WIP: Implement qcurve handling in tfont

[madig]

This makes the text tool work.

Todo: look at what's missing. Intersection to make ruler work.

TestFont.ufo was cribbed from defcon. Had to change public.backgrounds A to not be all-off-curves, otherwise UFOConverter would be stuck in an infinite loop trying to shuffle points around ;)

[adrientetar]

There is code for intersection here: https://github.com/trufont/trufont/blob/wx/src/trufont/util/bezierMath.py#L99

[madig]

Neat! Any reason to have a bezierMath.py in Trufont and tfont?

[madig]

Ugh. The TruFont function doesn't seem to work (aside from pc0 having a - instead of a + in it) or I'm confused. My trigonometry-fu is very weak. I found https://stackoverflow.com/questions/27664298/calculating-intersection-point-of-quadratic-bezier-curve but the math in there seems to work differently. E.g. in fontTools' solveQuadratic function, it computes DD = b * b - 4.0 * a * c which turns DD negative with the example curve and line and therefore returns no root, whereas the JS example computes DD = b * b - 4.0 * c and leaves out the / a. in the root calculation. Debugging...

[madig]

Ok, so this is a very rough implementation that works. I don't know why fontTools' solveQuadratic works differently. I'd have to work out the math to avoid the _lerp(). The previous way of computing s0 and s1 looked better.

[madig]

And for some reason, depending on ufoLib2 does not pull in fontTools[ufo]. Ugh.

[madig]

Still occasionally get

  File "/home/nikolaus/Entwicklung/tfont/src/tfont/util/bezierMath.py", line 132, in qcurveIntersections
    pc1 = (nx * bx + ny * by) / pc0
ZeroDivisionError: float division by zero

Just catch that and return []?

[madig]

https://pomax.github.io/bezierinfo/#what-about-curve-line-intersections- https://pomax.github.io/bezierinfo/#aligning

Hm :) Let's see.

[madig]

I gave up and simply adapted curveIntersections' math for quadratics. It werks! 🎉

[madig]

splitSegment is tricky I think, as we don't know which subsegment of the qcurve segment the t belongs to :thinking:

[madig]

I suppose I could change the return value of (q)curveIntersections to include the starting point of the curve the t belongs to, then it's just iterating over the implied subsegments until you hit the right starting point and splitting the subsegment.

[adrientetar]

Or the index of the segment. then it can be accessed directly https://github.com/trufont/trufont/blob/wx/src/trufont/objects/factories.py#L104

[madig]

What is the reason cmp is turned off for Point?

[adrientetar]

What is the reason cmp is turned off for Point?

Comparison is based on identity so two different points with the same coordinates wouldn't hash to the same value.

[madig]

I find this maddeningly tricky while it looks like there must be an easy solution.

[madig]

@adrientetar So this mostly works, please advise on the segment list bookkeeping and what to return as newSegment.

I have code like

points_inserted = len(points_to_insert) - 1
segments.insert(index, newSegment)
new_segments = []
index_start = start
for index, point in enumerate(points[start : start + points_inserted]):
    if point.type is not None:
        new_segments.append(Segment(points, index_start, index))
        index_start += index + 1
segments[index:index+1] = new_segments
newSegment = new_segments[0]
for seg in segments[index + 1 :]:
    seg._start += points_inserted
    seg._end += points_inserted

But that likes to delete everything except one point under certain circumstances.

Even with the sledgehammer method in the PR, sometimes I can literally draw a cutting line through a glyph, deleting everything below it, if I cut a glyph just right...

[madig]

Adding the fs dependency directly is ugly, but specifying fonttools[ufo] instead does not work...

Edit: alternative approach: always depend on fontools[ufo,lxml].