Planes on sphere with y-axis parallel to xy-plane

Dear all,

I have subdivided a sphere into parts sucessfully, but now would like to get a plane on each vertice of my sphere, with the y-axis of all planes parallel to the xy-plane of the real world.

I have encosed the rhino and grasshopper file which should explain the problem more clearly.

Thanks a lot

Sphere.3dm (81.4 KB)

Sphere.gh (8.9 KB)

If I understand correctly, you just need to use the “Align Plane” component, together with a direction vector to align to.

image Sphere2.gh (11.2 KB)

Dear Adam,

Thanks for your help, I appreciate it a lot!

I’ll try to rephrase, as I’m not sure my question is entirely clear;
What I would like as an end result is a plane on each point, with the z-axis pointing outwards, away from the center of the sphere (hence the 2pt vector), the x-axis of the created plane being in the yz plane of the real world, and the y-axis being in the xz plane of the real world.

While the “Align Plane” component sounds right, the end result in my grashopper file is not how I would like it, even when downloading your file.

Allow me to demonstrate with this picture; this is what the end result should more or less look like (although it’s done with a different method)

This is what I have now, with your file:


As you can see, the ones in circled in blue have the correct orientation. The ones circled in yellow need to be rotated somehow.

Thank you!

Like this?
(this definition only works for the specific amount of planes, do you want to change them dynamically?)

align.gh (12.1 KB)

I’m not sure if what you are asking for is possible.

When the vector between the centre of the sphere and the point (your z axis) aligns with either the world X or Y axis then it works.

Top view, z axis aligned:

When your z is not aligned, then I dont believe it is possible.

When the z of the plane is not aligned to the world X or Y, and the y of the plane is parallel to the world Y, then the cross product of these two (i.e. the plane x axis) can not be parallel to the world X. Hopefully this makes more sense in the screenshot below.

Top view, z axis not aligned:

If the z of the plane was parallel to the world Z, then you could do it.

Hmm. right. I realise now what I ask is not possible. I’m having a hard time communicating what I am asking for, I am sorry about that.

I do not mean to align the entire planes to the world planes, as this is indeed impossible if my z-axis goes from the center to the point. What I try to accomplish is indeed the z-axis having this vector away from the sphere, and the two other axis pointing to the north and east of the sphere; this for all created planes. So one axis should point up and the other should point right, while the final x-axis is still pointing outward, if that makes sense.

RIght now, in the definition, the x-axis points outwards as intended but the other two axis are chosen randomly it seems.

This is indeed the result I am looking for, however it should be parametrical.

there we might have a small problem, if we have 4x4 frames, what happens to the ones that are vertical to world y? their ‘local’ y points to world x or world -x ?

Maybe like this?

align2.gh (9.0 KB)

1 Like

Yes! Perfect! Thank you so much. I had to download Rhino 6 for it to work but it works perfectly.
I’m trying to understand what you did, exactly, but I will try to figure it out! If I don’t get it, I’ll get back to you!