Grasshopper

algorithmic modeling for Rhino

Dear All,

it seems like an easy thing to solve, but I am stuck here...

I want to construct the underside of a stair and I have both Points P1 and P2. I also have the straight landing underside L. What I need is P3, which is the point at which a circle or arc (through P1 and P2) is tangent to line L.

I know that Rhino's "Circle tangent to 3 curves" command features the switch between tangent and point as input parameters, so that I can easily construct the circle in Rhino. However - Grasshopper, Rhinoscript and RhinoCommon all don't feature that switch of parameters. I need to integrate this into a GH python component.

Maybe someone has an idea?

Thank you very much,

Dominik

Views: 1642

Replies to This Discussion

Hi Dominic,

Here's a solution based on classical geometry involving two parabolas, which I admit is not quite as elegant as a Gh command. If you can access the 'parabola from vertex and focus' in the script libraries then you can probably do it in several steps.

Attachments:

Hey Ethan,

thank you very much, looks also quite interesting...

I defer to Laguerre.

Ok, found it...

Following the “power-of-a-point theorem” from French mathematician Edmond Laguerre:

One can say that distance PT = Sqrt (PM x PN)

Applied to the stair underside you get the location of the tangent point T…

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