Grasshopper

algorithmic modeling for Rhino

Circle from Point, Point and Tangent

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: 1683

Replies to This Discussion

Permalink Reply by Ethan Gross on April 4, 2016 at 6:57am

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.

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Permalink Reply by dominik nuessen on April 4, 2016 at 7:07am

Hey Ethan,

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

Permalink Reply by Ethan Gross on April 4, 2016 at 7:25am

I defer to Laguerre.

Permalink Reply by dominik nuessen on April 4, 2016 at 7:03am

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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