Author Topic: Vector Geometry Problem, Reverse Curves with Tangents  (Read 352 times)

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Area51Visitor

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Vector Geometry Problem, Reverse Curves with Tangents
« on: January 11, 2017, 07:36:09 pm »
Please see attached.  I used to know how to solve this by drawing circles in autocad but I can't remember how anymore.  Anyone know how to solve this procedurally in cad?  The arcs need to be tangent on both ends with not straight segment in the middle. 

The white lines are at different bearings. Hope it makes sense.

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kdub

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #1 on: January 11, 2017, 09:13:22 pm »
It would be serendipitous for your construction method to work with a random middle ( common) tangent point.
By definition, for adjoining arcs, the arc centres and the common tangent point are collinear.

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Lee Mac

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #2 on: January 12, 2017, 01:48:50 pm »
I'm sure there is an easier way, but the following demonstrates one possible construction:



Snapping could have been made easier, but I didn't want to change the zoom in order to keep everything in frame.

Master_Shake

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #3 on: January 12, 2017, 03:29:13 pm »
Would blend accomplish this task?

lamarn

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #4 on: January 13, 2017, 03:59:37 am »
Wow! Super animation mr. Lee. :wideeyed2: It doesn't have to be lisp all the time..
Design is something you should do with both hands. My 2d hand , my 3d hand ..

roy_043

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #5 on: January 13, 2017, 06:10:58 am »
I assumed that the radii needed to be equal.
If that is indeed not required, here is my suggestion.

Explanation:
The angle between the red and yellow lines is 90 degrees.
The green circle is user defined.
The cyan circle is a copy of the green one.
The angle between the magenta lines is also 90 degrees.

Lee Mac

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #6 on: January 13, 2017, 01:30:37 pm »
I assumed that the radii needed to be equal.
If that is indeed not required, here is my suggestion.

Excellent work Roy.  :-)

I think we both followed essentially the same route, but I went the long way about constructing the perpendicular bisectors...

As you've deftly demonstrated, the key to the construction is forming this isosceles triangle:

« Last Edit: January 13, 2017, 01:36:37 pm by Lee Mac »

Area51Visitor

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #7 on: January 19, 2017, 01:47:43 pm »
Have I ever told you how great you guys are? I might be in love ;) lol jk

Thank you!
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Ausrod

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Re: Vector Geometry Problem, Reverse Curves with Tangents
« Reply #8 on: January 19, 2017, 10:01:06 pm »
Here is my solution

From two existing lines (Yellow)
Create Xline (bisect) with vertex and the start of the first line that bisects the extension of the first line and the line between the two endpoints (Blue)
Do the same for the other line
Create a circle 3P that uses the two endpoints of the lines and the intersection of the two xlines (Blue)
Any solution can be created where the two arcs will meet at a point on the circle (Cyan)

Cheers Rod
« Last Edit: January 19, 2017, 10:05:32 pm by Ausrod »