Create concave line between to points?

02-26-2013 09:12 AM
New Contributor III
I am trying to create a concave line (beziel or multiple straight-line segments) between two points. I have used the "Point to Line" tool successfully to get a straight line (red in graphic), and also buffered around a point and turned that into a polyline (purple in graphic). However, for my purposes I need a line that bends inward between the two points, not straight or outward (green in graphic).

Each of this lines is being created at the intersection of lines, and there is an intersection point, if that helps. Essentially I want to bend  the straight line inward, if only a small amount.

I am hoping that a tool or series of tools will do this, as the dataset that I am working with is much too large to do by hand.


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Regular Contributor
Here is an idea:
1. run Feature Vertices To Points tool to get thr MID point of the straight line.
2. run Buffer tool on the midpoint with a distance that is slightly smaller than the offset of the curve/arc you wish to create from the line.
3. run Feature Envelope To Polygon on the buffer. You get a square polygon.
4. run Feature Vertices To Points on the square poly with START option to get the point (normally lower-left).
5. run Append tool to add the startpoint to the original points.
6. run Minimum Bounding Geometry with ALL option to create a CIRCLE around the 3 points.
7. run Split Line At Points to split the circle by the original two points; the shorter arc could be what you need.

Of course if you can script and know the math, you can follow the logic:
- from the midpoint of the line, find a point along the line connecting the midpoint and the intersection of the seemingly x-axis and y-axis. The distance between this point and the midpoint sould be the desired offset of the arc.
- then create the shorter arc passing this point and the two input points.
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