Minimal Surfaces using Nurbs

Hi,

I would like to ask how to model minimal surface within this box frame, so that the continuity is good and boundary edge is within the box?

On the left you see 6 surfaces, but it is not continuous and on the right side is a simple patch, which results in more or less good continuity but the edge is bad (not linear).

In meshes I can find more or less minimal surface by smooth, but how to do this with nurbs:

Hello - Adjust the analysis mesh to use maybe 5000 minimum initial grid quads before judging too harshly…

-Pascal

This is adjusted, the problem is that one is continuous and on the left it has hard edges:
Any idea how to solve it?

Hello - can you please post the objects?

-Pascal

Sorry I forgot, here it is:

Models.3dm (1.7 MB)

Hello - the mesh setting will not help if the object is a mesh… but looking at the patch surface, I see the expected internal continuity:

image

The multi-surface version is tangent (corners in the Zebra stripes) but not curvature continuous.

image

-Pascal

Yup the continuity is a question.

I am wondering if this can be modeled, or the only way is to do it mathematically - such as Enneper Surface in LunchBox?

If you make the surface from 6 mesh quads, make extra copies around the periodic boundaries, convert to SubD, then convert that SubD to NURBS and select an interior patch which is not affected by the naked boundary, you get something pretty smooth, and continuous across the periodic boundaries.
Continuity is not absolutely perfect at the interior 6-valent vertex, but that’s what you get with the Catmull-Clark limit surface.


Positioning the control points with the standard parametric equations (as eg in Lunchbox) doesn’t actually solve the question of how to make a continuous and exact NURBS minimal surface either though - the resulting surface is only an approximation of a minimal one, since the equation is for the points on the minimal surface, and the NURBS surface does not interpolate these points.

Interestingly the quad mesh to NURBS converter in MoI does somehow manage to get what appears to be perfect G2 continuity even right at the star point. So it is possible. I haven’t figured out the magic recipe though except for in a few special cases.
Here’s a comparison - Rhino mesh-to-SubD-to-NURBS on the left, and MoI mesh-to-NURBS on the right


nurbsconversion_compare.3dm (393.2 KB)

1 Like

Thank you for the help, it solves the issue.

Could you tell me what is “Mol” ?

And was the initial mesh-to-nurbs was a smoothed mesh or 6 quad faces?

Moment of Inspiration

The guy behind MOI has a history with Rhino also.

// Rolf

2 Likes

Looks like Rhino4 twin :slight_smile: