Round join and all cap styles #414
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| @@ -280,39 280,95 @@ fn flatten_cubic(cubic: Cubic, local_to_device: Transform, offset: f32) { | |||
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| // Flattens the circular arc that subtends the angle begin-center-end. It is assumed that | |||
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It's not obvious from this comment how the direction is chosen. It must be based on the value of angle, but it feels like 'pacman' style arcs will be difficult.
I worry that if n_lines is big, the arc would draw the full way around, but if n_lines is small, it would end up drawing the closing part, rather than the full way around
I'm not sure that this is coherent - my last maths education was many years ago.
Maybe this would only be an issue if n_lines is 1, which is impossible?
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The direction of the arc is always a counter-clockwise rotation starting from begin, towards end, centered at center, and will be subtended by angle (which is assumed to be positive). If angle terminates the arc before it smoothly reaches end, a line will be drawn from the end of the arc towards end. I will document this.
n_lines only depends on the radius of the arc and the chosen tolerance. For n_lines to be theta must be close to acos can't return that by definition. If you somehow got n_lines == 1, basically no arc would be drawn and you'd get a line connecting begin and end.
Realistically, n_lines could be as low as x is very small, which can happen if tol and radius are close to each other (the code prevents radius from being smaller than tol, so that case isn't possible). You'd only get into that situation with a sub-pixel radius. At that scale, the coarseness of the approximation won't be easily noticeable. If you increased the tolerance to make this possible at larger radii, with n_lines == 2 you'd get a shape resembling a wedge/triangle (I tested this locally, which works as you'd expect).
That said, this function is meant for drawing caps and joins where anglebegin, center, and end points are chosen carefully (so that the angle and winding make sense).
Though there is something that should get fixed: I think selecting 1u when theta <= EPS is the wrong thing to do and this is a bug. That happens when the subdivision count tends to infinity. It's probably better to define a MAX_LINES and return that instead.
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To illustrate what I mean, here is what the code draws if I center the center of a round join directly below the join control point and hardcode an angle of
n_lines == 1:
n_lines == 2:
n_lines == 3:
n_lines == 6:
n_lines == 100:
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Thanks for the very detailed reply!
I hadn't clocked the additional invariants being maintained by the callers
Those pictures are very cool as well!
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I'm glad they were helpful 🙂. I updated the comment above flatten_arc in latest commit.
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Rather than using the `Cubic` struct, the flattening helpers operate on `CubicPts`, path index, and parallel curve offset directly. The older stroke bbox computation was removed since it's no longer used.
Implemented the logic for round join and cap styles. The logic generates lines directly from a circular arc. The arc gets flattened in the curve's local coordinate space and transformed to device-space coordinates post-flattening (just like strokes work in `flatten_arc`). An advantage of flattening an arc directly is that the logic is very simple and involves way less ALU compared to `flatten_cubic`. The disadvantage is that the structure of join/cap style handling is now highly divergent. To reduce divergence, the shader could be restructured to model a (not perfectly circular) arc with cubic Beziers and let the control flow converge at a call to `flatten_cubic`.
Implement butt/square/round start and end cap styles
If the segment angle falls below epsilon, return MAX_LINES instead of 1u for the line segment count. Total number of lines per arc is now capped at 1000.
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Clarified the function's behavior and input invariants
Implemented the logic for round join and cap styles. The logic generates lines directly from a circular arc. The arc gets flattened in the curve's local coordinate space and gets transformed to device-space coordinates post-flattening.
This completes the initial implementation of all stroke styles. This PR is based on #412.
#303