How to achieve quad mesh like thermal field on a sphere with holes?

[Crackmina]

Hi all . I wanna achieve this pattern on image 2 into the geometry of image 1. What tools can you suggest me to use ? I was learning kangaroo but its mainly used for minimal surfaces with catenoids and so on .

[laurent_delrieu]

Hello
you could use QuadRemesh that uses some field to quadrangulate the mesh.
You could also use some field and perpendicular field, there are tools for that on Millipede.

Millipede Plugin Grasshopper 3D — CREATIVE MUTATION

Heat Method

A script demonstrating the Heat Method for Distance Computation, as described here This came up recently in another thread, and I thought others might find it an interesting example. It is a fast way of getting approximate geodesic distances from a given point to all points on a mesh. Here solved in an iterative fashion, without any extra numerics library. This is not the fastest way to do it, but it does let you see what’s going on and interact with it. HeatMethod2.gh (163.7 KB) …

Also I did something similar here

Tween curves on mesh using Nautilus plugin

Combination of various tools from Nautilus plugin. [tween 3D on mesh] [tween 3D on mesh2] It is a bit similar to the Heat Method I didn’t compare with Tweener but it seems similar except it is in 3d. [tween 3D on mesh5] [tween 3D on mesh4] [tween 3D on mesh3] Arm brace [tween 3D on mesh6] In order to explain that, here a little script. A mesh is created here with 2 holes. The components in the middles allows to put some weights on each vertex of the mesh. 0 is on the border of th…

[Crackmina]

Such good information . What block can I use to get coordinates of each intersection point of each line ? Thanks for your answer .

[laurent_delrieu]

There is no general answer. If you use quad remesh you will need mesh deconstruct to have the points. For the others tools curve intersection could help.

[Crackmina]

In your post on “Tween curves on mesh using nautilus plugin” you did on a 2d mesh . I also have similar results using 2d fields , main problem occur when making it on a sphere with holes . How did you make considering a spheric surface ? . Also What other sources you recommend to understand this better ? like mathematical background or differential geometry ? What is the route to be proficient on meshes ? I even tried to do mesh and get this linepaths on a commertial software but it can not do it , just triangulations its possible , but you did it

[laurent_delrieu]

Example of sphere must be in the Nautilus examples that are on food4rhino.

[Crackmina]

There are no examples on food4rhino . Anyway its a good point to start with your recommendations . Thanks . I am quite new on this so …

[DanielPiker]

Here’s an example showing how to do this with Kangaroo

openings.gh (16.1 KB)

[DanielPiker]

You can adjust the warp and weft tension with the sliders to control how much the shape shrinks in around the necks:

[laurent_delrieu]

Seeing the answer of @DanielPiker I am not sure I well understood what you are after.
Can you make a drawing and post your geometry?
Examples of Nautilus here

[Crackmina]

I wanna achieve similar to your post , holes will be in another position but goal will be same after all . I do also want a full mesh in all the sphere with parametric spacing between lines (like 1,2,3 or 4 mm) in both directions . What is most important for me at the end is to deconstruct it and get the point coordinates of each line path

[DanielPiker]

I think there’s a bit of a disconnect between your description and the first images you show @Cleison_Armando_Manr .
Heat flow will be from sources to sinks, so you won’t get something like the grid on the 3 way branching minimal surface, because if one opening is a sink, the second a source, the third has to be the same as one of the others.
If you mean a conformal grid on a sphere with circular openings, then you can change the definition I posted above like this:

openings_sphere.gh (24.0 KB)

[Crackmina]

This is what i wanna achieve . Amazing , then postprocess to get linepaths or coordinates of each of them . Ill skip lines some lines , but yeah thats my goal . Do you know how to achieve this with Nautilus ?

[DanielPiker]

You won’t be able to get to this result with a heat flow approach for the reasons I described above.
The definition above gives you the separated curves and you can easily extract coordinates of vertices.

Note that the definition also uses Weaverbird and RhinoPolyhedra for the initial mesh generation before relaxation.

[Crackmina]

Sure I understand . Yeah but I am looking a solution with heat flow . I mean with heat I will get this but on a curved surface (sphere)

[DanielPiker]

Ah, that’s from my Rheotomic surface tool right?
This can be stereographically projected to a sphere.

[Crackmina]

Yeah it is . Could be projected but to conserve the holes in a shape of a circle could be quite challenging . Even to knit all the sphere , This is the surface I wanna mesh like that . It has symmetric holes . Your essay on rheothmic surfaces was quite interesting . I didnt know there were high level math’s on this

[DanielPiker]

Here’s an example stereographically projecting the planar mapping to a sphere
conformal_sphere.gh (28.6 KB)
You can get circular isocurves in a conformal mapping like this by inverting the sources and sinks in a circle.

[Crackmina]

yeah if you put sources and sinks in a symetric way . Paths or lines will be way better

[Crackmina]

Is there a way to do this and avoid using weaverbird ?