Principal curvature lines on surfaces: need some advice please

Hi,

To generate a grid structure based on a surface, I wanted to determine the principal curvature lines in a UV-point. This seems more complex than it sounds. Though, there is a Principal curvature component in GH, and it outputs the two values for the principal curvature in that point, and the two orthogonal directions. But how to construct a curve based on that data?

Anyone willing to share some experience?

I've included a snapshot of the (simple) definition generating a hypar, and a UV-point on that surface.

Also you can find the ghx attached

Thanks!

Niels

more info:

http://en.wikipedia.org/wiki/Principal_curvature

Attachments:

How to draw the principal curvature lines on a surface.pdf, 155 KB
Principal Curvature Test.ghx, 187 KB

Replies to This Discussion

Permalink Reply by Chris Tietjen on February 9, 2011 at 8:46am

There's some redundancy of components that could be eliminated.

Chris

Attachments:

Principal Curvatures.ghx, 215 KB

Permalink Reply by Niels De Temmerman on February 9, 2011 at 9:06am

Thank you Chris,

I've connected your definition to my surface and my point definition, and it shows two curves, as an intersection of the planes you defined with the base surface. This is indeed in that specific point, the principal curvature direction (min and max).

But the difficulty remains: how to construct or calculate the Principal Curvature Lines through that point. Maybe this cannot be solved in GH, but it should be obtained by solving a differential equation, perhaps, iteratively?

I think I am stuck...

Niels

Attachments:

Chris.pdf, 151 KB

Permalink Reply by Chris Tietjen on February 9, 2011 at 9:55am

Is this what you're looking for?

Chris

Attachments:

Principal Curvatures2.ghx, 308 KB

Permalink Reply by Chris Tietjen on February 9, 2011 at 10:18am

Sorry, I've been completely misunderstanding what you're looking for (and there's an osculating circle component in any case). I tried to do this once (that is create the curve of principal curvatures) but had no luck with it at all.

http://mathworld.wolfram.com/LineofCurvature.html

Chris

Permalink Reply by Evert Amador on February 9, 2011 at 10:32am

Hi Niels,

How about using Chris' approach as above, then get a line from the sample point to the circle, rotate this line 90 degrees over a plane built with 3 quadrants of the circle and move this rotated line to the sample point.

The first derivative at that point would give you the slope of the tangent line to the surface curvature, but you will still need a reference plan to draw it onto.

I hope it helps

Cheers

Evert