Biarc - can I use a 1/2 of an Ellipse instead of a true (circular) 'arc'

In the 'getting-started videos # 5 (creating biarcs) David does this example with ‘arcs’ - what I would LIKE is to use a 1/2 of an Ellipse (with the ‘1/2’ (arch) being 'about 5 feet ‘high’ and about 30" wide - and - yes - varying - this would yield a sort of a ‘tunnel’ - much like what he shows in the example (video 5), using ‘arcs’…

I see no ‘mathematical’ reason it won’t work (ellipse has a ‘tangent’ if it is cut in half?) - but I am NOT a Mathematician - so maybe I do not understand the underlying math / geometry? - maybe there is some reason it is called a ‘biarc’, not a ‘bi-curve’???

This is not a ‘rush’ - just a general question…

Ellipses are more flexible than circles typically. You can fit a circle through any 3 (non-colinear) points, but you can fit an ellipse through any 4 (non-colinear) points. I imagine that the tangent bi-arc problem is pretty undefined when using ellipse segments instead of circular arcs.

However perhaps what you’re after is totally doable directly in GH without the need for a complicated solver. I’m a bit fuzzy on the goal here, could you upload a napkin sketch of the geometry you’re looking to create?

David, I can upload both model-files as well as …jpg and/or …tiff (screen-shots) - BASICALLY I’m trying to ‘model’ a pottery-kiln (think about a simple-boat-hull-but up-side-down)- some of which are exceedingly close to what you show at the end of video #5

  • HOWEVER, we can not build an ‘arch’ out of brick, that has a ‘circular’ profile, that’s why we use ‘ellipses’(to model) (we actually build a ‘catenary’ but that is hard to find in a CAD software tool) - ellipses are close enough, mathematically, and structurally

NOTHING I have uses the ‘mind-set’ that I see in your work (in your 13 videos) - I NEED to change the way I THINK about the surface, model, etc. - but if you tell me where / how to upload, I can do that, but they are all ‘working’ drawings, meaning nothing is ‘finished’ but that shouldn’t bother you?

Grasshopper has a catenary component if you want a curve like that. Though there is no way to have a catenary through three points without using an iterative solver.

You’re absolutely correct, and the catenary doesn’t have the ‘tangent’ - so that is why we use ellipses, there are a whole bunch of ‘geometry / math’ issues that are made a LOT easier by using ellipses… -

let me know where / how you want me to upload, and I can do that?

Hi Bill, there is a special tool for compression only structures, just in case you’ve missed that:

You can upload files directly from the replying dialog menu (7th item or CTRL+G)

Jess, - thanks for the link, I’ve reviewed it, briefly, and found it will take more research. I have found, in the last few days , a LOT of things that will take more research… -

I will DEFINITELY have to re-think the way I’m building mental models - there is / are a LOT of
software tools to help me and I need to make sure I learn to use them effectively / efficiently - A LOT of mental work in my future!

thanks again!

nk_v2.3dm (261.2 KB)

this is a ‘basic’ (not any one in particular) design; using ‘ellipse’ rather than biarc, but similar concept

Sorry, I forgot I was supposed to come up with a solution to this post…

I’m afraid the file you posted didn’t enlighten me as much as I’d hoped. I’m still a bit fuzzy about what parts of the problem are variable, and what parts can be assumed to be constant. In my understanding the following sketch shows what you’re after, but I don’t know which of the values (if any) are supposed to be variable:

Are the base tangents always vertical? Is the apex tangent always horizontal? Are the base points always on the same elevation? Is the apex point exactly in the middle?

I made a cluster in GH that tries to make an ellipse segment based on fixed tangent directions. (17.3 KB)

Also note that two points with two tangents do not uniquely identify a single ellipse segment, any more than two points and two tangents identify a single bi-arc. There needs to be an additional constraint somewhere.


Sorry - I was out doing ‘Saturday Morning Things’ (here in South Eastern Florida where the temp is already about 73F…)

I’ll have to ‘re-wire’ my brain to think about ellipses & Grashopper rather than cycling …

BUT to answer your ‘quick’ questions (and yes, I’ll put your ‘’ on my Windows / Rhino3D box and see what it tells me) - but your picture looks GOOD!!!

1.) I know that two tangents don’t uniquely identify a single ellipse segment - I don’t expect them to
2.) YES - the base-tangents are always vertical (“Z” axis parallel)
3.) YES - the apex tangent is always horizontal (and all the things that implies)
4.) YES the ‘base points’ are always on the same ‘elevation’ (on the same ‘plane’ (the x-y plane) - at least theoretically…

Your 'Video 3 / 5 where you move the outside curve(s) vertically (“Z” axis) would (most probably) never happen in a ‘real’ pottery-kiln - that ability (to move those sides (‘kiln-floor’)) might be of value from a ‘theoretical’ (geometry / mathematical) viewpoint, but I don’t see it happening for a ‘real’ kiln - On the other hand I am NOT an EXPERT in this realm and there might be a way this might be necessary…

in more ‘complex’ pottery-kilns, for a given ellipse the end-points (what you’ve labelled ‘base point’ in your colored-sketch) will always be co-planar (x-y plane) but different ellipses might be 1 foot or 2 feet ‘higher’ (that is they would be on another ‘x-prime’ / ‘y-prime’ plane that was parallel to the original x-y-plane

5.) YES the apex point is exactly in the middle…

I TRIED (in the past) to do the same thing with modeling pottery-kilns that I previously used while designing boat-hulls, which was to model (spend my ‘hours’) on ONLY HALF of the boat-hull; then doing a 'Transform => Mirror" command to get the other ‘half’ of the hull -

since the Apex Point (ellipse-middle) is always exactly in the middle, one could use the same technique to model a pottery-kiln as one has used to model a boat-hull - that is to really FOCUS one’s time on the 1/2 model and then ‘when all done’ to do the 'Transform=>Mirror" and make the other half…

the ‘REAL KEY’ for doing what you’ve defined for me VERY NICELY, and I need to work on this ONE THING, since you’ve shown me how GH can ‘automagically’ do a LOT of the work…


in the ‘right’ view (viewing a kiln from the right side): (against a ‘y-z’ plane (what most could call a ‘vertical’ plane, I need to find a way to express the ‘apex-points’ (probably one every foot or so) as a ‘curve’ - it would normally be ‘about’ 4 feet high to start, then go to six feet high, then at the end ‘back’ - be about 3 feet high - that one curve, then defines the top-apex-point (apex tangent) for each ellipse…

with what you’ve done I need to FOCUS on using your Ellipse guide to do what it does best

I REALLY appreciate your support!!!

VERY Sincerely yours, Bill Schell