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Published 20 hours ago • verified publisher icon googlefonts

Handle cusps

Open behdad opened this issue 9 years ago • 2 comments

If any of the curves have a cusp, we should chop at the cusp and convert sides separately.

behdad avatar Nov 24 '15 19:11 behdad

Cusps are where the curve tangent falls to zero. That is, when dx/dt=0 and dy/dt=0. Each of those either has 0, 1, or 2 solutions in the [0,1] range, OR is zero for all values of t. So, the case where both are zero can have 0, 1, 2, or infinitely many solutions. The infinitely-many solution is when the curve is a single point. We can ignore that. For the cases of 1 or 2 cusps, we should just break the curve there. In fact, we should break the curves if any of the master curves has a cusp.

This is extremely unlikely to happen in real fonts though.

behdad avatar Dec 04 '15 05:12 behdad

For the cases of 1 or 2 cusps, we should just break the curve there.

The case of 2 cusps can only happen if the curve is degenerate, ie. a line.

behdad avatar Jun 20 '20 22:06 behdad