Arcs

I began by fixing the bug in my traversal code from yesterday. When selecting a branch to traverse first, I assign a heading to each branch based on its real heading from the current position, and then sort by clockwise or counter-clockwise. Each heading is in radians, so I can simply sort the floats.

The difficulty comes from choosing a starting position. My code looks at the heading of it’s parent, and then modifies any values greater than (or less than, depending on direction) it by two pi, so that the order is preserved, but the start is offset.

Once I fixed the bugs there, I was able to produce the following.

From here, I tried to find a way to build a curve around the traversal.

The only attempt I was able to complete today relied on the fact that my trees were built from the Delaunay Triangulation of the circles, meaning that any two connected points in a tree had a third connected point forming a triangle, and I could use the circumcircle through these points as part of the curve.

The initial results weren’t ideal, as you can see below.

While this is obviously not close to the final product this method may produce, its main shortcoming is evident. Because I traverse up and down each branch, every non-leaf node is visited twice, so that arcs on different points of the line meet at the same nodes. In the final version, the arcs will be smoothed so that this problem does not occur, but that is further down the line. For now, I will try another method based on connecting touching circles as some of that code will certainly be of use in other methods, and it’s final look is clearer in my mind.

Another problem I need to fix is the tree selection algorithm. I should consider:

• Swapping from leaf to leaf directly, as opposed to visiting parent nodes in between (although this would cause problem with the circumcircle method)

• Having separate start and stop nodes. Right now, the root of the tree is returned to before swapping trees, but this could be done in another way to avoid backtracking

• Changing the logic behind the selection. Similar to above, instead of choosing the one closest node to an edge, I should choose a start node near the previous tree and an end node near the next tree

This last point is important, as with more complexity it is easy not notice overlapping lines as trees are swapped between:

Tomorrow, I will also make a large effort to change the layout of my code to be in more files, as right now too many functions are crowded together, and it can be hard to find the one you are looking for (I’ll also redo some documentation).