Curves in Surface:
Curvature creation is the most important part of 3D model creation. A good surface must have a good curve. In Image 1 the curves look identical when editing is turned off. The "Bad Curve" as seen has a multiple of click points to create it, but the "Good Curve" has only two points per curve, a start point and an end point, this curve is a 2-degree curve. The curve is edited by weight pulls at the end to create the shape, when both are analyzed we can see that the curve on the right is much better and has a clean flow when analyzed. A curve should have the least amount of information possible when creating it. In Alias which I prefer for complex surfacing it has a range between 2 thru 7 degree curvature. Some argue that 5 is better, while others state 7, but which is the best? I say the least as possible. Image 2 gives an example where a 7 degree curve may be applicable, it's constructed on several planes and in maneuvers through the x y z world thus it's a must to move from 2 to seven. There are three types of continuity that exist where two curves connect, G0, G1 and G3. Image 3 shows the three. (G0) no continuity (G1) Tangent (G2) Continuous curvature, you can't create Class-A surfaces without G2 curvature.