Hi Brian, the ArcContinue factory relies on the first point having an object snap set on it which can only be done by having the point supplied by a pointpicker.

re:
> And what would be the correct type of point?

It needs to be a "PickedPoint" object which is generated by the pointpicker and has additional data such as a list of object snaps.


> Can pointpicker() be used, without picking a point?

Sorry no it can't.


> Can the line tangent be obtained by script, and fed into arccontinue?

Unfortunately no, the arccontinue factory is only set up to get the tangent from an osnap on a picked point object.

So to do it in your script without using a picked point, the script would need to do the calculation itself.

There's a solution explained here:
https://www.emathzone.com/tutorials/geometry/equation-of-a-circle-given-two-points-and-tangent-line.html

or also here:
https://www.youtube.com/watch?v=nRAT0cyp74o

The way it's done in the arc continue factory goes like this:

Goal - calculate a circle given a point (PointA), the unit tangent of the circle at that point (TangentA) and a second point that the circle goes through (PointB).

First form a coordinate frame with the tangent as the x axis.

Get a vector between PointA and PointB as a second vector to cross with the unit tangent to get a plane normal.

Get a Y axis by crossing the normal with the xaxis.

Now the coordinate frame is formed with origin at PointA with xaxis being TangentA and the Y axis from the last step.

Get a 2D point B2D in the plane using B2D.x = frame.distancex( PointB ), B2D.y = frame.distancey( PointB ).

Then the calculation of the radius goes like this:

	// The equation for a circle is (x - xcen) ^ 2 + (y - ycen) ^ 2 = radius ^ 2
	// The first circle point is at the origin, and the xaxis is tangent to the circle.
	// Since the xaxis is tangent, xcen = 0, and ycen = +/- radius.
	// Substituting in gives:
	//
	// x ^ 2 + (y - radius) ^ 2 = radius ^ 2
	//
	// Expanding, and moving the right side over to the left:
	// x ^ 2 + y ^ 2 - 2 * y * radius + radius ^ 2 - radius ^ 2 = 0
	//
	// The squared radius terms cancel out:
	// x ^ 2 + y ^ 2 - 2 * y * radius = 0
	//
	// Solving for radius:
	// 2 * y * radius = x ^ 2 + y ^ 2;
	// radius = (x ^ 2 + y ^ 2) / (2 * y)

	Radius = ((B2D.x * B2D.x) + (B2D.y * B2D.y)) / (2.0 * B2D.y);

	// The circle's origin is radius distance along the original frame's y axis.

- Michael