a circular arc knowing the center of the circle and two other points on the arc.

Replies to This Discussion

Permalink Reply by David Rutten on April 22, 2013 at 3:10am

Technically an arc defined by center point, start point and end point is overconstrained as the radius is defined by more than one value. However, assuming the distance from center-point to end-point is the one-and-only constraint for the radius, you can make this arc thusly:

It is also -in a way- underconstrained as the three points must define the plane of the arc. But this is not possible if all points are co-linear (i.e. for a 180 or 360 degree arc). It is also not entirely obvious whether you want the clockwise or counter-clockwise arc segment.

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David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by David Rutten on April 22, 2013 at 3:15am

Incidentally, if you already know the plane in which the arc is defined (for example if it's always in  the WorldXY plane) then you can adapt the logic. You'll need to calculate both angles so you can create an arc from a plane and an angle domain.

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Ahmed Hossam on April 22, 2013 at 7:48am

Hallo David,

thank you for your effort ...

The circular motion starts with a specific point on the circle and it goes counter-clockwise (mathematically positive) ... The arc is in the xy-plane ...

I am a beginner with this program and I still have some questions:

1- Could you please explain, what these symbols mean? What do they do? How to find them in the Program? What are they called? (The symbols in the photo)

2- Could you explain, what angles should I calculate?

3- Thanks again :)

Attachments:

• bild.jpg, 96 KB

Permalink Reply by David Rutten on April 22, 2013 at 8:13am

From left to right:

• Plane XY (create a plane parallel with the World XY plane at a specific location).
• Plane Decompose (decompose a plane into origin points and axis vectors).
• Domain (create a numeric domain from two numbers).

In Rhino, arcs are defined by a Plane (which specifies both center point and orientation), a radius value and an angle domain. The hard part here is computing the correct angle domain, but you can do it using the [Vector Angle] component.

Because centre-start-end is such an awkward way to define an arc (both over and under-constrained as mentioned above) there is no standard component for it. In Rhino it's ok because you actually have to click in viewports to define these points and Rhino can thus harvest plane and sweep information from the motions of the mouse, but in GH this is not possible.

--

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Ahmed Hossam on April 22, 2013 at 11:26am

Ok David.

So from left to right:

- A plane parallel to the XY-Plane through the center Point ... hmmm ... Why can't I just take the XY-Plane?! :D ...

- Decompose a plane ... hmmm ... what is the output of this? ... what exactly is O? What is X? What is Y? What is Z? ... I guess X, Y and Z are the cartesian unit vectors ... X=(1,0,0) ... Y=(0,1,0) ... Z=(0,0,1) ... Is this true? If yes, I still don't know, what O is? :D ...

- A numeric domain from two points ... hmmm ... What is a numeric domain? What does a numeric domain do?! ... you put the two angles inside the "numeric domain" and what is then the output? ... 

- Who mentioned angle domain? What is an angle domain?! ...

Hey David ... Thank you for your patience and your effort!!! :)

Permalink Reply by Ahmed Hossam on April 23, 2013 at 7:41am

Thank you very much :) ... Done :)