Geometric Problem Lofting Stairs from Curves

Hey,

I am having a geometric problem, where I hope somebody could help me with. I am designing some kind of promenade, where a stair is created from some 'twisted' curves. The point is that the stairs should go down in z-direction at some points and should become something like seating possibilities. Therefore the curves have all a different length and the z-position of their control points is controlled via a 'custom' graph mapper, where a curve in rhino controls the position. This is where the problem lies: because of their different length, the steps are at some points not horizontal but tilted. Does anybody know a way to solve this? The aim is to have only horizontal steps which follow the guide curves in top view and undulate in z-direction according to a curve.

Thanks a lot

Christian

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Replies to This Discussion

Permalink Reply by Christian Hämmerle on August 10, 2015 at 2:09am

no ideas on this one? I would be really happy if anybody could help me fix this. In the meantime I tried different ways of dividing curves (divide length/divide/control points only) but it didn't work out. The problem, from my point of view, lies in the different length of the curves. I think it should somehow work with Normals from division points on one curve, but this alters the other curves and would change the overall shape...any ideas?

Permalink Reply by Kim hauer on August 10, 2015 at 3:57pm

This is an Architectural problem that involves stair and ramp design, where the surface one is walking or driving on must remain horizontal, while the grade keeps changing.

Your pictures really don't express that relationship. Become a member of http://sketchucation.com/forums/ you will find Ruby scripts that perform that task.

Permalink Reply by Christian Hämmerle on August 11, 2015 at 2:27am

thanks, but in my opinion its also a geometrical thing...I think with galapagos it should be no big deal, starting from one curve and going down all the way. But I think this could be done easier...

Thanks for your link, but I think this is no real solution for me because I need a Nurbs solution inside Rhino...

Permalink Reply by Joseph Oster on August 11, 2015 at 6:08am

For what it's worth, I looked at your code a couple of times. The problem you describe isn't at all obvious to me, just looking at the output - I don't mean the solution, I mean I can't see the places where the steps are tilted?

Furthermore, if they are tilted, it's likely due to mis-placed loft lines instead of a sweep/torsion issue. There appear to be three or four stages of code that set the loft lines, including a cluster. Along with a bit of German language, it's hard to follow what is going on with all the adjustments.

Sorry, no help here.

Permalink Reply by Christian Hämmerle on August 11, 2015 at 7:51am

ok thanks a loft for having a look. a big sorry for the missunderstanding and being unclear. Actually this Promenade is a part of a bigger definition. To make it hopefully a little bit more clear I tried to show my problem in some sketches where in my opinion lies the main problem. The first sketch shows three curves with different length ('original curves in plan' - my base curves of the promenade are all curves with different length). What I did in my definition was to move the control points in z-direction (see blue curves, 'modified curves').

In sketch two the problem starts: when I now loft the curves the loft is tilted, or in other words the isocurves are not straight lines in plan (see the green lines 'lofting isocurves'). In 3d space this means, that the lofts are not horizontal but tilted.

In sketch three I tried to show a possible solution: when I take one guide curve (maybe the shortest curve) and divide the other curves by the same distance, then move the points according to the scale values, the loft should be horizontal in z-direction (or height). But when I interpolate these curves there is sometimes a big difference between the original curve and the new one which I like to avoid of course...

I hope this makes my issue a little bit clearer...thanks again for your time and help!

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Permalink Reply by Christian Hämmerle on August 11, 2015 at 7:51am

I also drew a cross section of the promenade to show the tilted steps (sketch four)...

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tiltedstairs004.jpg, 132 KB

Permalink Reply by Matt Gaydon on August 11, 2015 at 12:36pm

Hi Christian,

Running GH from a virtual machine remotely so made an example code of what i think your trying to do as can't download you code to it. Its still not perfect as to make the surface flat by adding section curves the more sections the flatter the surface.

Had a screen capture to post but the icons are too small. So just the code sorry all. Hope this helps,I will have a think if there is a way to do it more mathematically

Matt

P.s Really nice Setting Out Diagrams. Just hope i have understood them. ;)

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Wavy Flat Stairs.gh, 17 KB

Permalink Reply by Christian Hämmerle on August 12, 2015 at 2:13am

Well, this is a pretty convincing solution! You understood me absolutely right! I just took a look at your definition, which seems to be really good. I'll try to merge this with my definition and keep you updated!

Thanks a lot Matt!

Permalink Reply by Christian Hämmerle on August 12, 2015 at 4:01am

Ok, I tried your code on my curves but it didn't work out so easily. The problem is, that my curves are not tween curves but are more twisted. Because of this the horizontal frames of your definition intersect them selve at extreme points. But based on your logic I found a way to solve it: I used an offset instead of the horizontal frames, then lofted the curves to get the base surfaces. Then I just pulled the control points to these surfaces and lofted the new curves...worked out pretty good!

Thanks again, great idea with the projection on breps...

Christian

btw.: the 'check planar' code is pretty cool aswell!

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