PQ Mesh Model B 01

Comment

Comment by chenzg on June 20, 2017 at 8:36am

Hi Jesus,

Thanks for your definition.However,i find this link is  wrong.Could you please share it again?

Kindest regards

chenzg

Comment by Daniel Piker on May 11, 2013 at 4:28pm

Hi Jesus,

Thanks for your reply and for sharing the definition. I'm wondering if maybe there could be some interesting possibilities with a force-based way of spacing/aligning the curves, and looking at this could be useful. I'll let you know how it goes.

Yes, I'm familiar with Pottmann and his group's excellent work on this topic, and have talked a bit with them - in fact some of the planar meshes in that presentation you link to (the ones used as the initial input for the shape-space exploration work) were ones I generated for them using Kangaroo!

Comment by Jesus Galvez on May 11, 2013 at 12:38pm

Yes I too used David's script. It's a real pain to obtain evenly spaced lines. I did it manually because this was just a side project and I think you need scripting skills to do it properly. Another problem is [quoted from David]:

Currently the deviation between the sampled curve and the 'real' curve is compounded, which is a $3 way of saying it gets worse all the time and the worse it gets the faster it gets worse still.

In practical terms you obtain intersections between conjugate lines, or even worse, spirals which go on and on (mainly on spherical or conical regions). 

What would be interesting would be to obtain families of conjugates networks that are not principal. There are plenty of papers on the subject mainly from Pottmann and Yang Liu:

Designing Quad-dominant Meshes with Planar Faces

Freeform surfaces from single curved panels

General Planar Quadrilateral Mesh Design Using Conjugate Direction Field

Geometric Modeling with Conical Meshes and Developable Surfaces

Performative Curve Network Design

Presentation Pottmann (this presentation is quite nice because it commented)

Here's the Definition on dropbox. I implemented a sloppy (but effective) way of getting the intersections; the other methods I tried had problems. It takes time to load and there's a toggle to get the PQ Mesh (takes time). Have fun and I hope to hear more!

Comment by Mateusz Zwierzycki on May 11, 2013 at 7:20am

@Daniel - this property of surface is just awesome. I made some of these lines with David Rutten's script (dont remember now where is it on the forum). The biggest problem is to generate them as equally spaced as possible...

(Just in case anyone asks : the green lines are lines perpendicular to surface /surface normal vector/, connecting the 4 points gathered at the intersections makes planar quad).

Comment by Daniel Piker on May 11, 2013 at 7:01am

Very interesting!
I'd love to hear more about how this is generated.