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refactor(doc): move live.rs items to live/{blend_spec,envelope,expand,mesh,warp}.rs

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aiongg
2026-10-26 21:17:08 +00:00
parent d63c01628d
commit f5f430a56e
6 changed files with 1969 additions and 1924 deletions
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crates/doc/src/live.rs
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crates/doc/src/live/blend_spec.rs
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use super::*;
// =====================================================================================
// Data
// =====================================================================================
/// Blend Options → Spacing.
#[derive(Clone, Copy, Debug, Default, PartialEq, Serialize, Deserialize)]
#[serde(rename_all = "camelCase")]
pub enum BlendSpacing {
/// Step count chosen from the colour difference (or the distance when colours match).
#[default]
SmoothColor,
/// Specified number of steps between each pair of key objects (1–1000).
Steps(u32),
/// Specified distance (pt) between the steps.
Distance(f64),
}
/// Blend Options → Orientation.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Serialize, Deserialize)]
#[serde(rename_all = "camelCase")]
pub enum BlendOrientation {
#[default]
AlignToPage,
AlignToPath,
}
/// Distribution of blend steps, as offered by the Blend panel's Type menu.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Serialize, Deserialize)]
#[serde(rename_all = "camelCase")]
pub enum BlendEaseType {
#[default]
In,
Out,
InOut,
OutIn,
}
impl BlendEaseType {
pub fn id(self) -> &'static str {
match self {
Self::In => "easeIn",
Self::Out => "easeOut",
Self::InOut => "easeInOut",
Self::OutIn => "easeOutIn",
}
}
}
/// Blend panel Type and Ramp. Ramp is a fraction from 0 (even) to 1.
#[derive(Clone, Copy, Debug, Default, PartialEq, Serialize, Deserialize)]
pub struct BlendEase {
#[serde(default)]
pub kind: BlendEaseType,
#[serde(default, deserialize_with = "blend_ramp")]
pub ramp: f64,
}
impl BlendEase {
pub fn is_linear(&self) -> bool {
self.ramp <= 0.0
}
/// Only the default Type and Ramp can be omitted without losing a chosen Type at Ramp 0.
pub fn is_default(&self) -> bool {
self.kind == BlendEaseType::In && self.ramp == 0.0
}
/// A monotone polynomial distribution, blended with even spacing by Ramp. Public help
/// describes the four distributions, not their numeric curves; these curves are original.
pub fn apply(&self, u: f64) -> f64 {
let u = if u.is_finite() { u.clamp(0.0, 1.0) } else { 0.0 };
let r = if self.ramp.is_finite() { self.ramp.clamp(0.0, 1.0) } else { 0.0 };
let eased = match self.kind {
BlendEaseType::In => u * u,
BlendEaseType::Out => u * (2.0 - u),
BlendEaseType::InOut => u * u * (3.0 - 2.0 * u),
BlendEaseType::OutIn if u < 0.5 => 2.0 * u * (1.0 - u),
BlendEaseType::OutIn => 0.5 + 2.0 * (u - 0.5) * (u - 0.5),
};
u + r * (eased - u)
}
}
#[derive(Clone, Debug, Default, PartialEq, Serialize, Deserialize)]
pub struct BlendSpec {
#[serde(default)]
pub spacing: BlendSpacing,
#[serde(default)]
pub orientation: BlendOrientation,
/// Acceleration of the steps' shapes and positions along the spine between two keys.
#[serde(default, skip_serializing_if = "BlendEase::is_default")]
pub ease: BlendEase,
/// Independent color acceleration. -100..100, with 0 preserving the even color ramp.
#[serde(default, rename = "colorShift", skip_serializing_if = "is_zero", deserialize_with = "blend_color_shift")]
pub color_shift: f64,
/// Replaced spine. `None` = the straight lines between the key objects' centres.
#[serde(default, skip_serializing_if = "Option::is_none")]
pub spine: Option<PathData>,
/// The anchor of the spine's first subpath each key object sits on (a spine edited on the
/// canvas: moving a key moves its anchor and the other way round). Empty: the keys spread
/// evenly along the spine by arc length (Replace Spine).
#[serde(default, rename = "keyAnchors", skip_serializing_if = "Vec::is_empty")]
pub key_anchors: Vec<u32>,
/// Per key object, the anchor of its first subpath the blend starts from (Blend tool clicks
/// on anchor points); `None`: chosen so closed shapes don't twist.
#[serde(default, skip_serializing_if = "Vec::is_empty")]
pub starts: Vec<Option<u32>>,
}
impl BlendSpec {
/// The start anchor of key `i` (see [`Self::starts`]).
pub fn start(&self, i: usize) -> Option<usize> {
self.starts.get(i).copied().flatten().map(|a| a as usize)
}
}
/// Blend Options set with no blend selected: what new blends start with.
#[derive(Clone, Copy, Debug, Default, PartialEq, Serialize, Deserialize)]
pub struct BlendDefaults {
#[serde(default)]
pub spacing: BlendSpacing,
#[serde(default)]
pub orientation: BlendOrientation,
}
/// Reading a native file never fails over one bad blend number: out-of-range values clamp,
/// and anything that is not a finite number (NaN, null, text) becomes the default. The
/// commands still refuse such input (`ease_param`).
fn blend_number<'de, D: serde::Deserializer<'de>>(d: D, min: f64, max: f64) -> Result<f64, D::Error> {
let v = serde_json::Value::deserialize(d)?;
Ok(v.as_f64().filter(|n| n.is_finite()).map_or(0.0, |n| n.clamp(min, max)))
}
pub(super) fn blend_ramp<'de, D: serde::Deserializer<'de>>(d: D) -> Result<f64, D::Error> {
blend_number(d, 0.0, 1.0)
}
pub(super) fn blend_color_shift<'de, D: serde::Deserializer<'de>>(d: D) -> Result<f64, D::Error> {
blend_number(d, -100.0, 100.0)
}
/// Whether an optional stored color shift has its unchanged default.
fn is_zero(v: &f64) -> bool {
*v == 0.0
}
impl BlendSpec {
/// Shift the color transition independently of shape placement. The exponential curve is
/// original; the documented behavior specifies the direction, not numeric sample values.
pub fn color_position(&self, u: f64) -> f64 {
let u = if u.is_finite() { u.clamp(0.0, 1.0) } else { 0.0 };
let shift = if self.color_shift.is_finite() { self.color_shift.clamp(-100.0, 100.0) } else { 0.0 };
if shift == 0.0 { u } else { u.powf(2.0f64.powf(shift / 50.0)) }
}
}
crates/doc/src/live/envelope.rs
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use super::expand::{Hooks, Outliner, Warper, map_node};
use super::mesh::{GradientMesh, MeshPoint, grid_len, grid_points, nodes_bounds, surface_of};
use super::*;
/// How an envelope distorts its content.
#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
#[serde(tag = "type", rename_all = "camelCase")]
pub enum EnvelopeKind {
/// One of the 15 warp styles (`arc`, `arcLower`, … — see [`WarpStyle::from_id`]); bend and
/// distortions in percent (-100..100).
Warp {
style: String,
#[serde(default)]
bend: f64,
#[serde(default)]
h: f64,
#[serde(default)]
v: f64,
#[serde(default = "yes")]
horizontal: bool,
},
/// A `(rows+1)×(cols+1)` grid of points (row-major) the content's bounding box maps onto.
Mesh {
rows: u32,
cols: u32,
points: Vec<Point>,
/// Each point's bezier handles (offsets, see [`H_RIGHT`] …), row-major like `points`.
/// Empty: the smooth (Catmull-Rom) mesh through the points, as before handles existed;
/// editing the mesh's points or handles on the canvas fills them in.
#[serde(default, skip_serializing_if = "Vec::is_empty")]
handles: Vec<[Vec2; 4]>,
},
/// The content's bounding box maps onto the outline of this path.
TopObject { path: PathData },
}
/// Envelope Options → Preserve Shape Using: how a distorted raster keeps the envelope's shape.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Serialize, Deserialize)]
#[serde(rename_all = "camelCase")]
pub enum PreserveShape {
#[default]
ClippingMask,
Transparency,
}
impl PreserveShape {
pub fn id(self) -> &'static str {
match self {
Self::ClippingMask => "clippingMask",
Self::Transparency => "transparency",
}
}
pub fn parse(s: &str) -> Option<Self> {
match s {
"clippingMask" => Some(Self::ClippingMask),
"transparency" => Some(Self::Transparency),
_ => None,
}
}
}
/// Envelope Options besides Fidelity. `Default` is what envelopes saved before these options
/// existed do (their appearance applies after the distortion); new envelopes start from
/// [`EnvelopeOptions::NEW`], as in the reference app.
#[derive(Clone, Copy, Debug, PartialEq, Serialize, Deserialize)]
#[serde(rename_all = "camelCase", default)]
pub struct EnvelopeOptions {
/// Rasters: Anti-Alias.
pub anti_alias: bool,
/// Rasters: Preserve Shape Using.
pub preserve_shape: PreserveShape,
/// Distort Appearance: strokes and live effects are applied before the distortion, so they
/// bend with the art (off: they apply to the distorted paths).
pub distort_appearance: bool,
/// Distort Linear Gradients (with Distort Appearance): placed gradients bend with the art.
pub distort_linear_gradients: bool,
/// Distort Pattern Fills (with Distort Appearance): pattern tiles bend with the art.
pub distort_pattern_fills: bool,
}
impl Default for EnvelopeOptions {
fn default() -> Self {
Self {
anti_alias: true,
preserve_shape: PreserveShape::ClippingMask,
distort_appearance: false,
distort_linear_gradients: false,
distort_pattern_fills: false,
}
}
}
impl EnvelopeOptions {
/// The options a new envelope gets (the reference app's defaults).
pub const NEW: Self = Self {
anti_alias: true,
preserve_shape: PreserveShape::ClippingMask,
distort_appearance: true,
distort_linear_gradients: false,
distort_pattern_fills: false,
};
/// Do gradients bend with the art?
pub fn gradients(&self) -> bool {
self.distort_appearance && self.distort_linear_gradients
}
/// Do pattern tiles bend with the art?
pub fn patterns(&self) -> bool {
self.distort_appearance && self.distort_pattern_fills
}
}
/// Handle slots of a [`MeshPoint`]: towards the next column, previous column, next row, previous row.
pub const H_RIGHT: usize = 0;
pub const H_LEFT: usize = 1;
pub const H_DOWN: usize = 2;
pub const H_UP: usize = 3;
/// The envelope's point map for content whose bounding box is `src` (page axes).
pub fn envelope_mapper<'a>(kind: &'a EnvelopeKind, src: Rect) -> Box<dyn Fn(Point) -> Point + 'a> {
let s = surface_of(kind, src, Affine::IDENTITY);
let (w, h) = (src.width().max(1e-9), src.height().max(1e-9));
Box::new(move |q: Point| s((q.x - src.x0) / w, (q.y - src.y0) / h))
}
/// Catmull-Rom tangents of a `(rows+1)×(cols+1)` point grid (row-major) as mesh handles, a third
/// of the tangent towards each neighbour (past the borders the grid goes on straight): the curves
/// an envelope mesh without handles of its own runs along between its points.
pub fn smooth_handles(rows: u32, cols: u32, points: &[Point]) -> Vec<[Vec2; 4]> {
let (rows, cols) = (rows as usize, cols as usize);
let at = |r: usize, c: usize| points.get(r * (cols + 1) + c).copied().unwrap_or_default();
let tangent = |prev: Option<Point>, p: Point, next: Option<Point>| match (prev, next) {
(Some(a), Some(b)) => (b - a) / 2.0,
(None, Some(b)) => b - p,
(Some(a), None) => p - a,
(None, None) => Vec2::ZERO,
};
let mut out = Vec::with_capacity(points.len());
for r in 0..=rows {
for c in 0..=cols {
let p = at(r, c);
let du = tangent(c.checked_sub(1).map(|c| at(r, c)), p, (c < cols).then(|| at(r, c + 1))) / 3.0;
let dv = tangent(r.checked_sub(1).map(|r| at(r, c)), p, (r < rows).then(|| at(r + 1, c))) / 3.0;
// Handles pointing out of the grid are unused: they stay at the point.
let keep = |inside: bool, d: Vec2| if inside { d } else { Vec2::ZERO };
let mut h = [Vec2::ZERO; 4];
(h[H_RIGHT], h[H_LEFT], h[H_DOWN], h[H_UP]) = (keep(c < cols, du), keep(c > 0, -du), keep(r < rows, dv), keep(r > 0, -dv));
out.push(h);
}
}
out
}
/// A mesh envelope's grid (`rows`×`cols` patches, `points` and their `handles`; without handles
/// the smooth ones, see [`smooth_handles`]) as a gradient mesh with black points: what the
/// canvas draws and the Mesh tool and Direct Selection edit. `None` for a malformed grid.
pub fn envelope_grid(rows: u32, cols: u32, points: &[Point], handles: &[[Vec2; 4]]) -> Option<GradientMesh> {
if rows == 0 || cols == 0 || grid_len(rows, cols) != Some(points.len()) {
return None;
}
let smooth;
let handles = if handles.len() == points.len() {
handles
} else {
smooth = smooth_handles(rows, cols, points);
&smooth
};
let points = points.iter().zip(handles).map(|(p, h)| MeshPoint { p: *p, color: Color::BLACK, opacity: 1.0, handles: *h }).collect();
Some(GradientMesh { rows, cols, points })
}
/// The point of mesh `m` at (u, v) over the whole mesh (each patch an equal share; past the edges
/// the outer patches go on).
pub(super) fn mesh_at(m: &GradientMesh, u: f64, v: f64) -> Point {
let (rows, cols) = (m.rows.max(1) as i64, m.cols.max(1) as i64);
let (su, sv) = (u * cols as f64, v * rows as f64);
let (c, r) = ((su.floor() as i64).clamp(0, cols - 1), (sv.floor() as i64).clamp(0, rows - 1));
m.eval(r as usize, c as usize, su - c as f64, sv - r as f64)
}
/// The envelope `id` is, or the innermost one it sits in.
pub fn envelope_of(doc: &crate::Document, id: NodeId) -> Option<&Node> {
doc.ancestry(id)?.into_iter().rev().find_map(|a| doc.node(a).filter(|n| matches!(n.kind, NodeKind::Envelope { .. })))
}
/// What a selected envelope shows on the canvas: its mesh lines (a warp's surface on a 4×4 grid,
/// a mesh envelope's own grid) or its top object's outline, and for a mesh envelope the grid to
/// edit (its points and handles).
pub fn envelope_overlay(n: &Node) -> Option<(PathData, Option<GradientMesh>)> {
let NodeKind::Envelope { kind, .. } = &n.kind else { return None };
match &**kind {
EnvelopeKind::Mesh { rows, cols, points, handles } => {
let grid = envelope_grid(*rows, *cols, points, handles)?;
Some((grid.lines(), Some(grid)))
}
EnvelopeKind::Warp { .. } => Some((EnvelopeMap::of(n)?.surface_mesh(4, 4, Color::BLACK).lines(), None)),
EnvelopeKind::TopObject { path } => Some((path.clone(), None)),
}
}
/// The frame an envelope keeps after transform `m` (its frame so far composed with the
/// transform): identity when its axes stay square to the page, unflipped, since evaluating on
/// the page axes gives the same result then.
pub fn envelope_frame(m: Affine) -> Affine {
let [a, b, c, d, _, _] = m.as_coeffs();
if b.abs() < 1e-12 && c.abs() < 1e-12 && a > 0.0 && d > 0.0 { Affine::IDENTITY } else { m }
}
/// An envelope's point map: content placed in the envelope's own frame maps, by its bounds there,
/// onto the unit square and from there onto the envelope's surface ([`surface_of`]).
pub struct EnvelopeMap<'a> {
src: Rect,
frame: Affine,
to_frame: Affine,
surface: Box<dyn Fn(f64, f64) -> Point + 'a>,
}
impl<'a> EnvelopeMap<'a> {
/// The map of an envelope of `kind` around `content` with `frame`. `None` when the content
/// has no bounds.
pub fn new(content: &[Arc<Node>], kind: &'a EnvelopeKind, frame: Affine) -> Option<Self> {
let frame = if frame.is_finite() && frame.determinant().abs() > 1e-12 { frame } else { Affine::IDENTITY };
let to_frame = frame.inverse();
let src = if frame == Affine::IDENTITY {
nodes_bounds(content)?
} else {
content.iter().try_fold(None, |acc, c| {
let mut m = (**c).clone();
m.transform(to_frame, false);
Some(vectorcraft_geom::union_opt(acc, m.geometric_bounds()))
})??
};
Some(Self { src, frame, to_frame, surface: surface_of(kind, src, frame) })
}
/// The map of envelope node `n` (`None` for other nodes).
pub fn of(n: &'a Node) -> Option<Self> {
match &n.kind {
NodeKind::Envelope { content, kind, frame, .. } => Self::new(content, kind, **frame),
_ => None,
}
}
/// The content's bounds in the envelope's frame.
pub fn src(&self) -> Rect {
self.src
}
/// The surface point at (u, v) ∈ [0,1]².
pub fn at(&self, u: f64, v: f64) -> Point {
(self.surface)(u, v)
}
/// Where the envelope puts document point `p`.
pub fn map(&self, p: Point) -> Point {
let q = self.to_frame * p;
let (w, h) = (self.src.width().max(1e-9), self.src.height().max(1e-9));
self.at((q.x - self.src.x0) / w, (q.y - self.src.y0) / h)
}
/// A flat `(rows+1)×(cols+1)` grid over the content, in the envelope's frame (row-major).
pub fn grid(&self, rows: u32, cols: u32) -> Vec<Point> {
grid_points(self.src, rows, cols).into_iter().map(|p| self.frame * p).collect()
}
/// The surface sampled on a `rows`×`cols` grid as a mesh whose handles follow it and whose
/// points are `color`: Release gives it back as the envelope's shape, Reset with Mesh starts
/// from it.
pub fn surface_mesh(&self, rows: u32, cols: u32, color: Color) -> GradientMesh {
GradientMesh::from_surface(rows, cols, &|u, v| self.at(u, v), &|_, _| color)
}
/// The surface's bounds (sampled; a mesh's points and a top object's path bound it exactly).
fn bounds(&self) -> Option<Rect> {
const N: usize = 16;
let mut r: Option<Rect> = None;
for j in 0..=N {
for i in 0..=N {
let q = self.at(i as f64 / N as f64, j as f64 / N as f64);
r = Some(r.map_or(Rect::from_points(q, q), |r| r.union_pt(q)));
}
}
r
}
}
/// Evaluate an envelope of `kind` around `content` on the page axes with the options envelopes
/// had before Envelope Options (see [`expand_live_hooks`] for an envelope node).
pub fn envelope_expand(content: &[Arc<Node>], kind: &EnvelopeKind, fidelity: f64, outline: Outliner) -> Vec<Node> {
expand_envelope(content, kind, fidelity, EnvelopeOptions::default(), Affine::IDENTITY, outline.into())
}
/// An envelope's content pushed through its map: Fidelity sets how finely curves are cut (and
/// into how many pieces images are), the options what bends with the art.
pub(super) fn expand_envelope(
content: &[Arc<Node>],
kind: &EnvelopeKind,
fidelity: f64,
options: EnvelopeOptions,
frame: Affine,
hooks: Hooks,
) -> Vec<Node> {
let Some(map) = EnvelopeMap::new(content, kind, frame) else { return content.iter().map(|c| (**c).clone()).collect() };
let src = map.src();
let fid = if fidelity.is_finite() { fidelity.clamp(0.0, 100.0) / 100.0 } else { 0.5 };
let f = |p: Point| map.map(p);
let w = Warper {
f: &f,
piece: src.width().hypot(src.height()).max(1e-6) / (8.0 + fid * 56.0),
eps: (src.width().max(src.height()) * 0.05).max(0.5),
cells: (4.0 + fid * 12.0).round() as usize,
hooks,
options,
depth: 0,
};
content.iter().map(|c| map_node(c, &w)).collect()
}
/// Envelope bounds: a mesh's points, a top object's path, the warp's surface (sampled).
pub fn envelope_bounds(content: &[Arc<Node>], kind: &EnvelopeKind, frame: Affine) -> Option<Rect> {
match kind {
EnvelopeKind::Mesh { rows, cols, points, handles } if !handles.is_empty() => envelope_grid(*rows, *cols, points, handles)?.outline().bounds(),
EnvelopeKind::Mesh { points, .. } => {
let first = *points.first()?;
Some(points.iter().fold(Rect::from_points(first, first), |r, p| r.union_pt(*p)))
}
EnvelopeKind::TopObject { path } => path.bounds(),
EnvelopeKind::Warp { .. } => EnvelopeMap::new(content, kind, frame)?.bounds(),
}
}
crates/doc/src/live/expand.rs
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use super::envelope::{EnvelopeOptions, expand_envelope};
use super::mesh::GradientMesh;
use super::warp::map_nonlinear;
use super::*;
/// Optional hook that converts nodes the pure evaluation can't map (text) to outlines.
pub type Outliner<'a> = Option<&'a dyn Fn(&Node) -> Option<Node>>;
/// Distort Pattern Fills: the tiles pattern swatch `name` painted with placement `xf` lays over
/// `region` (see [`crate::PatternDef::instances_in`]); `None` without such a swatch.
pub type PatternTiles<'a> = &'a dyn Fn(&str, Affine, Rect) -> Option<Vec<Node>>;
/// What live evaluation asks of the crates above this one (`vectorcraft-effects` supplies them).
#[derive(Clone, Copy, Default)]
pub struct Hooks<'a> {
/// Type as its glyph outlines, a symbol instance as its art (see [`Outliner`]).
pub outline: Outliner<'a>,
/// Distort Appearance: a path's strokes and geometry effects baked into filled art (`None`
/// when it has none to bake).
pub appearance: Outliner<'a>,
/// Distort Pattern Fills: the tiles a pattern fill lays (see [`PatternTiles`]).
pub pattern: Option<PatternTiles<'a>>,
/// The document whose symbols' art counts toward the instance budget of a Repeat of their
/// instances ([`crate::RepeatSpec::expand`]).
pub symbols: Option<&'a crate::Document>,
}
impl<'a> From<Outliner<'a>> for Hooks<'a> {
fn from(outline: Outliner<'a>) -> Self {
Self { outline, ..Default::default() }
}
}
/// The affine map that best matches `f` near `p` (finite differences with step `eps`).
pub fn affine_near(f: &dyn Fn(Point) -> Point, p: Point, eps: f64) -> Affine {
let o = f(p);
let ex = (f(p + Vec2::new(eps, 0.0)) - f(p - Vec2::new(eps, 0.0))) / (2.0 * eps);
let ey = (f(p + Vec2::new(0.0, eps)) - f(p - Vec2::new(0.0, eps))) / (2.0 * eps);
let lin = Affine::new([ex.x, ex.y, ey.x, ey.y, 0.0, 0.0]);
Affine::translate(o.to_vec2()) * lin * Affine::translate(-p.to_vec2())
}
/// How deep hooks may nest art inside art (symbols in symbols, envelopes in envelopes) before
/// the rest is left as it is: a file can make a symbol contain itself.
const MAX_HOOK_DEPTH: u32 = 16;
/// How an envelope pushes art through its point map.
#[derive(Clone, Copy)]
pub(super) struct Warper<'a> {
pub(super) f: &'a dyn Fn(Point) -> Point,
/// Longest piece a segment is cut into before mapping.
pub(super) piece: f64,
/// Finite-difference step for the local affine maps gradients follow.
pub(super) eps: f64,
/// Rows and columns of the pieces an image is cut into.
pub(super) cells: usize,
pub(super) hooks: Hooks<'a>,
pub(super) options: EnvelopeOptions,
/// How many hooks the art being mapped came through.
pub(super) depth: u32,
}
impl Warper<'_> {
/// This warper one hook deeper (`None` past [`MAX_HOOK_DEPTH`]).
fn deeper(&self) -> Option<Self> {
(self.depth < MAX_HOOK_DEPTH).then_some(Self { depth: self.depth + 1, ..*self })
}
}
/// `to` (art standing in for `from`: its outlines, its art) with `from`'s name, transparency,
/// opacity mask and effects.
fn carry_look(from: &Node, mut to: Node) -> Node {
to.name = from.name.clone();
to.opacity = from.opacity;
to.blend = from.blend;
to.isolate = from.isolate;
to.knockout = from.knockout;
to.knockout_shape = from.knockout_shape;
to.extras_mut().mask = from.extras().mask.clone();
to.appearance.effects = from.appearance.effects.clone();
to
}
pub(super) fn map_node(n: &Node, w: &Warper) -> Node {
let deeper = w.deeper();
// Distort Appearance: strokes and geometry effects bend with the art.
if w.options.distort_appearance
&& let Some(d) = &deeper
&& let Some(o) = w.hooks.appearance.and_then(|h| h(n))
{
return map_node(&o, d);
}
// Distort Pattern Fills: the tiles bend with the art (not the patterns inside them).
if w.options.patterns()
&& let Some(d) = &deeper
&& let Some(o) = w.hooks.pattern.and_then(|p| pattern_art(n, p))
{
let inner = Warper { options: EnvelopeOptions { distort_pattern_fills: false, ..d.options }, ..*d };
return map_node(&o, &inner);
}
let mut out = n.clone();
// Distort Linear Gradients: the gradient vectors follow the warp where they sit.
if w.options.gradients()
&& let Some(b) = n.geometric_bounds()
{
out.appearance.warp_linear_gradients(b, &|p| affine_near(w.f, p, w.eps));
}
if let Some(m) = out.extras_if_any().and_then(|e| e.mask.as_mut()) {
m.art = Arc::new(map_node(&m.art, w));
}
match &mut out.kind {
NodeKind::Path { path, live, .. } => {
*path = map_nonlinear(path, w.piece, w.f);
*live = None;
}
NodeKind::Layer { children, .. } | NodeKind::Group { children, .. } | NodeKind::Compound { children, .. } => {
for c in children.iter_mut() {
*c = Arc::new(map_node(c, w));
}
}
NodeKind::Mesh(m) => m.map(w.f),
NodeKind::Blend { .. } | NodeKind::Envelope { .. } | NodeKind::Repeat(_) | NodeKind::Intertwine { .. } => {
if let Some(d) = &deeper {
return map_node(&expanded_group_hooks(n, w.hooks), d);
}
}
NodeKind::Text(_) | NodeKind::SymbolInstance { .. } => {
if let Some(d) = &deeper
&& let Some(o) = w.hooks.outline.and_then(|h| h(n))
{
return map_node(&carry_look(n, o), d);
}
}
NodeKind::Image(im) => {
let im = im.clone();
return warp_image(&out, &im, w);
}
// Its art is plain, so it warps at this depth.
NodeKind::PlacedDocument(_) => return map_node(&expanded_group_hooks(n, w.hooks), w),
}
out
}
/// The affine map taking triangle `s` to triangle `d` (`None` when `s` is degenerate).
fn affine_between(s: [Point; 3], d: [Point; 3]) -> Option<Affine> {
let basis = |p: [Point; 3]| Affine::new([p[1].x - p[0].x, p[1].y - p[0].y, p[2].x - p[0].x, p[2].y - p[0].y, p[0].x, p[0].y]);
let bs = basis(s);
if bs.determinant().abs() < 1e-12 {
return None;
}
let a = basis(d) * bs.inverse();
a.is_finite().then_some(a)
}
/// Image `n` (`im`) pushed through the warp as a raster mesh warp: its frame cut into
/// `w.cells`² cells of two triangles, each a clip group showing the image under the affine map
/// that takes the triangle where the warp takes its corners. Each piece reaches a little past its
/// edges (at most half a point) so neighbours overlap and no seams show.
fn warp_image(n: &Node, im: &ImageObject, w: &Warper) -> Node {
let k = w.cells.max(1);
// Two triangles a cell, three objects each; an image an inner envelope already cut into
// pieces is cut again here, so the pieces count against [`MAX_GENERATED`]. Past it, the image
// is left out.
if !Generating::charge(k.saturating_mul(k).saturating_mul(6)) {
let mut g = n.clone();
g.kind = NodeKind::Group { children: vec![], clip: false };
return g;
}
let (pw, ph) = (im.width as f64, im.height as f64);
let at = |i: usize, j: usize| Point::new(pw * i as f64 / k as f64, ph * j as f64 / k as f64);
let mut pieces = Vec::with_capacity(2 * k * k);
for j in 0..k {
for i in 0..k {
let s = [at(i, j), at(i + 1, j), at(i + 1, j + 1), at(i, j + 1)];
let d = s.map(|p| (w.f)(im.xf * p));
for t in [[0, 1, 2], [0, 2, 3]] {
let (st, dt) = (t.map(|v| s[v]), t.map(|v| d[v]));
let Some(xf) = affine_between(st, dt) else { continue };
let c = Point::new((dt[0].x + dt[1].x + dt[2].x) / 3.0, (dt[0].y + dt[1].y + dt[2].y) / 3.0);
let grow = (dt[0].distance(dt[1]).max(dt[1].distance(dt[2])) * 0.02).min(0.5);
let tri: Vec<Point> = dt
.iter()
.map(|p| {
let v = *p - c;
let len = v.hypot();
if len > 1e-12 { *p + v * (grow / len) } else { *p }
})
.collect();
let mut clip = Node::path(n.id, PathData::single(SubPath::polyline(&tri, true)), Appearance::default());
if let NodeKind::Path { clipping, .. } = &mut clip.kind {
*clipping = true;
}
let image = Node::new(n.id, NodeKind::Image(Box::new(ImageObject { xf, ..im.clone() })));
pieces.push(Arc::new(Node::new(n.id, NodeKind::Group { children: vec![Arc::new(clip), Arc::new(image)], clip: true })));
}
}
}
let mut g = n.clone();
g.kind = NodeKind::Group { children: pieces, clip: false };
g
}
/// Distort Pattern Fills: path or compound path `n` with each visible pattern fill turned into the
/// tiles it paints in a clip group shaped like `n` (with the fill's opacity and blend mode), its
/// other fills and strokes on copies of it, in paint order, under `n`'s transparency. `None`
/// without a pattern fill whose definition `pattern` finds.
fn pattern_art(n: &Node, tiles: PatternTiles) -> Option<Node> {
let (path, rule, _) = crate::blend::node_path(n)?;
let pattern_fill = |i: &AppearanceItem| matches!(i, AppearanceItem::Fill(f) if f.visible && matches!(f.paint, Paint::Pattern { .. }));
if !n.appearance.items.iter().any(pattern_fill) {
return None;
}
let bounds = path.bounds()?;
let def = |i: &AppearanceItem| match i {
AppearanceItem::Fill(f) if f.visible => match &f.paint {
Paint::Pattern { pattern: name, xf } => tiles(name, *xf, bounds).map(|t| (t, f.opacity, f.blend)),
_ => None,
},
_ => None,
};
let plain = |items: Vec<AppearanceItem>| {
let mut p = Node {
appearance: Appearance { items, ..Default::default() }.into(),
opacity: 1.0,
blend: Default::default(),
isolate: false,
knockout: Default::default(),
knockout_shape: false,
name: None,
..n.clone()
};
p.extras_mut().mask = None;
Arc::new(p)
};
let mut pieces = vec![];
let mut rest = vec![];
for i in &n.appearance.items {
let Some((tiles, opacity, blend)) = def(i) else {
rest.push(i.clone());
continue;
};
if !rest.is_empty() {
pieces.push(plain(std::mem::take(&mut rest)));
}
let mut clip = Node::path(n.id, path.clone(), Appearance::default());
if let NodeKind::Path { clipping, rule: r, .. } = &mut clip.kind {
(*clipping, *r) = (true, rule);
}
let children = std::iter::once(clip).chain(tiles).map(Arc::new).collect();
let mut g = Node::new(n.id, NodeKind::Group { children, clip: true });
g.opacity = opacity;
g.blend = blend;
pieces.push(Arc::new(g));
}
if !rest.is_empty() {
pieces.push(plain(rest));
}
Some(Node {
kind: NodeKind::Group { children: pieces, clip: false },
appearance: Appearance { effects: n.appearance.effects.clone(), ..Default::default() }.into(),
..n.clone()
})
}
// =====================================================================================
// Expansion
// =====================================================================================
/// Is this one of the live kinds?
pub fn is_live(n: &Node) -> bool {
matches!(
n.kind,
NodeKind::Blend { .. }
| NodeKind::Envelope { .. }
| NodeKind::Mesh(_)
| NodeKind::Repeat(_)
| NodeKind::PlacedDocument(_)
| NodeKind::Intertwine { .. }
)
}
/// Mesh tessellation as filled quad paths (no stroke), `n`×`n` per patch.
pub fn mesh_quad_nodes(m: &GradientMesh, n: usize) -> Vec<Node> {
m.quads(n)
.into_iter()
.map(|q| {
let mut ap = Appearance::default();
let mut fl = FillLayer::new(Paint::solid(q.color));
fl.opacity = q.opacity;
ap.items.push(AppearanceItem::Fill(fl));
Node::path(NodeId(0), PathData::single(SubPath::polyline(&q.pts, true)), ap)
})
.collect()
}
/// One level of evaluation of a live object (non-live nodes return themselves). Blend steps and
/// envelope results may still contain live objects (e.g. a blend of two meshes).
pub fn expand_live(n: &Node) -> Vec<Node> {
expand_live_with(n, None)
}
pub fn expand_live_with(n: &Node, outline: Outliner) -> Vec<Node> {
expand_live_hooks(n, outline.into())
}
/// [`expand_live_with`] with everything an envelope can ask of the crates above (see [`Hooks`]).
pub fn expand_live_hooks(n: &Node, hooks: Hooks) -> Vec<Node> {
let _generating = Generating::enter();
match &n.kind {
NodeKind::Blend { children, spec } => blend_expand(children, spec),
NodeKind::Envelope { content, kind, fidelity, options, frame, .. } => expand_envelope(content, kind, *fidelity, *options, **frame, hooks),
NodeKind::Mesh(m) => mesh_quad_nodes(m, 8),
NodeKind::Repeat(r) => r.expand(hooks.symbols),
NodeKind::PlacedDocument(p) => p.art(n),
NodeKind::Intertwine { children } => crate::intertwine::expand(children),
_ => vec![n.clone()],
}
}
/// A live object evaluated into a plain group (keeping the object's id, name and transparency).
pub fn expanded_group(n: &Node, outline: Outliner) -> Node {
expanded_group_hooks(n, outline.into())
}
/// [`expanded_group`] with [`Hooks`].
pub fn expanded_group_hooks(n: &Node, hooks: Hooks) -> Node {
let _generating = Generating::enter();
let children = expand_live_hooks(n, hooks).into_iter().map(Arc::new).collect();
let mut g = Node::new(n.id, NodeKind::Group { children, clip: false });
g.name = n.name.clone();
g.visible = n.visible;
g.locked = n.locked;
g.opacity = n.opacity;
g.blend = n.blend;
g.isolate = n.isolate;
g.knockout = n.knockout;
// Knocking out opaque blend steps changes nothing: don't make the outputs work for it.
if matches!(n.kind, NodeKind::Blend { .. }) && g.knockout == crate::Knockout::On && !crate::blend::knockout_shows(&g) {
g.knockout = crate::Knockout::Off;
}
g.knockout_shape = n.knockout_shape;
g.extras_mut().mask = n.extras().mask.clone();
g
}
/// Recursively replace every live object in `n` by plain geometry (for exporters).
pub fn expand_deep(n: &Node, outline: Outliner) -> Node {
expand_deep_hooks(n, outline.into())
}
/// [`expand_deep`] with [`Hooks`]. The objects live art makes here count against one
/// [`MAX_GENERATED`] ([`Generating`]): blends of blends kept their inner blends live, and each
/// copy expanded on its own, so step counts capped one by one multiplied. Past it, live art
/// expands to nothing.
pub fn expand_deep_hooks(n: &Node, hooks: Hooks) -> Node {
let _generating = Generating::enter();
let mut out = if is_live(n) {
let g = expanded_group_hooks(n, hooks);
if !Generating::charge(g.count()) {
return Node::new(n.id, NodeKind::Group { children: vec![], clip: false });
}
g
} else {
n.clone()
};
if let Some(ch) = out.children_mut() {
for c in ch.iter_mut() {
if subtree_has_live(c) {
*c = Arc::new(expand_deep_hooks(c, hooks));
}
}
}
out
}
/// Most objects one evaluation of live art (an expansion, an envelope's mapping and everything
/// inside them) may make.
pub const MAX_GENERATED: usize = 4_000_000;
std::thread_local! {
/// What is left of [`MAX_GENERATED`] for the evaluation running on this thread; `None` outside
/// one.
static GENERATED_LEFT: std::cell::Cell<Option<usize>> = const { std::cell::Cell::new(None) };
}
/// The outermost live evaluation on this thread: it starts [`GENERATED_LEFT`] and ends it.
struct Generating(bool);
impl Generating {
fn enter() -> Self {
let outermost = GENERATED_LEFT.get().is_none();
if outermost {
GENERATED_LEFT.set(Some(MAX_GENERATED));
}
Self(outermost)
}
/// Spend `n` objects; `false` (and nothing left) when there aren't that many.
fn charge(n: usize) -> bool {
match GENERATED_LEFT.get() {
None => true,
Some(left) => {
GENERATED_LEFT.set(Some(left.saturating_sub(n)));
n <= left
}
}
}
}
impl Drop for Generating {
fn drop(&mut self) {
if self.0 {
GENERATED_LEFT.set(None);
}
}
}
/// Does `n` or any descendant need live evaluation?
pub fn subtree_has_live(n: &Node) -> bool {
let mut any = false;
n.walk(&mut |c| any |= is_live(c));
any
}
/// Largest stroke outset in a subtree (for visual bounds of envelopes). With `symbols`, the
/// outsets in the art of the symbols its instances show count too
/// ([`crate::symbols::ArtBox::reach`]), grown by [`crate::SymbolBoxes::brush_pad`]. In boxes made
/// by [`crate::SymbolBoxes::without_art_strokes`], the outsets in the art do not count, and the pad
/// does.
pub(crate) fn max_outset(nodes: &[Arc<Node>], symbols: Option<&crate::SymbolBoxes>) -> f64 {
let mut o = 0.0f64;
for n in nodes {
n.walk(&mut |c| {
o = o.max(c.appearance.outset());
if let (Some(s), NodeKind::SymbolInstance { symbol, .. }) = (symbols, &c.kind)
&& let Some(art) = s.art(symbol)
{
let reach = if s.art_strokes() { art.reach } else { 0.0 };
o = o.max(reach + s.brush_pad(symbol));
}
});
}
o
}
crates/doc/src/live/mesh.rs
+761
View File
@@ -0,0 +1,761 @@
use super::envelope::{EnvelopeKind, H_DOWN, H_LEFT, H_RIGHT, H_UP, envelope_grid, mesh_at};
use super::warp::{WarpStyle, flatten_subpath, resample, warp_point};
use super::*;
#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
pub struct MeshPoint {
pub p: Point,
pub color: Color,
#[serde(default = "one")]
pub opacity: f32,
/// Tangent handles as offsets from `p` (see [`H_RIGHT`] …).
#[serde(default)]
pub handles: [Vec2; 4],
}
/// A gradient mesh: `(rows+1)×(cols+1)` points, row-major.
#[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
pub struct GradientMesh {
pub rows: u32,
pub cols: u32,
pub points: Vec<MeshPoint>,
}
/// One tessellated piece of a mesh: a small quad, its colour at the centre, and its colour and
/// opacity at each corner (in `pts` order), which a renderer shades between so neighbouring quads
/// meet without a step.
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct MeshQuad {
pub pts: [Point; 4],
pub color: Color,
pub opacity: f32,
pub corners: [(Color, f32); 4],
}
/// Create Gradient Mesh → Appearance.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
pub enum MeshAppearance {
#[default]
Flat,
ToCenter,
ToEdge,
}
impl MeshAppearance {
pub fn parse(s: &str) -> Option<Self> {
match s.to_ascii_lowercase().as_str() {
"flat" => Some(Self::Flat),
"center" | "tocenter" | "to center" => Some(Self::ToCenter),
"edge" | "toedge" | "to edge" => Some(Self::ToEdge),
_ => None,
}
}
}
/// Default envelope fidelity.
pub fn default_fidelity() -> f64 {
fifty()
}
const SIDE: usize = 65;
/// Four boundary curves (top TL→TR, right TR→BR, bottom BL→BR, left TL→BL), each resampled to
/// [`SIDE`] points, from the outline of a closed path split at the points nearest its bounding
/// box corners.
#[derive(Clone, Debug)]
pub struct Coons {
top: Vec<Point>,
right: Vec<Point>,
bottom: Vec<Point>,
left: Vec<Point>,
}
impl Coons {
/// A rectangle.
pub fn rect(r: Rect) -> Self {
let line = |a: Point, b: Point| (0..SIDE).map(|i| a.lerp(b, i as f64 / (SIDE - 1) as f64)).collect::<Vec<_>>();
let (tl, tr, br, bl) = (Point::new(r.x0, r.y0), Point::new(r.x1, r.y0), Point::new(r.x1, r.y1), Point::new(r.x0, r.y1));
Self { top: line(tl, tr), right: line(tr, br), bottom: line(bl, br), left: line(tl, bl) }
}
pub fn from_path(path: &PathData) -> Option<Self> {
// The largest subpath is the outline.
let sp = path.subpaths.iter().filter(|s| s.anchors.len() >= 2).max_by(|a, b| a.area().abs().total_cmp(&b.area().abs()))?;
let r = path.bounds()?;
let tol = (r.width() + r.height()).max(1e-6) / 2000.0;
let mut poly = flatten_subpath(sp, tol);
if poly.len() > 1
&& let (Some(a), Some(b)) = (poly.first(), poly.last())
&& a.distance(*b) < 1e-9
{
poly.pop();
}
if poly.len() < 3 {
return Some(Self::rect(r));
}
// Orient clockwise in y-down (TL → TR → BR → BL).
let area: f64 = (0..poly.len())
.map(|i| {
let (p, q) = (poly[i], poly[(i + 1) % poly.len()]);
p.x * q.y - q.x * p.y
})
.sum();
if area < 0.0 {
poly.reverse();
}
let nearest = |c: Point| (0..poly.len()).min_by(|i, j| poly[*i].distance_squared(c).total_cmp(&poly[*j].distance_squared(c))).unwrap_or(0);
let tl = nearest(Point::new(r.x0, r.y0));
let tr = nearest(Point::new(r.x1, r.y0));
let br = nearest(Point::new(r.x1, r.y1));
let bl = nearest(Point::new(r.x0, r.y1));
let n = poly.len();
let arc = |i: usize, j: usize| -> Vec<Point> {
let mut v = vec![poly[i]];
let mut k = i;
while k != j {
k = (k + 1) % n;
v.push(poly[k]);
}
v
};
let top = resample(&arc(tl, tr), SIDE);
let right = resample(&arc(tr, br), SIDE);
let mut bottom = resample(&arc(br, bl), SIDE);
bottom.reverse();
let mut left = resample(&arc(bl, tl), SIDE);
left.reverse();
Some(Self { top, right, bottom, left })
}
/// The point at `u` along a side; past its ends the end segments go on straight (art an
/// envelope bends can reach past the content's box: outlined strokes).
fn sample(side: &[Point], u: f64) -> Point {
let s = u * (side.len() - 1) as f64;
let i = (s.floor().max(0.0) as usize).min(side.len() - 2);
side[i].lerp(side[i + 1], s - i as f64)
}
/// The surface point at (u, v) ∈ [0,1]².
pub fn eval(&self, u: f64, v: f64) -> Point {
let (t, b, l, r) = (Self::sample(&self.top, u), Self::sample(&self.bottom, u), Self::sample(&self.left, v), Self::sample(&self.right, v));
let (p00, p10, p01, p11) = (self.top[0], self.top[SIDE - 1], self.bottom[0], self.bottom[SIDE - 1]);
let c = (1.0 - v) * t.to_vec2() + v * b.to_vec2() + (1.0 - u) * l.to_vec2() + u * r.to_vec2()
- ((1.0 - u) * (1.0 - v) * p00.to_vec2() + u * (1.0 - v) * p10.to_vec2() + (1.0 - u) * v * p01.to_vec2() + u * v * p11.to_vec2());
c.to_point()
}
/// The four corners TL, TR, BR, BL.
pub fn corners(&self) -> [Point; 4] {
[self.top[0], self.top[SIDE - 1], self.bottom[SIDE - 1], self.bottom[0]]
}
}
// =====================================================================================
// Gradient meshes
// =====================================================================================
/// `0, 1/n, …, 1` for `n` (clamped to 1..=200) even steps.
fn even_steps(n: u32) -> Vec<f64> {
let n = n.clamp(1, 200);
(0..=n).map(|i| i as f64 / n as f64).collect()
}
/// The number of points of a `(rows+1)×(cols+1)` grid, `None` past `usize`: counts come from
/// files, and u32::MAX rows and columns (65,535 on 32-bit targets) would wrap to an empty grid.
pub(super) fn grid_len(rows: u32, cols: u32) -> Option<usize> {
(rows as usize).checked_add(1)?.checked_mul((cols as usize).checked_add(1)?)
}
impl GradientMesh {
pub fn idx(&self, r: usize, c: usize) -> usize {
r * (self.cols as usize + 1) + c
}
pub fn is_valid(&self) -> bool {
self.rows >= 1 && self.cols >= 1 && grid_len(self.rows, self.cols) == Some(self.points.len())
}
/// A 1×1 mesh from its four corners (bottom-left, top-left, top-right, bottom-right in u/v
/// order: row 0 is v = 0, columns follow u), each with its handles ([`H_RIGHT`] …).
fn patch(corners: [(Point, [Vec2; 4], Color); 4]) -> Self {
let point = |(p, handles, color): (Point, [Vec2; 4], Color)| MeshPoint { p, color, opacity: 1.0, handles };
let [a, b, c, d] = corners;
Self { rows: 1, cols: 1, points: vec![point(a), point(d), point(b), point(c)] }
}
/// A 1×1 mesh from a Coons patch's twelve boundary points (in the order PDF and PostScript
/// shadings list them: v runs cp0 → cp3 along cp1 and cp2, u runs cp0 → cp9 along cp11 and
/// cp10) and its corner colours (at cp0, cp3, cp6, cp9); `None` if a point isn't finite.
pub fn coons(cp: &[Point; 12], colors: [Color; 4]) -> Option<Self> {
if !cp.iter().all(|p| p.is_finite()) {
return None;
}
let h = |a: usize, b: usize| cp[b] - cp[a];
let handles = |right: Vec2, left: Vec2, down: Vec2, up: Vec2| {
let mut h = [Vec2::ZERO; 4];
(h[H_RIGHT], h[H_LEFT], h[H_DOWN], h[H_UP]) = (right, left, down, up);
h
};
let [c0, c1, c2, c3] = colors;
Some(Self::patch([
(cp[0], handles(h(0, 11), Vec2::ZERO, h(0, 1), Vec2::ZERO), c0),
(cp[3], handles(h(3, 4), Vec2::ZERO, Vec2::ZERO, h(3, 2)), c1),
(cp[6], handles(Vec2::ZERO, h(6, 5), Vec2::ZERO, h(6, 7)), c2),
(cp[9], handles(Vec2::ZERO, h(9, 10), h(9, 8), Vec2::ZERO), c3),
]))
}
/// A 1×1 mesh of a Gouraud-shaded triangle (a patch with two corners together); `None` if a
/// point isn't finite.
pub fn triangle(corners: [(Point, Color); 3]) -> Option<Self> {
if !corners.iter().all(|(p, _)| p.is_finite()) {
return None;
}
let [a, b, c] = corners.map(|(p, color)| (p, [Vec2::ZERO; 4], color));
Some(Self::patch([a, b, c, c]))
}
/// A mesh over surface `s` (u, v ∈ [0,1]) with handles from its partial derivatives.
pub fn from_surface(rows: u32, cols: u32, s: &dyn Fn(f64, f64) -> Point, color: &dyn Fn(f64, f64) -> Color) -> Self {
let (us, vs) = (even_steps(cols), even_steps(rows));
Self::from_grid(&us, &vs, s, &|r, c, _| (color(us[c], vs[r]), 1.0))
}
/// A mesh over surface `s` (u, v ∈ [0,1]) whose column lines sit at `us` and row lines at `vs`
/// (ascending, at least two each; equal neighbours make a patch of no width, a sharp colour
/// change), with handles from its partial derivatives. `color(row, col, point)` gives each
/// point its colour and opacity.
pub fn from_grid(us: &[f64], vs: &[f64], s: &dyn Fn(f64, f64) -> Point, color: &dyn Fn(usize, usize, Point) -> (Color, f32)) -> Self {
let (rows, cols) = (vs.len().saturating_sub(1), us.len().saturating_sub(1));
let eps = 1e-3;
let mut points = Vec::with_capacity(us.len() * vs.len());
for (r, &v) in vs.iter().enumerate() {
for (c, &u) in us.iter().enumerate() {
let p = s(u, v);
let d_u = (s((u + eps).min(1.0), v) - s((u - eps).max(0.0), v)) / ((u + eps).min(1.0) - (u - eps).max(0.0));
let d_v = (s(u, (v + eps).min(1.0)) - s(u, (v - eps).max(0.0))) / ((v + eps).min(1.0) - (v - eps).max(0.0));
// A third of the way to the neighbouring line along the tangent; outward handles on
// the border are unused, so they stay at the point.
let h = |d: Vec2, from: f64, to: Option<&f64>| to.map_or(Vec2::ZERO, |to| d * ((to - from) / 3.0));
let handles = [
h(d_u, u, us.get(c + 1)),
h(d_u, u, c.checked_sub(1).map(|i| &us[i])),
h(d_v, v, vs.get(r + 1)),
h(d_v, v, r.checked_sub(1).map(|i| &vs[i])),
];
let (color, opacity) = color(r, c, p);
points.push(MeshPoint { p, color, opacity, handles });
}
}
Self { rows: rows as u32, cols: cols as u32, points }
}
/// Create Gradient Mesh for a path: the outline split at its corners, coloured per `appearance`.
pub fn for_path(path: &PathData, rows: u32, cols: u32, base: Color, appearance: MeshAppearance, highlight: f64) -> Option<Self> {
let mut m = Self::for_path_with(path, rows, cols, &|_| (base, 1.0))?;
m.highlight(appearance, highlight);
Some(m)
}
/// Create Gradient Mesh for a path: the outline split at its corners, each point taking the
/// colour and opacity `color_at` gives at its position (a gradient fill's, say).
pub fn for_path_with(path: &PathData, rows: u32, cols: u32, color_at: &dyn Fn(Point) -> (Color, f32)) -> Option<Self> {
let coons = Coons::from_path(path)?;
Some(Self::from_grid(&even_steps(cols), &even_steps(rows), &|u, v| coons.eval(u, v), &|_, _, p| color_at(p)))
}
/// Create Gradient Mesh → Appearance: lighten the points towards white, to the centre or to
/// the edges, by at most `highlight` %.
pub fn highlight(&mut self, appearance: MeshAppearance, highlight: f64) {
let h = (highlight / 100.0).clamp(0.0, 1.0) as f32;
let (rows, cols) = (self.rows as usize, self.cols as usize);
for r in 0..=rows {
for c in 0..=cols {
let (u, v) = (c as f64 / cols as f64, r as f64 / rows as f64);
let d = ((u - 0.5).abs().max((v - 0.5).abs()) * 2.0) as f32; // 0 centre … 1 edge
let w = match appearance {
MeshAppearance::Flat => 0.0,
MeshAppearance::ToCenter => (1.0 - d) * h,
MeshAppearance::ToEdge => d * h,
};
if w > 0.0 {
let i = self.idx(r, c);
self.points[i].color = lerp_color(&self.points[i].color, &Color::WHITE, w);
}
}
}
}
/// Horizontal edge from (r, c) to (r, c+1).
pub fn edge_u(&self, r: usize, c: usize) -> CubicBez {
let (a, b) = (&self.points[self.idx(r, c)], &self.points[self.idx(r, c + 1)]);
CubicBez::new(a.p, a.p + a.handles[H_RIGHT], b.p + b.handles[H_LEFT], b.p)
}
/// Vertical edge from (r, c) to (r+1, c).
pub fn edge_v(&self, r: usize, c: usize) -> CubicBez {
let (a, b) = (&self.points[self.idx(r, c)], &self.points[self.idx(r + 1, c)]);
CubicBez::new(a.p, a.p + a.handles[H_DOWN], b.p + b.handles[H_UP], b.p)
}
/// Coons patch point of patch (r, c) at local (u, v).
pub fn eval(&self, r: usize, c: usize, u: f64, v: f64) -> Point {
let (t, b) = (self.edge_u(r, c).eval(u), self.edge_u(r + 1, c).eval(u));
let (l, rr) = (self.edge_v(r, c).eval(v), self.edge_v(r, c + 1).eval(v));
let p00 = self.points[self.idx(r, c)].p.to_vec2();
let p10 = self.points[self.idx(r, c + 1)].p.to_vec2();
let p01 = self.points[self.idx(r + 1, c)].p.to_vec2();
let p11 = self.points[self.idx(r + 1, c + 1)].p.to_vec2();
((1.0 - v) * t.to_vec2() + v * b.to_vec2() + (1.0 - u) * l.to_vec2() + u * rr.to_vec2()
- ((1.0 - u) * (1.0 - v) * p00 + u * (1.0 - v) * p10 + (1.0 - u) * v * p01 + u * v * p11))
.to_point()
}
/// Bilinear colour and opacity of patch (r, c) at local (u, v). Corners all in CMYK (or all
/// grey) mix in that space, as a PDF shading mixes in its own colour space: the inks come out
/// exact, and a CMYK document separates no colour to draw them. Other corners mix in RGB.
pub fn color_at(&self, r: usize, c: usize, u: f64, v: f64) -> (Color, f32) {
let q =
[&self.points[self.idx(r, c)], &self.points[self.idx(r, c + 1)], &self.points[self.idx(r + 1, c)], &self.points[self.idx(r + 1, c + 1)]];
let w = [(1.0 - u) * (1.0 - v), u * (1.0 - v), (1.0 - u) * v, u * v];
let op = q.iter().zip(w).map(|(p, w)| p.opacity * w as f32).sum();
let cmyk: Option<Vec<[f32; 4]>> =
q.iter().map(|p| if let Color::Cmyk { c, m, y, k } = p.color { Some([c, m, y, k]) } else { None }).collect();
if let Some(inks) = cmyk {
let mut mix = [0.0f32; 4];
for (ink, w) in inks.iter().zip(w) {
for (m, x) in mix.iter_mut().zip(ink) {
*m += x * w as f32;
}
}
let [c, m, y, k] = mix;
return (Color::Cmyk { c, m, y, k }, op);
}
let grey: Option<Vec<f32>> = q.iter().map(|p| if let Color::Gray { k } = p.color { Some(k) } else { None }).collect();
if let Some(ks) = grey {
return (Color::Gray { k: ks.iter().zip(w).map(|(k, w)| k * w as f32).sum() }, op);
}
let mut rgb = [0.0f32; 3];
for (p, w) in q.iter().zip(w) {
for (ch, x) in rgb.iter_mut().zip(p.color.to_rgb()) {
*ch += x * w as f32;
}
}
(Color::rgb(rgb[0], rgb[1], rgb[2]), op)
}
/// Tessellate into `n`×`n` quads per patch, each coloured at its centre and its corners.
pub fn quads(&self, n: usize) -> Vec<MeshQuad> {
if !self.is_valid() {
return vec![];
}
let n = n.clamp(1, 64);
let mut out = Vec::with_capacity(self.rows as usize * self.cols as usize * n * n);
let mut grid = vec![Point::ZERO; (n + 1) * (n + 1)];
let mut colors = vec![(Color::default(), 0.0f32); (n + 1) * (n + 1)];
for r in 0..self.rows as usize {
for c in 0..self.cols as usize {
for j in 0..=n {
for i in 0..=n {
let (u, v) = (i as f64 / n as f64, j as f64 / n as f64);
grid[j * (n + 1) + i] = self.eval(r, c, u, v);
colors[j * (n + 1) + i] = self.color_at(r, c, u, v);
}
}
for j in 0..n {
for i in 0..n {
let (color, opacity) = self.color_at(r, c, (i as f64 + 0.5) / n as f64, (j as f64 + 0.5) / n as f64);
let g = |a: usize, b: usize| grid[b * (n + 1) + a];
let k = |a: usize, b: usize| colors[b * (n + 1) + a];
out.push(MeshQuad {
pts: [g(i, j), g(i + 1, j), g(i + 1, j + 1), g(i, j + 1)],
color,
opacity,
corners: [k(i, j), k(i + 1, j), k(i + 1, j + 1), k(i, j + 1)],
});
}
}
}
}
out
}
/// The mesh's outer boundary as a closed path.
pub fn outline(&self) -> PathData {
if !self.is_valid() {
return PathData::default();
}
let (rows, cols) = (self.rows as usize, self.cols as usize);
let mut segs: Vec<CubicBez> = vec![];
for c in 0..cols {
segs.push(self.edge_u(0, c));
}
for r in 0..rows {
segs.push(self.edge_v(r, cols));
}
for c in (0..cols).rev() {
let e = self.edge_u(rows, c);
segs.push(CubicBez::new(e.p3, e.p2, e.p1, e.p0));
}
for r in (0..rows).rev() {
let e = self.edge_v(r, 0);
segs.push(CubicBez::new(e.p3, e.p2, e.p1, e.p0));
}
let mut anchors: Vec<Anchor> = Vec::with_capacity(segs.len());
for (i, s) in segs.iter().enumerate() {
let prev = &segs[(i + segs.len() - 1) % segs.len()];
anchors.push(Anchor::with_handles(s.p0, prev.p2, s.p1));
}
PathData::single(SubPath::new(anchors, true))
}
/// Mesh lines (all row and column edges) as open paths, for outline view and editing overlays.
pub fn lines(&self) -> PathData {
if !self.is_valid() {
return PathData::default();
}
let (rows, cols) = (self.rows as usize, self.cols as usize);
let mut subs = vec![];
let cub = |e: CubicBez| SubPath::new(vec![Anchor::with_handles(e.p0, e.p0, e.p1), Anchor::with_handles(e.p3, e.p2, e.p3)], false);
for r in 0..=rows {
for c in 0..cols {
subs.push(cub(self.edge_u(r, c)));
}
}
for c in 0..=cols {
for r in 0..rows {
subs.push(cub(self.edge_v(r, c)));
}
}
PathData::new(subs)
}
/// Control bounds (points and handles).
pub fn bounds(&self) -> Option<Rect> {
let mut it = self.points.iter().flat_map(|p| std::iter::once(p.p).chain(p.handles.iter().map(move |h| p.p + *h)));
let first = it.next()?;
Some(it.fold(Rect::from_points(first, first), |r, q| r.union_pt(q)))
}
pub fn transform(&mut self, a: Affine) {
let lin = Affine::new({
let c = a.as_coeffs();
[c[0], c[1], c[2], c[3], 0.0, 0.0]
});
for p in &mut self.points {
p.p = a * p.p;
for h in &mut p.handles {
*h = (lin * h.to_point()).to_vec2();
}
}
}
/// Map points (and handle ends) through a non-linear function.
pub fn map(&mut self, f: &dyn Fn(Point) -> Point) {
for p in &mut self.points {
let q = f(p.p);
for h in &mut p.handles {
*h = f(p.p + *h) - q;
}
p.p = q;
}
}
/// Which patch and local (u, v) contains `p` (sampled search; `None` outside the mesh).
pub fn locate(&self, p: Point) -> Option<(usize, usize, f64, f64)> {
if !self.is_valid() {
return None;
}
let bp = self.outline().to_bezpath();
if bp.winding(p) == 0 {
return None;
}
const N: usize = 16;
let mut best = (f64::INFINITY, 0, 0, 0.0, 0.0);
for r in 0..self.rows as usize {
for c in 0..self.cols as usize {
for j in 0..=N {
for i in 0..=N {
let (u, v) = (i as f64 / N as f64, j as f64 / N as f64);
let d = self.eval(r, c, u, v).distance_squared(p);
if d < best.0 {
best = (d, r, c, u, v);
}
}
}
}
}
// Refine with a few Newton-free local searches.
let (_, r, c, mut u, mut v) = best;
let mut step = 0.5 / N as f64;
for _ in 0..12 {
let mut improved = false;
for (du, dv) in [(step, 0.0), (-step, 0.0), (0.0, step), (0.0, -step)] {
let (nu, nv) = ((u + du).clamp(0.0, 1.0), (v + dv).clamp(0.0, 1.0));
if self.eval(r, c, nu, nv).distance_squared(p) < self.eval(r, c, u, v).distance_squared(p) {
u = nu;
v = nv;
improved = true;
}
}
if !improved {
step /= 2.0;
}
}
Some((r, c, u, v))
}
/// Index of the mesh point within `tol` of `p`.
pub fn point_near(&self, p: Point, tol: f64) -> Option<usize> {
self.points
.iter()
.enumerate()
.filter(|(_, q)| q.p.distance(p) <= tol)
.min_by(|a, b| a.1.p.distance(p).total_cmp(&b.1.p.distance(p)))
.map(|(i, _)| i)
}
fn surface_du(&self, r: usize, c: usize, u: f64, v: f64) -> Vec2 {
let e = 1e-3;
let (a, b) = ((u - e).max(0.0), (u + e).min(1.0));
(self.eval(r, c, b, v) - self.eval(r, c, a, v)) / (b - a)
}
fn surface_dv(&self, r: usize, c: usize, u: f64, v: f64) -> Vec2 {
let e = 1e-3;
let (a, b) = ((v - e).max(0.0), (v + e).min(1.0));
(self.eval(r, c, u, b) - self.eval(r, c, u, a)) / (b - a)
}
/// Insert a mesh row through patch row `r` at local `v`.
pub fn insert_row(&mut self, r: usize, v: f64) {
let cols = self.cols as usize;
let v = v.clamp(0.01, 0.99);
let mut row = Vec::with_capacity(cols + 1);
// Split the vertical edges.
let mut ups = vec![];
for c in 0..=cols {
let e = self.edge_v(r, c);
let (l, rr) = (e.subsegment(0.0..v), e.subsegment(v..1.0));
ups.push((l.p1 - l.p0, rr.p2 - rr.p3));
let pc = c.min(cols - 1);
let u = if c == cols { 1.0 } else { 0.0 };
let (color, opacity) = self.color_at(r, pc, u, v);
// Horizontal handles: isocurve derivatives on either side.
let right = if c < cols { self.surface_du(r, c, 0.0, v) / (3.0) } else { Vec2::ZERO };
let left = if c > 0 { -self.surface_du(r, c - 1, 1.0, v) / 3.0 } else { Vec2::ZERO };
row.push(MeshPoint { p: l.p3, color, opacity, handles: [right, left, rr.p1 - rr.p0, l.p2 - l.p3] });
}
for (c, (down, up)) in ups.into_iter().enumerate() {
let i0 = self.idx(r, c);
let i1 = self.idx(r + 1, c);
self.points[i0].handles[H_DOWN] = down;
self.points[i1].handles[H_UP] = up;
}
let at = self.idx(r + 1, 0);
self.points.splice(at..at, row);
self.rows += 1;
}
/// Insert a mesh column through patch column `c` at local `u`.
pub fn insert_col(&mut self, c: usize, u: f64) {
let rows = self.rows as usize;
let u = u.clamp(0.01, 0.99);
let mut col = Vec::with_capacity(rows + 1);
for r in 0..=rows {
let e = self.edge_u(r, c);
let (l, rr) = (e.subsegment(0.0..u), e.subsegment(u..1.0));
let pr = r.min(rows - 1);
let v = if r == rows { 1.0 } else { 0.0 };
let (color, opacity) = self.color_at(pr, c, u, v);
let down = if r < rows { self.surface_dv(r, c, u, 0.0) / 3.0 } else { Vec2::ZERO };
let up = if r > 0 { -self.surface_dv(r - 1, c, u, 1.0) / 3.0 } else { Vec2::ZERO };
col.push((MeshPoint { p: l.p3, color, opacity, handles: [rr.p1 - rr.p0, l.p2 - l.p3, down, up] }, l.p1 - l.p0, rr.p2 - rr.p3));
}
let cols = self.cols as usize;
let mut pts = Vec::with_capacity((rows + 1) * (cols + 2));
for (r, (mp, right, left)) in col.into_iter().enumerate() {
for cc in 0..=cols {
let mut q = self.points[r * (cols + 1) + cc].clone();
if cc == c {
q.handles[H_RIGHT] = right;
}
if cc == c + 1 {
q.handles[H_LEFT] = left;
}
pts.push(q);
if cc == c {
pts.push(mp.clone());
}
}
}
self.points = pts;
self.cols += 1;
}
/// Mesh tool click: add a row and a column through `p` (inside the mesh). Returns the new point index.
pub fn add_lines_at(&mut self, p: Point) -> Option<usize> {
let (r, c, u, v) = self.locate(p)?;
let mut rr = r;
let mut cc = c;
let row_new = v > 0.02 && v < 0.98;
let col_new = u > 0.02 && u < 0.98;
if row_new {
self.insert_row(r, v);
rr = r + 1;
} else if v >= 0.98 {
rr = r + 1;
}
if col_new {
self.insert_col(c, u);
cc = c + 1;
} else if u >= 0.98 {
cc = c + 1;
}
Some(self.idx(rr, cc))
}
/// Mesh tool Alt-click: delete the mesh lines through point `index` (interior lines only).
pub fn remove_point_lines(&mut self, index: usize) -> bool {
// A mesh from a file may not have the points its rows and columns need: it is indexed below.
if !self.is_valid() || index >= self.points.len() {
return false;
}
let w = self.cols as usize + 1;
let (r, c) = (index / w, index % w);
let mut changed = false;
if r > 0 && r < self.rows as usize {
// Merge the edges above and below: keep the outer handles.
for cc in 0..w {
let above = self.idx(r - 1, cc);
let below = self.idx(r + 1, cc);
let mid = self.idx(r, cc);
let (pa, pm, pb) = (self.points[above].p, self.points[mid].p, self.points[below].p);
let _ = pm;
self.points[above].handles[H_DOWN] = (pb - pa) / 3.0;
self.points[below].handles[H_UP] = (pa - pb) / 3.0;
}
self.points.drain(r * w..(r + 1) * w);
self.rows -= 1;
changed = true;
}
let w = self.cols as usize + 1;
if c > 0 && c < self.cols as usize {
let rows = self.rows as usize;
for rr in 0..=rows {
let (l, rt) = (rr * w + c - 1, rr * w + c + 1);
let (pl, pr) = (self.points[l].p, self.points[rt].p);
self.points[l].handles[H_RIGHT] = (pr - pl) / 3.0;
self.points[rt].handles[H_LEFT] = (pl - pr) / 3.0;
}
let mut k = 0;
self.points.retain(|_| {
let keep = k % w != c;
k += 1;
keep
});
self.cols -= 1;
changed = true;
}
changed
}
}
// =====================================================================================
// Envelopes
// =====================================================================================
/// Union of the geometric bounds of `nodes`.
pub fn nodes_bounds(nodes: &[Arc<Node>]) -> Option<Rect> {
nodes.iter().fold(None, |acc, c| vectorcraft_geom::union_opt(acc, c.geometric_bounds()))
}
/// A `(rows+1)×(cols+1)` grid over `r` (row-major).
pub fn grid_points(r: Rect, rows: u32, cols: u32) -> Vec<Point> {
let mut v = Vec::with_capacity(((rows + 1) * (cols + 1)) as usize);
for i in 0..=rows {
for j in 0..=cols {
v.push(Point::new(r.x0 + r.width() * j as f64 / cols.max(1) as f64, r.y0 + r.height() * i as f64 / rows.max(1) as f64));
}
}
v
}
fn catmull(p0: Vec2, p1: Vec2, p2: Vec2, p3: Vec2, t: f64) -> Vec2 {
let t2 = t * t;
let t3 = t2 * t;
0.5 * (2.0 * p1 + (p2 - p0) * t + (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3) * t2 + (3.0 * p1 - p0 - 3.0 * p2 + p3) * t3)
}
/// Point map from the unit square onto a point grid (tensor-product Catmull-Rom; linear
/// extrapolation at the borders so an undistorted grid is the identity, also past the square).
pub(super) fn grid_eval(rows: usize, cols: usize, pts: &[Point], u: f64, v: f64) -> Point {
let at = |r: i64, c: i64| -> Vec2 {
let rr = r.clamp(0, rows as i64);
let cc = c.clamp(0, cols as i64);
let base = pts[rr as usize * (cols + 1) + cc as usize].to_vec2();
// Linear extrapolation outside the grid.
let er = r - rr;
let ec = c - cc;
let mut p = base;
if er != 0 && rows >= 1 {
let inner = (rr - er.signum()).clamp(0, rows as i64);
p += (base - pts[inner as usize * (cols + 1) + cc as usize].to_vec2()) * er.abs() as f64;
}
if ec != 0 && cols >= 1 {
let inner = (cc - ec.signum()).clamp(0, cols as i64);
p += (base - pts[rr as usize * (cols + 1) + inner as usize].to_vec2()) * ec.abs() as f64;
}
p
};
// Past the grid's edges the outer patches go on (art can reach past the content's box).
let (su, sv) = (u * cols as f64, v * rows as f64);
let (ci, ri) = ((su.floor() as i64).clamp(0, cols as i64 - 1), (sv.floor() as i64).clamp(0, rows as i64 - 1));
let (fu, fv) = (su - ci as f64, sv - ri as f64);
let mut rowsv = [Vec2::ZERO; 4];
for (k, rv) in rowsv.iter_mut().enumerate() {
let r = ri - 1 + k as i64;
*rv = catmull(at(r, ci - 1), at(r, ci), at(r, ci + 1), at(r, ci + 2), fu);
}
catmull(rowsv[0], rowsv[1], rowsv[2], rowsv[3], fv).to_point()
}
/// The surface (u, v ∈ [0,1]) an envelope of `kind` maps content onto, for content whose bounds in
/// the envelope's own `frame` (its axes → the document) are `src`: a warp bends along the frame's
/// axes; a mesh's points and a top object's path are in the document already.
pub(super) fn surface_of<'a>(kind: &'a EnvelopeKind, src: Rect, frame: Affine) -> Box<dyn Fn(f64, f64) -> Point + 'a> {
let flat = move |u: f64, v: f64| frame * Point::new(src.x0 + u * src.width(), src.y0 + v * src.height());
match kind {
EnvelopeKind::Warp { style, bend, h: dh, v: dv, horizontal } => {
let st = WarpStyle::from_id(style).unwrap_or(WarpStyle::Arc);
let b = bend.clamp(-100.0, 100.0) / 100.0;
let (dh, dv) = (dh.clamp(-100.0, 100.0) / 100.0, dv.clamp(-100.0, 100.0) / 100.0);
let c = src.center();
let (hw, hh) = (src.width() / 2.0, src.height() / 2.0);
let horizontal = *horizontal;
Box::new(move |u: f64, v: f64| {
let (x, y) = (2.0 * u - 1.0, 2.0 * v - 1.0);
let (x2, y2) = if horizontal {
warp_point(st, b, dh, dv, hh / hw.max(1e-9), x, y)
} else {
let (a, b2) = warp_point(st, b, dh, dv, hw / hh.max(1e-9), y, x);
(b2, a)
};
frame * Point::new(c.x + x2 * hw, c.y + y2 * hh)
})
}
EnvelopeKind::Mesh { rows, cols, points, handles } => {
if !handles.is_empty()
&& let Some(m) = envelope_grid(*rows, *cols, points, handles)
{
return Box::new(move |u: f64, v: f64| mesh_at(&m, u, v));
}
if *rows == 0 || *cols == 0 || grid_len(*rows, *cols) != Some(points.len()) {
return Box::new(flat);
}
let (rows, cols) = (*rows as usize, *cols as usize);
Box::new(move |u: f64, v: f64| grid_eval(rows, cols, points, u, v))
}
EnvelopeKind::TopObject { path } => match Coons::from_path(path) {
Some(co) => Box::new(move |u: f64, v: f64| co.eval(u, v)),
None => Box::new(flat),
},
}
}
crates/doc/src/live/warp.rs
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use super::*;
// =====================================================================================
// Warp maps (shared with vectorcraft-effects' Warp effects)
// =====================================================================================
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum WarpStyle {
Arc,
ArcLower,
ArcUpper,
Arch,
Bulge,
ShellLower,
ShellUpper,
Flag,
Wave,
Fish,
Rise,
Fisheye,
Inflate,
Squeeze,
Twist,
}
impl WarpStyle {
/// From the id suffix (`arc`, `arcLower`, …).
pub fn from_id(s: &str) -> Option<Self> {
use WarpStyle::*;
Some(match s {
"arc" => Arc,
"arcLower" => ArcLower,
"arcUpper" => ArcUpper,
"arch" => Arch,
"bulge" => Bulge,
"shellLower" => ShellLower,
"shellUpper" => ShellUpper,
"flag" => Flag,
"wave" => Wave,
"fish" => Fish,
"rise" => Rise,
"fisheye" => Fisheye,
"inflate" => Inflate,
"squeeze" => Squeeze,
"twist" => Twist,
_ => return None,
})
}
}
/// The warp map on normalised coordinates: `b` = bend (-1..1), `dh`/`dv` = distortion (-1..1);
/// `aspect` is the box's half-height over its half-width along the warp (Arc bends in real
/// proportions).
pub fn warp_point(style: WarpStyle, b: f64, dh: f64, dv: f64, aspect: f64, x: f64, y: f64) -> (f64, f64) {
use WarpStyle::*;
let t = (y + 1.0) / 2.0; // 0 at top, 1 at bottom
let par = 1.0 - x * x; // parabola: 1 at centre, 0 at sides
let (mut x2, mut y2) = match style {
Arc => {
if b.abs() < 1e-6 {
(x, y)
} else {
// Bend the centre line into a circular arc of equal length (sweep = |b|·180°), in
// the box's real proportions (lengths in half-widths, so y counts `aspect` each):
// the edges are concentric arcs, and one that would pass the centre stops there
// instead of folding over (#1578).
let k = if aspect.is_finite() && aspect > 0.0 { aspect } else { 1.0 };
let sweep = b.abs() * PI;
let r0 = 2.0 / sweep;
let yy = if b > 0.0 { y } else { -y } * k;
let a = x / r0;
let r = (r0 - yy).max(0.0);
let (s, c) = a.sin_cos();
let (nx, ny) = (r * s, (r0 - r * c) / k);
(nx, if b > 0.0 { ny } else { -ny })
}
}
ArcLower => (x, y + b * par * t),
ArcUpper => (x, y - b * par * (1.0 - t)),
Arch => (x, y - b * par),
Bulge => (x, y + b * par * y),
ShellLower => (x * (1.0 - 0.5 * b * (1.0 - t)), y + b * par * t),
ShellUpper => (x * (1.0 - 0.5 * b * t), y - b * par * (1.0 - t)),
Flag => (x, y + 0.5 * b * (PI * x).sin()),
Wave => (x + 0.1 * b * (PI * y).sin(), y + 0.3 * b * (2.0 * PI * x).sin() * (0.5 + 0.5 * t)),
Fish => (x, y * (1.0 + 0.5 * b * (0.75 * PI * (x + 1.0)).sin())),
Rise => (x, y - b * ((x + 1.0) / 2.0).powi(2) * 2.0 + b),
Fisheye => {
let r2 = x * x + y * y;
let s = if r2 < 1.0 { 1.0 + 0.5 * b * (1.0 - r2) } else { 1.0 };
(x * s, y * s)
}
Inflate => (x * (1.0 + 0.5 * b * (1.0 - y * y)), y * (1.0 + 0.5 * b * par)),
Squeeze => (x * (1.0 - 0.5 * b * (1.0 - y * y)), y * (1.0 + 0.3 * b * par)),
Twist => {
let r = (x * x + y * y).sqrt();
let a = -b * PI * 0.5 * (1.0 - r / std::f64::consts::SQRT_2).max(0.0);
let (s, c) = a.sin_cos();
(x * c - y * s, x * s + y * c)
}
};
// Perspective-like distortion: horizontal narrows one side, vertical one end.
if dh != 0.0 {
y2 *= (1.0 + dh * x2 * 0.5).max(0.0);
}
if dv != 0.0 {
x2 *= (1.0 + dv * y2 * 0.5).max(0.0);
}
(x2, y2)
}
/// Segment as a cubic; straight lines get handles at 1/3 and 2/3 so a non-linear map bends them.
fn seg_cubic(sp: &SubPath, i: usize) -> CubicBez {
let c = sp.segment(i);
if sp.segment_is_line(i) { CubicBez::new(c.p0, c.p0.lerp(c.p3, 1.0 / 3.0), c.p0.lerp(c.p3, 2.0 / 3.0), c.p3) } else { c }
}
fn poly_len(c: &CubicBez) -> f64 {
c.p0.distance(c.p1) + c.p1.distance(c.p2) + c.p2.distance(c.p3)
}
/// Running length along a polyline: `0, |p0p1|, |p0p1| + |p1p2|, …` (one entry per point).
fn cumulative_lengths(pts: &[Point]) -> Vec<f64> {
let mut total = 0.0;
let mut cum = Vec::with_capacity(pts.len());
cum.push(0.0);
for w in pts.windows(2) {
total += w[0].distance(w[1]);
cum.push(total);
}
cum
}
/// Most pieces [`map_nonlinear`] splits one segment into.
const MAX_PIECES: usize = 64;
/// How many pieces of about `piece` a segment of length `len` is split into: one to `most`.
pub fn pieces(len: f64, piece: f64, most: usize) -> usize {
((len / piece).ceil() as usize).clamp(1, most.max(1))
}
/// The piece length to split segments of lengths `lens` with ([`pieces`], at most `most` each) so
/// that the pieces past each segment's first number at most `room`: `piece` when they already do,
/// longer pieces otherwise. A segment of `n` pieces adds `n - 1 ≤ len / piece` points to a path,
/// so pieces of the total length over `room` fit; with no room every segment stays one piece.
pub fn fit_piece(lens: &[f64], piece: f64, most: usize, room: usize) -> f64 {
let added = lens.iter().map(|&len| pieces(len, piece, most) - 1).fold(0, usize::saturating_add);
if added <= room {
return piece;
}
if room == 0 {
return f64::INFINITY;
}
// A NaN length is always one piece.
piece.max(lens.iter().filter(|len| !len.is_nan()).sum::<f64>() / room as f64)
}
/// Map every point of `path` through the non-linear function `f`. Segments are split into pieces
/// no longer than about `max_piece` (up to 64 per segment) and their control points mapped, which
/// approximates the image curve to O(h²). Closedness and subpath structure are preserved.
pub fn map_nonlinear(path: &PathData, max_piece: f64, f: impl Fn(Point) -> Point) -> PathData {
map_nonlinear_within(path, max_piece, usize::MAX, f)
}
/// [`map_nonlinear`] whose result has at most `max` anchors, or `path`'s count when that is more:
/// where pieces of `max_piece` would make more, the pieces grow until they don't ([`fit_piece`]),
/// a coarser approximation of the image curve. Geometry effects map within their anchor budget.
pub fn map_nonlinear_within(path: &PathData, max_piece: f64, max: usize, f: impl Fn(Point) -> Point) -> PathData {
let mut max_piece = max_piece.max(1e-3);
// Each segment adds one anchor per piece past its first.
let room = max.saturating_sub(path.anchor_count());
let segs = path.subpaths.iter().map(SubPath::segment_count).fold(0, usize::saturating_add);
if segs.saturating_mul(MAX_PIECES - 1) > room {
let lens: Vec<f64> = path.subpaths.iter().flat_map(|sp| (0..sp.segment_count()).map(|i| poly_len(&seg_cubic(sp, i)))).collect();
max_piece = fit_piece(&lens, max_piece, MAX_PIECES, room);
}
let mut subs = Vec::with_capacity(path.subpaths.len());
for sp in &path.subpaths {
let n = sp.anchors.len();
if n == 0 {
continue;
}
let segs = sp.segment_count();
let mut res: Vec<Anchor> = Vec::new();
let mut pending_in: Option<Point> = None;
for i in 0..n {
let a = &sp.anchors[i];
let h_in = pending_in.take().unwrap_or_else(|| f(a.h_in));
res.push(Anchor { p: f(a.p), h_in, h_out: f(a.h_out), kind: a.kind });
if i < segs {
let c = seg_cubic(sp, i);
let k = pieces(poly_len(&c), max_piece, MAX_PIECES);
for j in 0..k {
let sub = c.subsegment((j as f64 / k as f64)..((j + 1) as f64 / k as f64));
if let Some(last) = res.last_mut() {
last.h_out = f(sub.p1);
}
if j + 1 < k {
res.push(Anchor { p: f(sub.p3), h_in: f(sub.p2), h_out: f(sub.p3), kind: Default::default() });
} else {
pending_in = Some(f(sub.p2));
}
}
}
}
if let Some(h) = pending_in
&& sp.closed
&& let Some(first) = res.first_mut()
{
first.h_in = h;
}
let anchors = res.into_iter().map(|a| Anchor::with_handles(a.p, a.h_in, a.h_out)).collect();
subs.push(SubPath::new(anchors, sp.closed));
}
PathData::new(subs)
}
// =====================================================================================
// Coons patches from outlines
// =====================================================================================
pub(super) fn flatten_subpath(sp: &SubPath, tol: f64) -> Vec<Point> {
let mut bp = BezPath::new();
sp.to_bezpath_into(&mut bp);
let mut pts: Vec<Point> = Vec::new();
vectorcraft_geom::kurbo::flatten(bp.iter(), tol, |el| match el {
vectorcraft_geom::PathEl::MoveTo(p) | vectorcraft_geom::PathEl::LineTo(p) if pts.last().is_none_or(|q| q.distance(p) > 1e-9) => pts.push(p),
_ => {}
});
pts
}
pub(super) fn resample(poly: &[Point], m: usize) -> Vec<Point> {
if poly.is_empty() {
return vec![Point::ZERO; m];
}
if poly.len() == 1 {
return vec![poly[0]; m];
}
let cum = cumulative_lengths(poly);
let total = cum.last().copied().unwrap_or(0.0);
let mut out = Vec::with_capacity(m);
let mut i = 0;
for k in 0..m {
let s = if m > 1 { total * k as f64 / (m - 1) as f64 } else { 0.0 };
while i + 2 < cum.len() && cum[i + 1] < s {
i += 1;
}
let seg = (cum[i + 1] - cum[i]).max(1e-12);
out.push(poly[i].lerp(poly[i + 1], ((s - cum[i]) / seg).clamp(0.0, 1.0)));
}
out
}