Hi Dan,

Thanks for a pretty amazing exploration of the possibilities. It's both educational and entertaining (for those of us who like this kind of thing).

My apologies for dropping the ball on getting back to you. This is one of those projects that I just keep whittling away at because each step seems a little more complex than I had expected or was ready to deal with.

You provided quite an array of methods for finding the starting angle of a circle, and I'm sure some of those will be useful as I move forward.

As for my current stuck spot, I think what I'm really trying to figure out is how to specify the starting angle of a circle, a polygon, or a curve, relative to the previously placed circle or polygon, as I go around the knot placing circles.

When I use the usual tools to create a circle, the starting angle does not seem to be a parameter that is under my control. The image at the top of this thread shows where it defaults to, just using the standard circle-creating functions. I do not need to understand the logic behind those defaults, because that's not going to help me with my actual problem.

If I create a polygon, like a circle, I also do not know how to specify a starting angle.

I have to wonder, when you draw a circle or a polygon manually in SU, the point you drag out from the center becomes the starting angle. So what's going on under the hood? Is a default circle being generated and then rotated so that it's starting angle is where the cursor is?

Lacking that methodology, the only way I can see to create either a circle or a polygon where I get to specify the staring angle is to make a 360 degree curve. That feels unnecessarily limiting, but that's where I've gotten to.

My current thinking on my original problem is that I need to figure out how to place the new curve, based on the information I have from the previous circle/curve. I have the normal, which is derived from the current segment of the knot curve. I have the previous circle/curve. And I have the previous circle/curve's starting angle.

And, as you suggested, I have to deal with what the starting angle is relative to.

I have to figure out what starting angle I want to specify, based on the previous normal, the previous starting angle, and the current normal.

I think I'm going to have to nudge the starting angle of the next successive circle by just a little, so that as the sequence progresses around the knot, it does a slow rotation and comes back to the beginning. Does it want to go around only once? Or three times for the three lobes of this knot? Or what?

You gave me a great nudge that percolated for a while and now I think I know what I need to figure out for my next step. I hope that's not another year, but who knows?

Anyway, thanks for all the tips.

August