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kui_core/
line.rs

1//! Strokes: what a `line` node draws.
2//!
3//! A line is a run of points and a [`Stroke`]; the core flattens a curve
4//! into a polyline here, boxes the run, and emits one
5//! [`crate::QuadKind::Segment`] per straight piece. The points live in a
6//! per-frame list beside the tree — rebuilt every frame, capacities kept —
7//! and a node refers to its run by [`LineId`] the way a text node refers to
8//! the frame's text list. The previous frame's list is kept by the same
9//! gated buffer swap the text list uses, so a departing line can copy its
10//! points out for its ghost.
11
12use crate::color::Color;
13use crate::geom::{Rect, Vec2};
14use crate::retain::Kept;
15
16/// Index into the frame's line list.
17#[derive(Clone, Copy, Debug, PartialEq, Eq)]
18pub struct LineId(pub u32);
19
20/// How a `line` is drawn: a width, a colour, and whether the points are
21/// the corners of a polyline or the knots of a curve through them.
22#[derive(Clone, Copy, Debug, PartialEq)]
23pub struct Stroke {
24    /// Stroke width in logical px. Round caps at both ends of every
25    /// segment, which is also the join between two of them.
26    pub width: f32,
27    /// The stroke colour. Inside the core it rides in the node's `bg`
28    /// slot, so a `transition` eases it and `enter` / `exit` can start
29    /// or end it there.
30    pub color: Color,
31    /// Draw a smooth curve *through* the points (a centripetal Catmull-Rom
32    /// spline, flattened by [`flatten_curve`]) instead of the polyline. Two
33    /// points are a straight segment either way.
34    pub curve: bool,
35    /// The marks and gaps the stroke is cut into; [`Dash::SOLID`], the
36    /// default, is none.
37    pub dash: Dash,
38}
39
40impl Stroke {
41    pub fn new(width: f32, color: Color) -> Self {
42        Self {
43            width,
44            color,
45            curve: false,
46            dash: Dash::SOLID,
47        }
48    }
49
50    pub fn curve(mut self) -> Self {
51        self.curve = true;
52        self
53    }
54
55    /// Cuts the stroke into marks `on` long with gaps `off` long between
56    /// them; see [`Dash`].
57    pub fn dash(mut self, on: f32, off: f32) -> Self {
58        self.dash = Dash {
59            offset: self.dash.offset,
60            ..Dash::new(on, off)
61        };
62        self
63    }
64
65    /// The whole pattern at once, for a dash-dot or one read from data.
66    pub fn dashed(mut self, dash: Dash) -> Self {
67        self.dash = dash;
68        self
69    }
70
71    /// How far into the pattern the stroke starts; see [`Dash::offset`].
72    pub fn dash_offset(mut self, offset: f32) -> Self {
73        self.dash.offset = offset;
74        self
75    }
76}
77
78/// A stroke's dash pattern (backlog V2): a mark, a gap, a second mark and
79/// a second gap, repeated along the stroke's length from its first point.
80///
81/// The lengths are the ones **seen**, in logical px. Every mark is
82/// round-capped, as the stroke itself is, so a mark `on` long is drawn as
83/// a capsule whose centre line is `on − width` long, and a mark no longer
84/// than the stroke is wide is a dot. (SVG's `stroke-dasharray` measures
85/// the centre line instead, which with a round cap makes `4 4` at a width
86/// of 4 a solid line; this pattern at any width is SVG's
87/// `on − width, off + width`.) The first mark's cap sits where a solid
88/// stroke's would, half the width before the first point.
89///
90/// The pattern runs along the arc length of the whole stroke, so it keeps
91/// its phase across the corners of a polyline and the pieces of a curve;
92/// on a `path` it restarts at every subpath, as SVG's does.
93#[derive(Clone, Copy, Debug, PartialEq)]
94pub struct Dash {
95    /// Mark, gap, mark, gap. A two-length pattern is the same pair twice.
96    pub pattern: [f32; 4],
97    /// How far into the pattern the stroke starts, in logical px: growing
98    /// it moves the marks towards the stroke's first point, which is what
99    /// a marquee's marching ants are. Any number; it wraps.
100    pub offset: f32,
101}
102
103impl Default for Dash {
104    fn default() -> Self {
105        Dash::SOLID
106    }
107}
108
109/// What a dashed stroke is cut by: the centre-line lengths of the
110/// pattern's four entries — mark, gap, mark, gap — and where in it the
111/// stroke starts, `0 <= offset < period`. Logical px.
112#[derive(Clone, Copy, Debug, PartialEq)]
113pub struct Cut {
114    pub lens: [f32; 4],
115    pub offset: f32,
116}
117
118impl Cut {
119    pub fn period(&self) -> f32 {
120        self.lens.iter().sum()
121    }
122
123    /// Whether a mark and its gap come to less than `min` together, on
124    /// average: a pattern that fine reads as a tint, and is drawn solid.
125    pub fn finer_than(&self, min: f32) -> bool {
126        let pair = self.period() * 0.5;
127        pair.is_nan() || pair < min
128    }
129
130    /// The pattern as one number, for a mask's key and for telling a
131    /// pattern that moved from one that held.
132    pub(crate) fn hash(&self) -> u64 {
133        let [a, b, c, d] = self.lens.map(|l| u64::from(l.to_bits()));
134        let mut h = a ^ b.rotate_left(16) ^ c.rotate_left(32) ^ d.rotate_left(48);
135        h = h.wrapping_mul(0x0000_0100_0000_01b3) ^ u64::from(self.offset.to_bits());
136        h.wrapping_mul(0x0000_0100_0000_01b3)
137    }
138}
139
140/// The most marks one stroke is cut into; a pattern that would make more
141/// — a period of a pixel along a line no screen is long enough for —
142/// draws solid, which is what it would read as.
143pub const MAX_MARKS: usize = 16384;
144
145impl Dash {
146    /// No dashes: the stroke unbroken.
147    pub const SOLID: Dash = Dash {
148        pattern: [0.0; 4],
149        offset: 0.0,
150    };
151
152    /// Marks `on` long with gaps `off` long between them.
153    pub fn new(on: f32, off: f32) -> Self {
154        Dash {
155            pattern: [on, off, on, off],
156            offset: 0.0,
157        }
158    }
159
160    /// The pattern as the bindings spell it: one length (marks and gaps
161    /// alike), two (a mark and a gap) or four (a mark, a gap, a second
162    /// mark, a second gap — a dash-dot). None for any other count.
163    pub fn of(lengths: &[f32]) -> Option<Self> {
164        let pattern = match *lengths {
165            [a] => [a, a, a, a],
166            [a, b] => [a, b, a, b],
167            [a, b, c, d] => [a, b, c, d],
168            _ => return None,
169        };
170        Some(Dash {
171            pattern,
172            offset: 0.0,
173        })
174    }
175
176    /// [`Self::offset`] set.
177    pub fn offset(mut self, offset: f32) -> Self {
178        self.offset = offset;
179        self
180    }
181
182    /// Whether the pattern leaves the stroke unbroken: no gap in it, or a
183    /// length that is not a number.
184    pub fn is_solid(&self) -> bool {
185        self.cut(0.0).is_none()
186    }
187
188    /// The pattern as centre-line lengths for a stroke `width` wide, or
189    /// None for one that draws solid: a length that is not finite, or no
190    /// gap anywhere. Negative lengths are zero, and a pair that is zero
191    /// altogether is the other pair.
192    #[inline]
193    pub fn cut(&self, width: f32) -> Option<Cut> {
194        // The solid stroke, which is nearly every stroke, is told by its
195        // zeroes and pays for nothing below (backlog C52).
196        if self.pattern == Dash::SOLID.pattern {
197            return None;
198        }
199        self.cut_pattern(width)
200    }
201
202    #[cold]
203    #[inline(never)]
204    fn cut_pattern(&self, width: f32) -> Option<Cut> {
205        if !self.pattern.iter().all(|l| l.is_finite()) || !self.offset.is_finite() {
206            return None;
207        }
208        let [a, b, c, d] = self.pattern.map(|l| l.max(0.0));
209        if b <= 0.0 && d <= 0.0 {
210            return None;
211        }
212        let (first, second) = match (a + b > 0.0, c + d > 0.0) {
213            (true, true) => ([a, b], [c, d]),
214            (true, false) => ([a, b], [a, b]),
215            (false, _) => ([c, d], [c, d]),
216        };
217        let w = width.max(0.0);
218        // The mark's caps are part of what is seen, so they come out of
219        // its centre line and go into the gap's.
220        let centre = |[on, off]: [f32; 2]| {
221            let mark = (on - w).max(0.0);
222            [mark, on + off - mark]
223        };
224        let ([m0, g0], [m1, g1]) = (centre(first), centre(second));
225        let lens = [m0, g0, m1, g1];
226        let period: f32 = lens.iter().sum();
227        Some(Cut {
228            lens,
229            offset: self.offset.rem_euclid(period),
230        })
231    }
232}
233
234impl Cut {
235    /// Calls `mark(from, to)` for every mark along the polyline `points`,
236    /// in order — a mark that turns a corner is one call per piece it
237    /// lies on, meeting at the corner, and a dot is a call with both ends
238    /// the same. False, with nothing called, for a stroke that draws
239    /// solid instead: a pattern [`Self::finer_than`] `min`, more than
240    /// [`MAX_MARKS`] marks, or a length that is zero or not finite.
241    pub fn marks(&self, points: &[Vec2], min: f32, mut mark: impl FnMut(Vec2, Vec2)) -> bool {
242        let period = self.period();
243        let piece = |pair: &[Vec2]| (pair[1].x - pair[0].x).hypot(pair[1].y - pair[0].y);
244        let total: f32 = points.windows(2).map(piece).sum();
245        // Two marks a period; `!(..)` so a NaN draws solid too.
246        let marks = total / period * 2.0;
247        // A stroke of no length has no mark to lie on and is the dot its
248        // solid one is (RG116).
249        if self.finer_than(min) || marks.is_nan() || marks > MAX_MARKS as f32 || total <= 0.0 {
250            return false;
251        }
252        // Where the stroke starts in the pattern: the entry and what is
253        // left of it.
254        let (mut i, mut left) = (0, self.lens[0]);
255        let mut skip = self.offset;
256        while skip >= left && skip > 0.0 {
257            skip -= left;
258            i = (i + 1) & 3;
259            left = self.lens[i];
260        }
261        left -= skip;
262        // A mark that ended exactly on a corner has been drawn up to it;
263        // the entry after it starts on the next piece.
264        for pair in points.windows(2) {
265            let len = piece(pair);
266            if len <= 0.0 {
267                continue;
268            }
269            let (a, b) = (pair[0], pair[1]);
270            let at = |s: f32| {
271                let t = s / len;
272                Vec2::new(a.x + (b.x - a.x) * t, a.y + (b.y - a.y) * t)
273            };
274            let mut pos = 0.0;
275            loop {
276                let take = left.min(len - pos);
277                if i & 1 == 0 {
278                    mark(at(pos), at(pos + take));
279                }
280                pos += take;
281                left -= take;
282                if left > 0.0 {
283                    break;
284                }
285                i = (i + 1) & 3;
286                left = self.lens[i];
287                // The piece is used up: what starts here starts on the
288                // next one, except a dot, which has nowhere else to be
289                // when this is the last.
290                if pos >= len && left > 0.0 {
291                    break;
292                }
293            }
294        }
295        true
296    }
297}
298
299/// One stroke's run in the frame's point list. The points are stored
300/// relative to the node's box, so a node that eases or slides carries
301/// them along.
302#[derive(Clone, Copy, Debug, PartialEq)]
303pub(crate) struct Run {
304    pub first: u32,
305    pub len: u32,
306    /// Logical px.
307    pub width: f32,
308    /// What cuts the stroke into marks; None for a solid one.
309    pub dash: Option<Cut>,
310}
311
312/// The frame's strokes, and the previous frame's while an `exit` needs it.
313#[derive(Default)]
314pub struct LineStore {
315    runs: Kept<Run>,
316    points: Kept<Vec2>,
317}
318
319/// How far a stroke's box extends past its points: half the width, plus
320/// two logical px so a backend's edge ramp (`AA` = 0.75 physical px each
321/// side, sampled at pixel centres) is never cut by the quad, at scale 1
322/// included.
323pub(crate) fn pad(width: f32) -> f32 {
324    width.max(0.0) * 0.5 + 2.0
325}
326
327/// A curve span is flattened into one piece per this many logical px of
328/// chord, at least one and at most [`CURVE_MAX_PIECES`]. Fixed rather than
329/// tolerance-driven so the piece count is a function of the declared
330/// geometry alone — every binding gets the same segments, and the
331/// conformance corpus can pin them.
332pub const CURVE_STEP: f32 = 6.0;
333pub const CURVE_MAX_PIECES: usize = 32;
334
335impl LineStore {
336    /// Starts a frame. `keep_prev` retains the list just finished so a
337    /// departing line's ghost can copy its points out of it.
338    pub(crate) fn begin_frame(&mut self, keep_prev: bool) {
339        self.runs.begin(keep_prev);
340        self.points.begin(keep_prev);
341    }
342
343    /// Adds a stroke through `points` (parent-box coordinates): flattens a
344    /// curve, boxes the run, and stores the points relative to the box.
345    /// Returns the id and the box, or None for fewer than two points,
346    /// which draw nothing.
347    pub(crate) fn push(&mut self, points: &[Vec2], stroke: &Stroke) -> Option<(LineId, Rect)> {
348        if points.len() < 2 {
349            return None;
350        }
351        let first = self.points.len();
352        if stroke.curve && points.len() > 2 {
353            flatten_curve(points, &mut self.points);
354        } else {
355            self.points.extend_from_slice(points);
356        }
357        let run = &mut self.points[first..];
358        let (mut min, mut max) = (run[0], run[0]);
359        for p in run.iter() {
360            min.x = min.x.min(p.x);
361            min.y = min.y.min(p.y);
362            max.x = max.x.max(p.x);
363            max.y = max.y.max(p.y);
364        }
365        let pad = pad(stroke.width);
366        let origin = Vec2::new(min.x - pad, min.y - pad);
367        for p in run.iter_mut() {
368            p.x -= origin.x;
369            p.y -= origin.y;
370        }
371        let rect = Rect::new(
372            origin.x,
373            origin.y,
374            max.x - min.x + 2.0 * pad,
375            max.y - min.y + 2.0 * pad,
376        );
377        let id = LineId(self.runs.len() as u32);
378        self.runs.push(Run {
379            first: first as u32,
380            len: (self.points.len() - first) as u32,
381            width: stroke.width,
382            dash: stroke.dash.cut(stroke.width),
383        });
384        Some((id, rect))
385    }
386
387    /// This frame's run: its width and its points, relative to the node.
388    pub(crate) fn run(&self, id: LineId) -> (Run, &[Vec2]) {
389        let run = self.runs[id.0 as usize];
390        (
391            run,
392            &self.points[run.first as usize..(run.first + run.len) as usize],
393        )
394    }
395
396    /// The same, read from the previous frame's list (a departing line's
397    /// id indexes that list, not this frame's). Empty for an id the kept
398    /// frame does not have, which cannot happen while `begin_frame` keeps
399    /// the two in step.
400    pub(crate) fn prev_run(&self, id: LineId) -> (Run, &[Vec2]) {
401        match self.runs.prev().get(id.0 as usize) {
402            Some(run) => (
403                *run,
404                &self.points.prev()[run.first as usize..(run.first + run.len) as usize],
405            ),
406            None => (
407                Run {
408                    first: 0,
409                    len: 0,
410                    width: 0.0,
411                    dash: None,
412                },
413                &[],
414            ),
415        }
416    }
417
418    /// Runs this frame.
419    pub fn len(&self) -> usize {
420        self.runs.len()
421    }
422
423    pub fn is_empty(&self) -> bool {
424        self.runs.is_empty()
425    }
426}
427
428/// Flattens a **centripetal** Catmull-Rom spline through `knots` (at least
429/// three) into `out`, starting at the first knot and ending at the last.
430/// Each span is cut into `ceil(chord / CURVE_STEP)` pieces, clamped to
431/// `1..=CURVE_MAX_PIECES`.
432///
433/// Centripetal means the spline's knot parameter advances by the square
434/// root of each chord instead of by 1. A *uniform*
435/// spline — the textbook one, and what this was until it drew a mind
436/// map — ignores how far apart its knots are, so knots that are close
437/// together get as much parameter as knots that are far apart, and the
438/// curve has to move fast through the tight ones. On an elbow (a long run,
439/// then a sharp turn) that shows up as a bow out of the wrong side of the
440/// corner; on knots spaced unevenly enough it becomes a cusp or a loop,
441/// which a centripetal span provably never has. It bows less
442/// too, though it is not overshoot-free: a spline that must pass *through*
443/// a corner has to lean into it. A shape that should only be *pulled*
444/// towards its middle points is a Bézier, and the caller samples one
445/// (`examples/rust/widgets/line.rs`).
446///
447/// The end knots are not doubled — a repeated knot is a zero-length chord,
448/// which centripetal has no parameter for. Each end gets a mirrored
449/// phantom instead (`2·p1 − p2`), which spaces evenly and leaves the first
450/// span's tangent along its own chord. A coincident pair of *real* knots
451/// takes the same branch, so a duplicated point in a caller's list stays a
452/// harmless kink rather than a division by zero.
453///
454/// The chords are rolled forward rather than recomputed, so a span costs
455/// two square roots and not six; `frame_1k_curves` is the bench that
456/// watches the rest of it.
457pub fn flatten_curve(knots: &[Vec2], out: &mut Vec<Vec2>) {
458    let n = knots.len();
459    if n < 2 {
460        return;
461    }
462    out.push(knots[0]);
463    // This span's chord and its knot step (√chord), and the span before's:
464    // a zero chord means there is no neighbour on that side, either
465    // because the run ends there or because the two knots coincide.
466    let (mut prev, mut prev_step) = (0.0, 0.0);
467    let (mut chord, mut step) = chord_and_step(knots[0], knots[1]);
468    for i in 0..n - 1 {
469        let (p1, p2) = (knots[i], knots[i + 1]);
470        let (next, next_step) = match knots.get(i + 2) {
471            Some(&p) => chord_and_step(p2, p),
472            None => (0.0, 0.0),
473        };
474        let pieces = ((chord / CURVE_STEP).ceil() as usize).clamp(1, CURVE_MAX_PIECES);
475        if chord == 0.0 {
476            // Nothing to parameterize: the span is a point.
477            out.push(p2);
478        } else {
479            let mirror = |p: Vec2, q: Vec2| Vec2::new(2.0 * p.x - q.x, 2.0 * p.y - q.y);
480            let (p0, s0) = match prev > 0.0 {
481                true => (knots[i - 1], prev_step),
482                false => (mirror(p1, p2), step),
483            };
484            let (p3, s2) = match next > 0.0 {
485                true => (knots[i + 2], next_step),
486                false => (mirror(p2, p1), step),
487            };
488            // Knot times: 0, then one step per span.
489            let span = Span::new([p0, p1, p2, p3], [0.0, s0, s0 + step, s0 + step + s2]);
490            for k in 1..pieces {
491                out.push(span.at(s0 + step * (k as f32 / pieces as f32)));
492            }
493            // The knot itself rather than the evaluation at its time, so
494            // the run passes through it bit for bit whatever the
495            // arithmetic rounds to.
496            out.push(p2);
497        }
498        (prev, prev_step) = (chord, step);
499        (chord, step) = (next, next_step);
500    }
501}
502
503/// A span's length and the parameter it is worth: `√chord` is Lee's
504/// α = ½, the centripetal one. α = 0 would be `1.0` (uniform) and α = 1
505/// the chord itself (chordal).
506fn chord_and_step(a: Vec2, b: Vec2) -> (f32, f32) {
507    let chord = ((b.x - a.x).powi(2) + (b.y - a.y).powi(2)).sqrt();
508    (chord, chord.sqrt())
509}
510
511/// One span of the spline, evaluated between `p[1]` and `p[2]` by Barry
512/// and Goldman's pyramid: three interpolations of the knots in their own
513/// times, then two of those, then one. Written this way rather than as a
514/// cubic in `t` because the times are no longer evenly spaced.
515///
516/// A span is built once and asked for every piece, because the pyramid's
517/// five distinct denominators are the same five numbers each time. They
518/// are reciprocals, so `at(t[2])` is only *nearly* `p[2]` — the caller
519/// pushes the knot itself instead of asking for it.
520struct Span {
521    p: [Vec2; 4],
522    t: [f32; 4],
523    /// `1/(t[1]-t[0])`, `1/(t[2]-t[1])`, `1/(t[3]-t[2])`, `1/(t[2]-t[0])`,
524    /// `1/(t[3]-t[1])`, in the order the pyramid needs them.
525    inv: [f32; 5],
526}
527
528impl Span {
529    fn new(p: [Vec2; 4], t: [f32; 4]) -> Self {
530        let inv = [
531            1.0 / (t[1] - t[0]),
532            1.0 / (t[2] - t[1]),
533            1.0 / (t[3] - t[2]),
534            1.0 / (t[2] - t[0]),
535            1.0 / (t[3] - t[1]),
536        ];
537        Span { p, t, inv }
538    }
539
540    fn at(&self, u: f32) -> Vec2 {
541        let (p, t) = (&self.p, &self.t);
542        let blend = |a: Vec2, b: Vec2, ta: f32, inv: f32| {
543            let w = (u - ta) * inv;
544            Vec2::new(a.x + (b.x - a.x) * w, a.y + (b.y - a.y) * w)
545        };
546        let a1 = blend(p[0], p[1], t[0], self.inv[0]);
547        let a2 = blend(p[1], p[2], t[1], self.inv[1]);
548        let a3 = blend(p[2], p[3], t[2], self.inv[2]);
549        let b1 = blend(a1, a2, t[0], self.inv[3]);
550        let b2 = blend(a2, a3, t[1], self.inv[4]);
551        blend(b1, b2, t[1], self.inv[1])
552    }
553}
554
555#[cfg(test)]
556mod tests {
557    use super::*;
558
559    #[test]
560    fn a_curve_passes_through_its_knots_and_ends_where_they_end() {
561        let knots = [
562            Vec2::new(0.0, 0.0),
563            Vec2::new(30.0, 40.0),
564            Vec2::new(60.0, 0.0),
565        ];
566        let mut out = Vec::new();
567        flatten_curve(&knots, &mut out);
568        assert_eq!(out[0], knots[0]);
569        assert_eq!(*out.last().unwrap(), knots[2]);
570        // Chord 50 → 9 pieces per span, 1 + 9 + 9 points.
571        assert_eq!(out.len(), 19);
572        assert_eq!(out[9], knots[1]);
573    }
574
575    /// How sharply the run doubles back, worst piece, in degrees. A
576    /// smoothly flattened curve turns a few degrees a piece; a cusp turns
577    /// most of the way round.
578    fn worst_turn(pts: &[Vec2]) -> f32 {
579        pts.windows(3).fold(0.0f32, |worst, w| {
580            let (a, b) = (
581                Vec2::new(w[1].x - w[0].x, w[1].y - w[0].y),
582                Vec2::new(w[2].x - w[1].x, w[2].y - w[1].y),
583            );
584            let len = |v: Vec2| (v.x * v.x + v.y * v.y).sqrt();
585            let (la, lb) = (len(a), len(b));
586            if la < 1e-6 || lb < 1e-6 {
587                return worst;
588            }
589            let cos = ((a.x * b.x + a.y * b.y) / (la * lb)).clamp(-1.0, 1.0);
590            worst.max(cos.acos().to_degrees())
591        })
592    }
593
594    /// Whether any two non-adjacent pieces of the run cross.
595    fn ties_a_loop(pts: &[Vec2]) -> bool {
596        let side =
597            |a: Vec2, b: Vec2, c: Vec2| (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
598        (0..pts.len() - 1).any(|i| {
599            (i + 2..pts.len() - 1).any(|j| {
600                let (a, b, c, d) = (pts[i], pts[i + 1], pts[j], pts[j + 1]);
601                side(a, b, c) * side(a, b, d) < 0.0 && side(c, d, a) * side(c, d, b) < 0.0
602            })
603        })
604    }
605
606    /// The reason the parameterization is centripetal and not uniform.
607    /// Chords 671, 36 and 328: a knot pair nineteen times tighter than its
608    /// neighbours. A uniform parameter hands that 36px chord as much curve
609    /// as the 671px one, and the middle span has to tie a loop to spend
610    /// it — at `CURVE_STEP`'s own sampling, one crossing and a piece that
611    /// turns 95°. Centripetal spends parameter by `√chord`, so the tight
612    /// pair is just a corner.
613    #[test]
614    fn a_tight_knot_between_two_long_ones_neither_loops_nor_cusps() {
615        let knots = [
616            Vec2::new(0.0, 400.0),
617            Vec2::new(600.0, 100.0),
618            Vec2::new(630.0, 80.0),
619            Vec2::new(560.0, 400.0),
620        ];
621        let mut out = Vec::new();
622        flatten_curve(&knots, &mut out);
623        assert!(!ties_a_loop(&out), "the run crosses itself");
624        assert!(worst_turn(&out) < 45.0, "cusp: {:.1}°", worst_turn(&out));
625    }
626
627    /// A caller's list may repeat a point — a mind map with two cards at
628    /// the same place, a path snapped to a grid. The mirrored phantom
629    /// covers it: a zero chord has no `√chord` to divide by, and every
630    /// point that comes back is a number.
631    #[test]
632    fn a_repeated_knot_is_a_kink_and_not_a_division_by_zero() {
633        let knots = [
634            Vec2::new(0.0, 0.0),
635            Vec2::new(40.0, 0.0),
636            Vec2::new(40.0, 0.0),
637            Vec2::new(40.0, 40.0),
638            Vec2::new(80.0, 40.0),
639        ];
640        let mut out = Vec::new();
641        flatten_curve(&knots, &mut out);
642        assert!(out.iter().all(|p| p.x.is_finite() && p.y.is_finite()));
643        assert_eq!(out[0], knots[0]);
644        assert_eq!(*out.last().unwrap(), knots[4]);
645    }
646
647    #[test]
648    fn two_points_are_one_segment_even_as_a_curve() {
649        let mut store = LineStore::default();
650        let (id, rect) = store
651            .push(
652                &[Vec2::new(10.0, 10.0), Vec2::new(50.0, 40.0)],
653                &Stroke::new(2.0, Color::WHITE).curve(),
654            )
655            .unwrap();
656        let (run, pts) = store.run(id);
657        assert_eq!(run.len, 2);
658        assert_eq!(run.width, 2.0);
659        // Padded by half the width plus two: the box starts at (7, 7).
660        assert_eq!((rect.x, rect.y, rect.w, rect.h), (7.0, 7.0, 46.0, 36.0));
661        assert_eq!(pts[0], Vec2::new(3.0, 3.0));
662        assert_eq!(pts[1], Vec2::new(43.0, 33.0));
663    }
664
665    #[test]
666    fn one_point_draws_nothing() {
667        let mut store = LineStore::default();
668        assert!(
669            store
670                .push(&[Vec2::new(1.0, 1.0)], &Stroke::new(1.0, Color::WHITE))
671                .is_none()
672        );
673    }
674
675    #[test]
676    fn the_previous_frame_is_kept_only_when_asked() {
677        let mut store = LineStore::default();
678        let (id, _) = store
679            .push(
680                &[Vec2::new(0.0, 0.0), Vec2::new(4.0, 0.0)],
681                &Stroke::new(1.0, Color::WHITE),
682            )
683            .unwrap();
684        store.begin_frame(true);
685        assert_eq!(store.prev_run(id).0.len, 2);
686        assert!(store.is_empty());
687        store.begin_frame(false);
688        assert_eq!(store.prev_run(id).0.len, 0);
689    }
690}