Curvature displays interpretation

[jeffescott]

Firstly I am unclear as to the precise definition used for a curvature display.

Secondly I am very clear that I desire a smooth curve which would mean very low ''curvature''

Thirdly pls take a look at the screenshot.

It shows a curve made from a fit point and another curve from a control point.  i have tried to make them very similar curves.

Yet the fit point curve shows way more ''curvature'' than the control point.

The fit point curve ends abruptly at a horizontal tangent at each end (only front half of ski)

The control point ends at an intersection with the x axis so I can accept that the curvature of the fit point is affected by this.

However i did not expect the massive difference in curvature????

[jeffescott]

I understand curvature is mathematical defined as the rate of change of the unit tangent vector in rads/s. (wiki).

This would mean that the curvature should decrease as the curve gets "flatter" ie as it approaches the tangent end......

This is not the case; visually the fit point curve does get flatter as it approaches the tangent end.

Yet the curvature increases drastically.

What is going on???

[TrippyLighting · Accepted solution]

The Autodesk Alias Theory Builders have a very good explanation (IMHO):

The video below also explains a lot of these concepts:

[jeffescott]

Well that was a big help

[jeffescott]

I still have a question that i can't seem to find an answer for:

In the attached file I have two curves a small radius arc (ski tip) and a gentle sloping curve (ski side cut)

I have toggled the curvature comb and set the scales of each to 1.

My dilemma is the curvature comb for the ski tip is much lower than the gentle curve it is attached to....why

Is it because the scale is based on a the length of the arc rather the the absolute curvature....I dont thinks so because in a g2 spline the curvature combs end up equal and the intersection.

[jeffescott]

I take that back the g2 specification does not result in the curvature comb being equal in size....therefore scale shown in the curvature display must be normalized somehow for each curve ???

[TrippyLighting]

Not sure the scale on sketch curve matters.

Extrude a surface, pre-select the two resulting edges on one side of the surface and use the Curvature Analysis tool in the Inspect meu, or the IsoCurve analysis tool.

I am not sure why this would matter for your application. I am assuming that you'll sand pieces at some point in the manufacturing process and in that case even normal tangency would likely be fine.

[jeffescott]

yeah it only matters cause you have to bend the steel edges....and that particular point allows gives me grief

Also still trying to understand....yeah i think the curvature analysis is normalized scale based on length off line.

G2 appears to make the slope handles aligned