Statement of the problem:
Conceptually, what I'm trying to achieve is pretty simple. I have some code that generates a set of diagrams from a list of sets of points using BSplineCurve. Certain conditions cause some of these diagrams to come out differently from what I need. With SplineDegree -> 1 the images look like:
and with SplineDegree -> 3 the images become:
The problematic cases are images a7, a8 and a9, which I need to look like:
The general rule is that I need closed smooth curves through the specified points, but the curve must not lie on top of itself when the points all lie on a straight line (I also need the curves to pass directly through the points, but this is another issue that is probably fairly easily solved - I've tried clamping without much success so far).
I have tried to solve this problem by implementing clunky IF statements that add additional guide points, but in addition to the fact that I struggle to make it work, it's very undesirable, because I need this to generalize to more complicated diagrams. For example, here is a preview of the higher dimensional case (the full list is very long):
The last five images are problematic and should look like
I have also considered using Graph to try and do this, but I'm not really sure where to start.
Code:
I can't provide the full code, because the process of generating the list of points is exceptionally long. Here is the section that is relevant:
Clear[\[Delta]ToBirdTrack1]; Options[\[Delta]ToBirdTrack1] = {Background -> White, Trace -> Tr, Scale -> 1}; \[Delta]ToBirdTrack1[expr_, A_: a, B_: b, options___Rule] := \[Delta]ToBirdTrack1[expr, A, B, options] = Module[{l, s, aa, bb, h, res, res1, hsep, vsep, samesep, bgcolor, trace, scale, split}, (* options *) bgcolor = Background /. {options} /. Options[\[Delta]ToBirdTrack1]; trace = Trace /. {options} /. Options[\[Delta]ToBirdTrack1]; scale = Scale /. {options} /. Options[\[Delta]ToBirdTrack1]; hsep = 5; vsep = 2; samesep = hsep/6; l = (expr // Cases[#, Subscript[A, i], Infinity, Heads -> True] & // Union // Length); h = l*vsep; (*line 1*) res = (expr /. Tr[aa__] :> m[Line[(*Append[*)aa(*,First[aa]]*)]] //. m[aa__] m[bb__] -> m[aa, bb]) /. UP -> Sequence /. Subscript[t, i_] -> i; (*line 2*) res = res // (# /. m[aa__] :> (m[aa] /. a_Line :> pos /@ a)) &; (*line 3*) res // (# /. Line[aa__] :> BSplineCurve[{aa}, SplineClosed -> True]) & // (# /. m[aa__] :> Graphics[{aa}]) & ]; ExplicitList[NgI[2]] // Sum[Subscript[\[Alpha], i] #[[i]], {i, Length[#]}] & // \[Delta]ToBirdTrack1[#] & I can't provide the data being put into this code, again because of length, but I can however show what it looks like. At "line 1" res is being shaped into this list:
At "line 2" it is shaped into this list:
And at "line 3" the "aa's" that are being considered by the Spline Curve plotting look like this:
Any and all help would be greatly appreciated, with the most general solution being the goal.
