May I ask if a member of the Rhino team could make an Ellipse Arc curve tool, like this (first video) in MoI, please?
I am looking to use it for Classical Greek mouldings, such as this from The Temple of Apollo at Phigaleia. I enjoy the seamlessness of playing with Ellipse arcs over trimming whole Ellipse’s. As well as the creative possibilities to play with smaller sections of an Ellipse arcs as shown in the (first) video; so as to create a wider variety of possible mouldings.
I enjoy using the Rhino Conic tool to create mouldings too, though it doesn’t have quite the ability to play with Ellipses like an Ellipse Arc tool does.
I love Rhino and it would mean a lot to me to be able to use a feature like this in the application!
With thanks in advance for any help or thoughts you can provide
Thanks for the heads up, I’ll make a new thread for the other feature request.
Yes, I believe an Elliptic arc input would be:
Centre
Endpoint first radius
Endpoint second radius
I have tried tried the _conic command. However it works differently and the resultant ellipse arc has a different shape to an elliptic arc beginning at the centre (then selecting the endpoint of the first radius, and then the endpoint of the second radius).
I have added a couple more videos, hoping these help.
I appreciate your interest & help with this Tom!
More Elliptic Arcs (showing the input: centre → endpoint first radius → endpoint second radius):
Similar _conic command/tool contrasted with an elliptic arc (in MoI):
i am not getting the precise construction for all solutions.
one first solution is easy to find - see screenshot above.
the resulting curve can be described as an intersection between the grey cone and the blue main surface.
But as far as i understand there should be many solutions - and all should be presented by a cone intersecting with a plane…
… knowing how to construct the curve - it should be easy to implement a script that can do it..
@davidcockey and @menno
you both have big geometric brains … any hint / help / thoughts ?
Moi elliptical arc method uses the first end point as the end of the major or minor axis of the ellipse. With that constraint the ellipse is unique when the center point, first end point / end of ellipse axis, and second end point are specified.
Method for creating ellipse from center point, end of ellipse axis, second point:
Create a circle using the center point and the first end point / end of major axis.
Line from center point to first end point. If needed extend the line to the other side of the center. This line will be on an axis of the ellipse.
Line perpendicular to the ellipse axis through the second point. Extend this line to the circle if needed.
Optional - create points at the intersection of the perpendicular line with axis line and the circle.
Scale1D the circle using the intersection of the axis and perpendicular line as the base point, the intersection of the circle and perpendicular line as the first reference point, and the input second point as the second reference point.
Additional comments:
Two additional points for defining the ellipse and cone can be obtained by reflecting (mirroring) the first and second end points about the center point.
The vertex of the cone will lie on a plane containing the center point and the first point, and normal to the Cplane.
Added: Ellipse in V9 WIP has a FitPoints options but it requires a minimum of 5 points and cannot use the center point. Therefore it is not applicable to this situation. (Unless I’m missing how to generate an additional point.)
You can convert an arc segment to an ellipse segment by using Rotate3d and then projecting the result back to the arc plane. See file: ellipse.3dm (2.4 MB)
If you apply History to the Project step you can rotate the arc and the new ellipse will update. Viewing the rotated arc from the normal direction of the plane will show the shape of the ellipse as the arc is rotated.
I took Davids 's input points - just moved the center to the origin.
what i am interested in is a ellipse, that is not only going through the last point (by scaling 1d or rotating…) but a cone, that intersects with the plane (defined by the 3 points) and results in a curve that starts and ends with tangents (blue) that are perpendicular to both input radii.
one solution is the magenta curve in above screenshot.
but i guess there is more then one solution - and maybe a much simple construction.
my construction is maybe not the one for the schoolbook - but the only one i was able to figure out:
Thank you for all your inputs and ideas. I’m excited and hopeful, that in time, a script or Rhino feature may happen!
I especially appreciate David, your clear explanation of the MoI ellipitcal arc method here:
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Amazing ideas and rigorous thinking!
I have started playing around with each of your ideas. though unfortunately I am getting lost at points (I’m not very skilled at geometry) and finding it difficult to focus on playing with finding a moulding shape. (I will continue to try & figure them out!) Due to the difficulty, I do tend to go back to using MoI3D for the ellipse arc.
Appreciate all your help so far!
p.s.
Hoping they give up their secrets!
I will look through old geometry text books relating to ellipses and architecture. As there was a resurgence in using ellipses in mouldings, in the late 19th and early 20th centuries. There might be something there…
