G0 ; G1 ; G2 ???

 From:  Michael Gibson
290.7 In reply to 290.5 
> Thanks for the info. It's quite clear now (apart the terms "rate of change"
> in the explanation - from Rhino - for G3 and G4 which remain "obscure").

G3 and G4 do become increasingly more difficult, but I will try to tackle these here. Basically, when you see "rate of change", think of the tangent on a graph of something.

One common way to examine the curvature of a curve is by a "curvature graph". This is done by having a line stick out from the curve that shows the radius of curvature. Actually normally it shows the reciprocal (1/x) of the radius of curvature since it is nice to see magnified values in areas of tight curvature (where the radius actually is becoming smaller).

Here is an example:

Check out the indicated area - the curvature of each piece is equal there - there are actually two lines being displayed there, one for each side but it looks like one line because they have equal values. So the curve has a bend of the same radius at that point. That means it is G2.

But look at the curve formed by the outer points of those curvature hairs - if you imagine another curve going through those spots, it looks like it has a sharp kink in it right at that point. This is what determines G3 or not (which it is not in this case) - a G3 curve will have a curvature graph that is tangent continuous throughout with no kinks like that. G4 is a lot more difficult to show because typically there are not tools to display the additional calculated properties of that outside "curvature curve", but basically each "rate of change" means having a kink or lack of kinks in some additionally calculated curve.

G1 and G2 have some fairly distinct visual properties associated with them. However, by the time you get to G3 there is much, much less of a visually perceptive difference to that. Then G4 is extremely hard to detect. Basically G3 and G4 are used only by people who have an extreme obsession with the formation of reflection lines, most notably reflected lights off of a car body.

The other thing that is quite deceptive about these labels is that just because you have a G4 curve or surface does not in itself guarantee that you have a good quality overall curve or surface. For example you can have a G4 curve that has a bunch of little wiggles in it - G4 doesn't mean no wiggles in a curve, it means that two pieces are equal in "form" (tangent/curvature/etc) just at their juncture point.

These labels also don't measure how evenly curvature is distributed throughout a curve - in addition to wiggles, having curvature sort of "bunched up" in one area and then go through a rapid shift can be bad for quality, which the "G" measurement in itself won't tell you.

I'll handle the "degree" in an additional post, it is quite a bit by itself.

> but I think understanding what's "behing the engine" always permits a
> better understanding of the software and generally speaking why
> sometimes the results are not exactly what the user expected.

Certainly there are situations where it can help. But also I have been trying pretty hard to make it possible to run MoI successfully without having to know all of these specific technical details.

- Michael