Hi, I would like to create a mesh based on ellipsoid curvature curves. First I was wondering to get curvature lines and intersect in u and v directions. But I believe there is some specific way to create a mesh of this form. Could someone point me where to start? I searching for only one form - …

Hi Daniel, Could you please shine some light on the attached trial to get the isothermic goal working? isothermic_v1.gh (24.7 KB) The mesh edges are currently approximately following principal curvature directions. Even when the goal has a relatively small, close to negligible, strength compared …

Hi Timothy, For the isothermic goal to work, the initial mesh needs to be either fairly good to start with, or quite free (in terms of fixed corners/boundaries, or pulling onto surfaces). If a grid is fully aligned with principal curvature directions, there can’t ever be any odd valence irregular …

Hi @timothytai how did you get that mesh? a kind of remeshing with vectors in grasshopper?

I took your mesh and cut out some of the more problematic areas, released the corners and boundaries, and applied that goal I mentioned above that lets points slide off the edges, and this is what happens: TT_reply.gh (41.4 KB) [image] If you let it slide around a while it finds a more natural o…

Hi Daniel, Thanks a lot for the insight and the file! I thought the aspect ratio of the faces in the initial mesh was not too terrible, but was not thinking about the valences and how odd ones may be causing the issue. I was under the impression that by following the curvature directions, it would…

The ‘Range’ input in the SlideOff goal is the maximum search distance. For each point in the goal, if it is within this range of the target mesh, and its closest point on the mesh is not on the boundary of the mesh, it gets pulled towards that point. Optimising the quad mesh geometry at the same ti…

Thank you very much, Daniel. This is particularly illuminating for me: [image] DanielPiker: Looking at how you generate your initial mesh, it seems a large part of the problem is that the curvature field does not match the boundaries of your surface, yet you are forcing the grid to. Does th…

If the input surface has its principal curvature directions matching its boundaries, then great - that makes things easier. Frequently though we have to deal with geometry where this isn’t the case, meaning a planar quad mesh can’t possibly align with both the boundary and the curvature field, sinc…

That makes a lot of sense - Enabling the finding of a solution by first extending the geometry is something that I haven’t really been thinking about or am used to, so the approaches have been limited; thanks a lot again for all the explanations!

Ellipsoid mesh from curvature lines

Grasshopper

DanielPiker (Daniel Piker) April 23, 2019, 4:29pm 11

isothermic_quads.gh (24.9 KB)

Here’s an idea of how I’d approach this.

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Ellipsoid mesh from curvature lines

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