Mesh curvature lines

[Petras_Vestartas]

Hi,

Is there any rhino method or plugin that allows to extract mesh curvature lines?

I know existing methods for nurbs surfaces, but not any mesh method.

[zhuangjia777]

I guess a mesh doesn’t have any curvature.

[Petras_Vestartas]

You are wrong, because mesh have discrete curvature.
I created this plugin a while ago: https://www.food4rhino.com/app/mesh-curvature

But principal curvature is what I am asking for.

[stefan.schmaelzle]

You mean to extract principal curvature directions? There is a lot of research on mesh curvature estimations. Can you post an example mesh?
Next step is then to ‘integrate’ the locally defined pcd into curves on mesh?

[zhuangjia777]

I don’t think anyone can find a general method for calculate principal curvature of mesh. Because principal curvature is production of curvatures of two tangent planes perpendicular to each other across the measure point on a surface. Nurbs’ U and V directions are always perpendicular to each other, thus a nurbs surface is easy to calculate its principal curvatures through a surface point. But mesh’s topology is much more variety. For triangle face mesh, there is no two certain tangent planes perpendicular to each other which you can possibly locate.

I think of one way to calculate principal curvature is to convert mesh to nurbs.

[Petras1 (Petras Vestartas)]

Milipede has mesh principal curvature component. They are not continuous as in nurbs, but is something what I was searching for.

[davidcockey]

A mesh by itself does not have implicitly have curvature. A mesh can be interperted as representing a smooth surface which does have curvature, and the curvature of such a surface might be considered as the curvature of the mesh. There are multiple ways to create a surface from a mesh. One method would be to use Sub-D.

@zhuangjia777

Because principal curvature is production of curvatures of two tangent planes perpendicular to each other across the measure point on a surface.

Where did you find that definition of principal curvature? I do not think it is correct.

@zhuangjia777

Nurbs’ U and V directions are always perpendicular to each other, thus a nurbs surface is easy to calculate its principal curvatures through a surface point.

Incorrect. The U and V directions of NURBS surfaces are not always perpendicular to each other. Example:Isocurve directions.3dm (61.5 KB)

[RIL (Rolf)]

Starting from the idea for principal curvature spots (pcs) as posted & illustrated by @DanielPiker a while ago, it should be possible to postprocess them by putting together strings of such pcs (seaching for them tangentially) and then draw (poly)lines between them, smoothing/straighten them out a bit, (keeping them on the surface) and… well, I should be possible.

Principal curvature approximation on meshes

[crvtr3] At the weekend I was looking at this paper The curvature line parametrization from circular nets on a surface, by Bobenko and Tsarev …and they describe what I thought was an interesting purely geometric construction for finding principal curvature directions on a mesh. I tried it out in Grasshopper, and it seems to work fairly well. I’m just sharing it here in case it is of use or interest to anyone else. It may not be the fastest or most robust method for doing this, but I though…

// Rolf

[seulfc110]

Hi, Petras
Could you please tell me how to extract the curvature lines from urbs surfaces? Thank you very much!

[marteen.petrov]

Hi
You can use Dodo’s Integrate Curvature Field

[Petras_Vestartas]

Hi,

For nurbs follow this thread https://www.grasshopper3d.com/forum/topics/principal-curvature-lines-on?overrideMobileRedirect=1

[Petras_Vestartas]

Thanks I will try to use it:)

[seulfc110]

Thanks a lot

[seulfc110]

Thanks very much