oxideav-scribe 0.1.3

//! Quadratic-Bezier outline flattening.
//!
//! TrueType glyph outlines are sequences of contours, where each contour
//! is a closed loop of *on-curve* and *off-curve* points. The off-curve
//! points are quadratic-Bezier control handles. Two consecutive
//! off-curve points imply an *implicit* on-curve midpoint at their
//! midpoint — the standard TrueType reconstruction rule documented in
//! the Apple TrueType Reference Manual.
//!
//! This module turns a [`oxideav_ttf::TtOutline`] into a flat polyline
//! (`Vec<Vec<(f32, f32)>>`, one inner Vec per contour) at the
//! rasterisation scale. Each Bezier segment is recursively subdivided by
//! the de Casteljau split until the chord length is below a tolerance
//! (we use 0.5 px which is a standard scanline AA threshold).
//!
//! The de Casteljau subdivision for a quadratic Bezier
//! `B(t) = (1-t)^2 P0 + 2(1-t)t P1 + t^2 P2` at `t = 0.5` yields:
//!
//! ```text
//! M01 = (P0 + P1) / 2
//! M12 = (P1 + P2) / 2
//! M = (M01 + M12) / 2
//! left  = (P0, M01, M)
//! right = (M, M12, P2)
//! ```
//!
//! The two halves can be concatenated to reconstruct the full curve;
//! this is the textbook "split + recurse" algorithm.
//!
//! Coordinate convention: TrueType is Y-up with the origin on the
//! baseline; the rasterizer wants Y-down with the origin at the
//! top-left of the glyph bounding box. Conversion is done at flatten
//! time so downstream code never has to think about it.

use oxideav_ttf::TtOutline;

/// Maximum chord length (in raster pixels) we tolerate before splitting
/// a Bezier segment further.
const FLATTEN_TOLERANCE_PX: f32 = 0.5;

/// Hard cap on subdivision depth — guards against pathological control
/// points that would otherwise loop forever in floating-point. A real
/// glyph at sane sizes converges in 4..6 levels; 16 levels gives 65536
/// intermediate samples which is way past anything sensible.
const MAX_SUBDIV_DEPTH: u8 = 16;

/// A flattened glyph outline ready for the scanline rasterizer.
///
/// Coordinates are in raster pixels with the origin at the **top-left**
/// of `bounds`. The `bounds` field is the bounding box used for that
/// translation (in raster pixels, also Y-down).
#[derive(Debug, Clone, Default)]
pub struct FlatOutline {
    pub contours: Vec<Vec<(f32, f32)>>,
    pub bounds: FlatBounds,
}

/// Bounding box of a flattened outline, in raster pixels (Y-down).
#[derive(Debug, Clone, Copy, Default)]
pub struct FlatBounds {
    pub x_min: f32,
    pub y_min: f32,
    pub x_max: f32,
    pub y_max: f32,
}

impl FlatBounds {
    pub fn width(&self) -> f32 {
        (self.x_max - self.x_min).max(0.0)
    }
    pub fn height(&self) -> f32 {
        (self.y_max - self.y_min).max(0.0)
    }
    /// Pixel width rounded up.
    pub fn width_px(&self) -> u32 {
        self.width().ceil() as u32
    }
    /// Pixel height rounded up.
    pub fn height_px(&self) -> u32 {
        self.height().ceil() as u32
    }
}

/// Flatten a TrueType outline at `scale` (raster-pixel-per-font-unit),
/// translating to a Y-down coordinate system with the origin at the
/// top-left of the glyph bounding box.
///
/// Returns `None` for empty outlines (e.g. the space glyph).
pub fn flatten(outline: &TtOutline, scale: f32) -> Option<FlatOutline> {
    flatten_with_shear(outline, scale, 0.0)
}

/// Flatten with an optional horizontal shear. `shear_x_per_y` is the
/// `tan(angle)` value to apply in TT (Y-up) coordinates: each input
/// point at `(x, y)` becomes `(x + shear * y, y)` *before* the
/// raster-down conversion. Used by the rasterizer when synthesising
/// italic for an upright face — see [`crate::style`].
///
/// `shear_x_per_y == 0.0` is identical to [`flatten`].
///
/// The bounding box is recomputed from the actual mapped points (the
/// font's cached bbox is invalid once shear is applied).
pub fn flatten_with_shear(
    outline: &TtOutline,
    scale: f32,
    shear_x_per_y: f32,
) -> Option<FlatOutline> {
    flatten_with_shear_offset(outline, scale, shear_x_per_y, 0.0)
}

/// Flatten with shear AND a horizontal sub-pixel offset (raster-pixel
/// units, applied AFTER scale + Y-flip). The offset shifts every
/// flattened point right by `x_subpixel`, growing the right edge of
/// the bbox by the same amount and leaving the left edge fixed at
/// `floor(x_min)`. The composer queries [`subpixel_offset`] for the
/// fractional X it baked in and uses `floor(pen_x)` as the blit
/// origin so the bitmap lands at the correct fractional position.
///
/// `x_subpixel == 0.0` is bit-identical to [`flatten_with_shear`].
///
/// [`subpixel_offset`]: crate::cache::subpixel_offset
pub fn flatten_with_shear_offset(
    outline: &TtOutline,
    scale: f32,
    shear_x_per_y: f32,
    x_subpixel: f32,
) -> Option<FlatOutline> {
    if outline.contours.is_empty() {
        return None;
    }

    // Without shear: derive bbox from the font's cached bbox. The
    // bitmap LEFT edge is pixel-aligned at `floor(raw.x_min * scale)`
    // and the bitmap WIDTH is `(raw.x_max - raw.x_min).ceil() + 1` so
    // every fractional sub_x slot ends up with the same dimensions
    // (round-3 invariant) and the analytical rightmost
    // partial-coverage column always lands inside the bitmap. The +1 px
    // slack is required by the trapezoidal coverage path at sub_x > 0
    // (and harmless at sub_x = 0 — the rightmost pixel just stays 0).
    let bounds = if shear_x_per_y == 0.0 {
        let raw = outline.bounds?;
        let raw_xmin = raw.x_min as f32 * scale;
        let raw_xmax = raw.x_max as f32 * scale;
        let xmin_aligned = raw_xmin.floor();
        let xmax_aligned = (raw_xmax - xmin_aligned).ceil() + xmin_aligned + 1.0;
        FlatBounds {
            x_min: xmin_aligned,
            y_min: -(raw.y_max as f32) * scale,
            x_max: xmax_aligned,
            y_max: -(raw.y_min as f32) * scale,
        }
    } else {
        // Sheared: compute bbox from the sheared points themselves
        // (the cached font bbox is invalid once shear is applied). The
        // bitmap LEFT edge is pixel-aligned and we leave a 1-px right-
        // hand slack column for the trapezoidal coverage's rightmost
        // partial fill — same rule as the unsheared branch.
        // Importantly, compute the bbox *without* the x_subpixel shift
        // so all sub-pixel slots produce the same dims.
        let mut x_min = f32::INFINITY;
        let mut y_min = f32::INFINITY;
        let mut x_max = f32::NEG_INFINITY;
        let mut y_max = f32::NEG_INFINITY;
        for c in &outline.contours {
            for p in &c.points {
                let (sx, sy) = shear_point(p.x as f32, p.y as f32, shear_x_per_y);
                let rx = sx * scale;
                let ry = -sy * scale;
                x_min = x_min.min(rx);
                y_min = y_min.min(ry);
                x_max = x_max.max(rx);
                y_max = y_max.max(ry);
            }
        }
        if !x_min.is_finite() {
            return None;
        }
        let xmin_aligned = x_min.floor();
        let xmax_aligned = (x_max - xmin_aligned).ceil() + xmin_aligned + 1.0;
        FlatBounds {
            x_min: xmin_aligned,
            y_min,
            x_max: xmax_aligned,
            y_max,
        }
    };

    let mut contours = Vec::with_capacity(outline.contours.len());
    for c in &outline.contours {
        let pts = flatten_contour(&c.points, scale, &bounds, shear_x_per_y, x_subpixel);
        if pts.len() >= 2 {
            contours.push(pts);
        }
    }

    if contours.is_empty() {
        return None;
    }
    Some(FlatOutline { contours, bounds })
}

/// Apply horizontal shear in TT (Y-up) coordinates. Italic-positive y
/// (above the baseline) shifts to the right when `shear_x_per_y > 0`.
#[inline]
fn shear_point(x: f32, y: f32, shear_x_per_y: f32) -> (f32, f32) {
    (x + shear_x_per_y * y, y)
}

/// Apply scale + Y-flip + bounds-relative translation to a single TT
/// point so the result is in raster pixels with origin at top-left of
/// the glyph bbox. Honour an optional horizontal shear (applied in TT
/// Y-up coordinates BEFORE the Y-flip) so synthesised italic produces
/// the visually-expected forward slant. `x_subpixel` is added in
/// raster-X after scaling so sub-pixel positioning shifts the glyph
/// inside its bitmap.
#[inline]
fn map_point(
    x: i16,
    y: i16,
    scale: f32,
    bounds: &FlatBounds,
    shear_x_per_y: f32,
    x_subpixel: f32,
) -> (f32, f32) {
    let (sx, sy) = shear_point(x as f32, y as f32, shear_x_per_y);
    let rx = sx * scale + x_subpixel - bounds.x_min;
    let ry = -sy * scale - bounds.y_min;
    (rx, ry)
}

/// Flatten a single contour (closed loop, mix of on/off-curve points).
///
/// Implements the standard TrueType implicit-on-curve rule: when two
/// off-curve points are adjacent, the implied on-curve midpoint
/// becomes the segment endpoint, then a fresh quadratic continues from
/// it.
/// One ordered point in the rotated contour: (x, y, on-curve flag).
type OrderedPoint = (f32, f32, bool);

fn flatten_contour(
    pts: &[oxideav_ttf::Point],
    scale: f32,
    bounds: &FlatBounds,
    shear_x_per_y: f32,
    x_subpixel: f32,
) -> Vec<(f32, f32)> {
    if pts.is_empty() {
        return Vec::new();
    }
    let n = pts.len();

    // Find a starting on-curve point. If every point is off-curve (rare
    // but legal — Apple's "phantom on-curve" case), synthesise one at
    // the midpoint of pts[0]..pts[1] and rotate.
    let start_idx = pts.iter().position(|p| p.on_curve);
    let (start_xy, ordered): ((f32, f32), Vec<OrderedPoint>) = if let Some(s) = start_idx {
        let mut ord: Vec<OrderedPoint> = Vec::with_capacity(n);
        for i in 0..n {
            let p = pts[(s + i) % n];
            let (x, y) = map_point(p.x, p.y, scale, bounds, shear_x_per_y, x_subpixel);
            ord.push((x, y, p.on_curve));
        }
        let s_xy = (ord[0].0, ord[0].1);
        (s_xy, ord)
    } else {
        // All-off-curve: the start is the midpoint of pts[0]..pts[1].
        let p0 = pts[0];
        let p1 = pts[1 % n];
        let (x0, y0) = map_point(p0.x, p0.y, scale, bounds, shear_x_per_y, x_subpixel);
        let (x1, y1) = map_point(p1.x, p1.y, scale, bounds, shear_x_per_y, x_subpixel);
        let mid = ((x0 + x1) * 0.5, (y0 + y1) * 0.5);
        let mut ord: Vec<OrderedPoint> = Vec::with_capacity(n + 1);
        // Insert the synthetic on-curve start, then walk the original
        // ring in order.
        ord.push((mid.0, mid.1, true));
        for p in pts.iter().take(n) {
            let (x, y) = map_point(p.x, p.y, scale, bounds, shear_x_per_y, x_subpixel);
            ord.push((x, y, p.on_curve));
        }
        (mid, ord)
    };

    let mut prev_was_off = false;
    let mut prev_off_xy: Option<(f32, f32)> = None;
    let mut out: Vec<(f32, f32)> = Vec::with_capacity(ordered.len() * 2);
    out.push(start_xy);

    // Iterate the ordered points (skipping index 0, which is the start
    // we already pushed).
    for &(x, y, on) in ordered.iter().skip(1) {
        if on {
            if prev_was_off {
                // Quadratic from out.last() — well, no: from the segment
                // start point — through prev_off_xy to (x, y).
                let p0 = *out.last().expect("started with start_xy");
                let p1 = prev_off_xy.expect("prev_was_off");
                subdivide_quad(&mut out, p0, p1, (x, y), 0);
                prev_was_off = false;
                prev_off_xy = None;
            } else {
                out.push((x, y));
            }
        } else if prev_was_off {
            // Two off-curve points in a row → implicit on-curve at
            // their midpoint terminates the previous quadratic, and a
            // new one starts.
            let prev_off = prev_off_xy.expect("prev_was_off");
            let mid = ((prev_off.0 + x) * 0.5, (prev_off.1 + y) * 0.5);
            let p0 = *out.last().expect("at least start");
            subdivide_quad(&mut out, p0, prev_off, mid, 0);
            prev_off_xy = Some((x, y));
            // prev_was_off stays true.
        } else {
            prev_was_off = true;
            prev_off_xy = Some((x, y));
        }
    }

    // Close the contour: handle a trailing off-curve point by curving
    // back to the start.
    if prev_was_off {
        let p1 = prev_off_xy.expect("prev_was_off");
        let p0 = *out.last().expect("non-empty");
        subdivide_quad(&mut out, p0, p1, start_xy, 0);
    } else {
        // Ensure the contour explicitly closes — the rasterizer doesn't
        // assume implicit closure.
        if let (Some(&last), first) = (out.last(), start_xy) {
            if (last.0 - first.0).abs() > 1e-3 || (last.1 - first.1).abs() > 1e-3 {
                out.push(start_xy);
            }
        }
    }

    out
}

/// Recursively subdivide a quadratic Bezier (`p0`, `p1`, `p2`) until
/// the chord between `p0` and `p2` is below `FLATTEN_TOLERANCE_PX` *and*
/// the off-curve handle `p1` lies within that tolerance of the chord.
/// Pushes one or more *output* points (excluding `p0`, including `p2`).
fn subdivide_quad(
    out: &mut Vec<(f32, f32)>,
    p0: (f32, f32),
    p1: (f32, f32),
    p2: (f32, f32),
    depth: u8,
) {
    let dx = p2.0 - p0.0;
    let dy = p2.1 - p0.1;
    let chord_sq = dx * dx + dy * dy;
    // Distance from p1 to the chord — perpendicular component of
    // (p1 - p0) projected against the chord normal. We bound this
    // because a tiny chord with a wild control handle still produces a
    // visible bulge.
    let d_pdx = p1.0 - p0.0;
    let d_pdy = p1.1 - p0.1;
    let cross = d_pdx * dy - d_pdy * dx;
    let chord_len = chord_sq.sqrt();
    let perp = if chord_len > 1e-6 {
        (cross / chord_len).abs()
    } else {
        // Degenerate chord: fall back to the direct distance from p0
        // to p1 (which equals "how far the curve might bulge").
        (d_pdx * d_pdx + d_pdy * d_pdy).sqrt()
    };

    if depth >= MAX_SUBDIV_DEPTH
        || (chord_sq <= FLATTEN_TOLERANCE_PX * FLATTEN_TOLERANCE_PX && perp <= FLATTEN_TOLERANCE_PX)
    {
        out.push(p2);
        return;
    }

    // de Casteljau split at t = 0.5.
    let m01 = ((p0.0 + p1.0) * 0.5, (p0.1 + p1.1) * 0.5);
    let m12 = ((p1.0 + p2.0) * 0.5, (p1.1 + p2.1) * 0.5);
    let m = ((m01.0 + m12.0) * 0.5, (m01.1 + m12.1) * 0.5);

    subdivide_quad(out, p0, m01, m, depth + 1);
    subdivide_quad(out, m, m12, p2, depth + 1);
}

// ---- CFF / cubic-Bezier flattening ----------------------------------

/// Flatten a CFF (cubic-Bezier) outline at `scale` (raster pixels per
/// font unit). Coordinate convention matches [`flatten`]: Y-down,
/// origin at the top-left of the glyph bounding box.
///
/// Type 2 charstrings (Adobe TN5177) emit explicit cubic Beziers and
/// `ClosePath` markers, so this implementation is simpler than the
/// quadratic path — there's no on-curve / off-curve dance.
///
/// Returns `None` for empty outlines.
pub fn flatten_cubic(outline: &oxideav_otf::CubicOutline, scale: f32) -> Option<FlatOutline> {
    flatten_cubic_with_shear(outline, scale, 0.0)
}

/// Sheared variant of [`flatten_cubic`]. The Y-flipped Y-down output
/// is post-multiplied by a horizontal shear `[1, shear; 0, 1]` —
/// matches the synthetic-italic transform in `style.rs`.
pub fn flatten_cubic_with_shear(
    outline: &oxideav_otf::CubicOutline,
    scale: f32,
    shear: f32,
) -> Option<FlatOutline> {
    if outline.contours.is_empty() {
        return None;
    }
    // Map the source bbox (Y-up, font units) to raster (Y-down, px).
    // Sheared output's bbox needs to account for points shifted by
    // shear * y; we recompute by walking emitted points below.
    let raw = outline.bounds;
    if raw.x_max <= raw.x_min || raw.y_max <= raw.y_min {
        return None;
    }

    let mut contours: Vec<Vec<(f32, f32)>> = Vec::with_capacity(outline.contours.len());
    let mut x_min = f32::INFINITY;
    let mut y_min = f32::INFINITY;
    let mut x_max = f32::NEG_INFINITY;
    let mut y_max = f32::NEG_INFINITY;

    for contour in &outline.contours {
        let mut pen = (0.0f32, 0.0f32);
        let mut start = (0.0f32, 0.0f32);
        let mut pts: Vec<(f32, f32)> = Vec::new();
        for seg in &contour.segments {
            match *seg {
                oxideav_otf::CubicSegment::MoveTo(p) => {
                    let xy = scribe_map(p.x, p.y, scale, shear);
                    pen = xy;
                    start = xy;
                    pts.push(xy);
                }
                oxideav_otf::CubicSegment::LineTo(p) => {
                    let xy = scribe_map(p.x, p.y, scale, shear);
                    pts.push(xy);
                    pen = xy;
                }
                oxideav_otf::CubicSegment::CurveTo { c1, c2, end } => {
                    let p0 = pen;
                    let p1 = scribe_map(c1.x, c1.y, scale, shear);
                    let p2 = scribe_map(c2.x, c2.y, scale, shear);
                    let p3 = scribe_map(end.x, end.y, scale, shear);
                    subdivide_cubic(&mut pts, p0, p1, p2, p3, 0);
                    pen = p3;
                }
                oxideav_otf::CubicSegment::ClosePath => {
                    if pts.first() != Some(&start) {
                        pts.push(start);
                    } else if let Some(&last) = pts.last() {
                        if (last.0 - start.0).abs() > 1e-3 || (last.1 - start.1).abs() > 1e-3 {
                            pts.push(start);
                        }
                    }
                    if pts.len() >= 2 {
                        for &(x, y) in &pts {
                            x_min = x_min.min(x);
                            y_min = y_min.min(y);
                            x_max = x_max.max(x);
                            y_max = y_max.max(y);
                        }
                        contours.push(std::mem::take(&mut pts));
                    } else {
                        pts.clear();
                    }
                    pen = start;
                }
            }
        }
        // Flush a trailing open subpath (a font that didn't emit a
        // ClosePath before endchar — uncommon but legal).
        if pts.len() >= 2 {
            for &(x, y) in &pts {
                x_min = x_min.min(x);
                y_min = y_min.min(y);
                x_max = x_max.max(x);
                y_max = y_max.max(y);
            }
            contours.push(pts);
        }
    }

    if contours.is_empty() || !x_min.is_finite() {
        return None;
    }

    // Translate so the bbox top-left lands at (0, 0).
    for c in &mut contours {
        for p in c.iter_mut() {
            p.0 -= x_min;
            p.1 -= y_min;
        }
    }
    let bounds = FlatBounds {
        x_min: 0.0,
        y_min: 0.0,
        x_max: x_max - x_min,
        y_max: y_max - y_min,
    };
    // Suppress an unused-variable warning if the bbox sanity check
    // above ever gets relaxed.
    let _ = raw;
    Some(FlatOutline { contours, bounds })
}

/// Apply `scale` + Y-flip + shear to a single CFF point. Note that
/// CFF point coordinates are floats already (the Type 2 interpreter
/// keeps fixed-real precision), so we don't have to round on input.
#[inline]
fn scribe_map(x: f32, y: f32, scale: f32, shear: f32) -> (f32, f32) {
    // y_raster = -y * scale (Y-up → Y-down). The shear is applied
    // post-Y-flip so it matches what the rasterizer expects.
    let rx = x * scale + shear * (-y * scale);
    let ry = -y * scale;
    (rx, ry)
}

/// Recursively subdivide a cubic Bezier (`p0`, `p1`, `p2`, `p3`)
/// using the de Casteljau split at t = 0.5. Pushes output points
/// (excluding `p0`, including `p3`).
///
/// The flatness test is the standard "max of perpendicular
/// distances from c1 / c2 to the chord (p0, p3) is below the
/// tolerance" — see e.g. Hain et al., "Fast, precise flattening of
/// cubic Bezier path and offset curves" (CAGD 2005). This is the
/// same test scribe's quadratic path uses, generalised to two
/// control points.
fn subdivide_cubic(
    out: &mut Vec<(f32, f32)>,
    p0: (f32, f32),
    p1: (f32, f32),
    p2: (f32, f32),
    p3: (f32, f32),
    depth: u8,
) {
    let dx = p3.0 - p0.0;
    let dy = p3.1 - p0.1;
    let chord_sq = dx * dx + dy * dy;
    let chord_len = chord_sq.sqrt();
    let perp = |p: (f32, f32)| -> f32 {
        let dpx = p.0 - p0.0;
        let dpy = p.1 - p0.1;
        let cross = dpx * dy - dpy * dx;
        if chord_len > 1e-6 {
            (cross / chord_len).abs()
        } else {
            (dpx * dpx + dpy * dpy).sqrt()
        }
    };
    let perp1 = perp(p1);
    let perp2 = perp(p2);
    let max_perp = perp1.max(perp2);

    if depth >= MAX_SUBDIV_DEPTH
        || (chord_sq <= FLATTEN_TOLERANCE_PX * FLATTEN_TOLERANCE_PX
            && max_perp <= FLATTEN_TOLERANCE_PX)
    {
        out.push(p3);
        return;
    }

    // de Casteljau split at t = 0.5.
    let q0 = ((p0.0 + p1.0) * 0.5, (p0.1 + p1.1) * 0.5);
    let q1 = ((p1.0 + p2.0) * 0.5, (p1.1 + p2.1) * 0.5);
    let q2 = ((p2.0 + p3.0) * 0.5, (p2.1 + p3.1) * 0.5);
    let r0 = ((q0.0 + q1.0) * 0.5, (q0.1 + q1.1) * 0.5);
    let r1 = ((q1.0 + q2.0) * 0.5, (q1.1 + q2.1) * 0.5);
    let s = ((r0.0 + r1.0) * 0.5, (r0.1 + r1.1) * 0.5);

    subdivide_cubic(out, p0, q0, r0, s, depth + 1);
    subdivide_cubic(out, s, r1, q2, p3, depth + 1);
}

#[cfg(test)]
mod tests {
    use super::*;
    use oxideav_ttf::{BBox, Contour, Point as TtPoint};

    fn outline_from(points: Vec<(i16, i16, bool)>) -> TtOutline {
        let pts: Vec<TtPoint> = points
            .into_iter()
            .map(|(x, y, on)| TtPoint { x, y, on_curve: on })
            .collect();
        let mut x_min = i16::MAX;
        let mut y_min = i16::MAX;
        let mut x_max = i16::MIN;
        let mut y_max = i16::MIN;
        for p in &pts {
            x_min = x_min.min(p.x);
            y_min = y_min.min(p.y);
            x_max = x_max.max(p.x);
            y_max = y_max.max(p.y);
        }
        TtOutline {
            contours: vec![Contour { points: pts }],
            bounds: Some(BBox {
                x_min,
                y_min,
                x_max,
                y_max,
            }),
        }
    }

    #[test]
    fn empty_outline_yields_none() {
        let o = TtOutline::default();
        assert!(flatten(&o, 0.05).is_none());
    }

    #[test]
    fn straight_triangle_round_trips() {
        // Triangle with all on-curve points.
        let o = outline_from(vec![(0, 0, true), (100, 0, true), (50, 100, true)]);
        let f = flatten(&o, 1.0).expect("non-empty outline");
        assert_eq!(f.contours.len(), 1);
        // 3 corner points + closing point = 4.
        assert_eq!(f.contours[0].len(), 4);
    }

    #[test]
    fn quadratic_curve_subdivides() {
        // A "tall" curve from (0, 0) to (100, 0) with control at
        // (50, 100) — visible bulge so subdivision must produce
        // intermediate points.
        let o = outline_from(vec![(0, 0, true), (50, 100, false), (100, 0, true)]);
        let f = flatten(&o, 1.0).expect("non-empty outline");
        // Should produce many intermediate points along the curve.
        assert!(
            f.contours[0].len() > 5,
            "expected subdivided curve, got {} points",
            f.contours[0].len()
        );
    }
}