sharp corners.
G3-Curvature tangent continuous: refers to the continuous surface or curve points, and the curvature curve or curvature surface analysis result is tangent continuous.
Judgment method: analyze the curvature of the curve, the curvature curve is continuous, and smooth without sharp corners. Because there is less continuous use of G3, I don't know any better G3 surface determination method, please add it.
Mathematical explanation: The intersection of a curve or any plane and the surface is continuous, and the third derivative is continuous.
