mirror of
https://github.com/storytold/cadcraft.git
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6ee6e652fd
* fix(snap): keep an arc's sweep for TAN, PER and deferred snaps An arc was snapped as its full circle: TAN and PER solutions on the circle that fall outside the arc's sweep were offered as if they touched the arc, and a deferred tangent lost the sweep when it was stored. - SnapCurve gains an Arc variant carrying start and end, so a deferred snap keeps the sweep and resolves onto the arc. - TAN and PER filter their solutions with Arc::contains_angle; PER clamps to the arc with Arc::closest instead of the circle's closest point. - Tangents and perpendiculars between two deferred snaps are filtered on both ends. - The viewport projection maps the new variant. - Tests: a tangent in the gap is not offered, the perpendicular clamps to an end, and a deferred tangent keeps its sweep and solves onto the arc. Fixes #1697 * fix(snap): correct direct PER, support Arc in deferred pairs Addresses the review on #1698: - Direct PER on an arc used `arc.closest(bp)`, which clamps a gap solution to an end and misses the valid opposite antipode; both antipodes are now offered, filtered to the arc's sweep. - `deferred_pairs` matched only circles and lines, so any deferred pair with an arc operand fell through to None. An arc is now matched as its carrier circle for the math, with the sweep filter still applied to the solutions. - Tests: the direct PER case now expects the antipode on the arc, and a TAN-TAN pair between an arc and a circle only keeps the tangent on the arc. * test(snap): use a margin over the boundary in the arc PER test Addresses the review on #1698: the cursor is 5 units from the antipode, so the aperture is 5.5 rather than 5.0 to keep the distance comparison off the boundary; the comment now describes the antipode rather than the nearest end. * cargo fmt Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> --------- Co-authored-by: Brandon Thomas <echelon@gmail.com> Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
1338 lines
60 KiB
Rust
1338 lines
60 KiB
Rust
//! Object snaps (OSNAP), polar tracking and ortho.
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mod curves;
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pub mod iso;
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pub mod tracking;
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mod viewport;
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pub use viewport::ViewportPoint;
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use cadcraft_doc::{Drawing, EntityKind, Insert, MAX_BLOCK_DEPTH, Prim, Space};
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use cadcraft_geom::{Bounds2, Circle, EPS, Ellipse, Mat3, PI, Segment, Vec2, intersect_ext};
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use serde::Serialize;
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/// OSMODE bits.
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pub mod mode {
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pub const END: u32 = 1;
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pub const MID: u32 = 2;
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pub const CEN: u32 = 4;
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pub const NOD: u32 = 8;
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pub const QUA: u32 = 16;
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pub const INT: u32 = 32;
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pub const INS: u32 = 64;
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pub const PER: u32 = 128;
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pub const TAN: u32 = 256;
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pub const NEA: u32 = 512;
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pub const GCEN: u32 = 1024;
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pub const APP: u32 = 2048;
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pub const EXT: u32 = 4096;
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pub const PAR: u32 = 8192;
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/// Running snaps temporarily off (F3).
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pub const OFF: u32 = 16384;
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/// Not an OSMODE bit: snaps also find hatch objects (OSNAPHATCH = 1).
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pub const HATCH: u32 = 1 << 16;
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pub const ALL: [(u32, &str); 14] = [
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(END, "Endpoint"),
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(MID, "Midpoint"),
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(CEN, "Center"),
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(GCEN, "Geometric Center"),
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(NOD, "Node"),
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(QUA, "Quadrant"),
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(INT, "Intersection"),
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(EXT, "Extension"),
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(INS, "Insertion"),
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(PER, "Perpendicular"),
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(TAN, "Tangent"),
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(NEA, "Nearest"),
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(APP, "Apparent Intersection"),
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(PAR, "Parallel"),
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];
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}
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#[derive(Clone, Copy, Debug, PartialEq, Serialize)]
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#[serde(rename_all = "camelCase")]
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pub struct SnapHit {
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pub point: Vec2,
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pub mode: u32,
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pub name: &'static str,
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/// Model coordinates when this paper-space hit is inside a layout viewport.
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#[serde(skip_serializing_if = "Option::is_none")]
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pub viewport: Option<ViewportPoint>,
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/// A deferred tangent/perpendicular: `point` is only provisional (the nearest point on the
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/// curve) until the other end of the line is known. See [`resolve_deferred`].
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#[serde(skip_serializing_if = "Option::is_none")]
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pub deferred: Option<Deferred>,
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}
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impl SnapHit {
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/// The command input a pick at this snap gives: a deferred snap or a plain point.
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pub fn input(&self) -> crate::Input {
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match self.deferred {
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Some(d) => crate::Input::Deferred(d),
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None => crate::Input::Point(self.point),
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}
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}
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}
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/// The curve a deferred snap refers to.
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#[derive(Clone, Copy, Debug, PartialEq, Serialize)]
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#[serde(tag = "kind", rename_all = "camelCase")]
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pub enum SnapCurve {
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/// A circle, or the circle an arc lies on; an arc's sweep is carried by [`SnapCurve::Arc`].
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Circle { center: Vec2, radius: f64 },
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/// An arc: the points of `Circle { center, radius }` swept CCW from `start` to `end` (radians).
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Arc { center: Vec2, radius: f64, start: f64, end: f64 },
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/// The infinite line through `a` and `b` (a line, xline or ray).
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Line { a: Vec2, b: Vec2 },
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}
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impl SnapCurve {
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/// Whether `p` lies on the drawn curve: always on a circle or a line, and only within the
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/// sweep on an arc. Tangent and perpendicular solutions on an arc's circle that fall off the
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/// arc are filtered out with this, so they never snap into the gap.
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pub fn contains(&self, p: Vec2) -> bool {
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match self {
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// A zero sweep is how a full circle is stored (see `fix_circle`): the whole circle.
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SnapCurve::Arc { center, radius, start, end } => {
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(*start - *end).abs() < 1e-12 || cadcraft_geom::Arc::new(*center, *radius, *start, *end).contains_angle(center.angle_to(p))
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}
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_ => true,
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}
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}
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/// Points on the curve whose tangent passes through `p` (a circle's or an arc's).
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fn tangents(&self, p: Vec2) -> Vec<Vec2> {
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match self {
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SnapCurve::Circle { center, radius } | SnapCurve::Arc { center, radius, .. } => {
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Circle::new(*center, *radius).tangent_points(p).into_iter().filter(|t| self.contains(*t)).collect()
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}
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SnapCurve::Line { .. } => Vec::new(),
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}
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}
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/// Points on the curve whose perpendicular passes through `p`; `picked` is where the curve
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/// was picked, kept when `p` is the center of a circle or arc (every radius is perpendicular).
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fn perpendiculars(&self, p: Vec2, picked: Vec2) -> Vec<Vec2> {
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match self {
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SnapCurve::Circle { center, radius } | SnapCurve::Arc { center, radius, .. } => {
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let u = (p - *center).normalized();
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if u == Vec2::ZERO {
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vec![Circle::new(*center, *radius).closest(picked)]
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} else {
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[*center + u * *radius, *center - u * *radius].into_iter().filter(|q| self.contains(*q)).collect()
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}
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}
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SnapCurve::Line { a, b } => line_dir(*a, *b).map(|_| vec![cadcraft_geom::Line::new(*a, *b).project(p)]).unwrap_or_default(),
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}
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}
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}
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/// A deferred tangent ([`mode::TAN`]) or perpendicular ([`mode::PER`]) snap, picked while there
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/// is no base point yet (the first point of a line). The real point depends on the other end of
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/// the line, so it is resolved later with [`resolve_deferred`].
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#[derive(Clone, Copy, Debug, PartialEq, Serialize)]
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#[serde(rename_all = "camelCase")]
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pub struct Deferred {
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pub mode: u32,
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pub curve: SnapCurve,
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/// Where the curve was picked (the nearest point on it); chooses between solutions.
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pub at: Vec2,
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}
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/// The point on `curve` whose tangent has direction `dir`, picking the solution
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/// nearest `hint`. Used to resolve a deferred TAN first point when the next point
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/// is typed as `@distance<angle`.
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pub fn tangent_point_in_direction(curve: &SnapCurve, dir: f64, hint: Vec2) -> Option<Vec2> {
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match curve {
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SnapCurve::Circle { center, radius } => {
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let n = dir + std::f64::consts::FRAC_PI_2;
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let c1 = *center + Vec2::new(n.cos(), n.sin()) * *radius;
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let c2 = *center - Vec2::new(n.cos(), n.sin()) * *radius;
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Some(if c1.dist(hint) < c2.dist(hint) { c1 } else { c2 })
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}
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SnapCurve::Arc { center, radius, start, end } => {
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let n = dir + std::f64::consts::FRAC_PI_2;
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let c1 = *center + Vec2::new(n.cos(), n.sin()) * *radius;
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let c2 = *center - Vec2::new(n.cos(), n.sin()) * *radius;
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let on = cadcraft_geom::Arc::new(*center, *radius, *start, *end);
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let ok = |c: Vec2| on.contains_angle(center.angle_to(c));
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let (c1, c2) = (ok(c1).then_some(c1), ok(c2).then_some(c2));
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match (c1, c2) {
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(Some(a), Some(b)) => Some(if a.dist(hint) < b.dist(hint) { a } else { b }),
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(a, b) => a.or(b),
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}
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}
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_ => None,
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}
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}
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/// One end of a line being solved: a known point or a deferred snap.
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#[derive(Clone, Copy, Debug, PartialEq)]
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pub enum LineEnd {
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Point(Vec2),
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Deferred(Deferred),
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}
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fn name_of(m: u32) -> &'static str {
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mode::ALL.iter().find(|(b, _)| *b == m).map(|(_, n)| *n).unwrap_or("Snap")
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}
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fn prim_segments(p: &Prim) -> Vec<Segment> {
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match p {
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Prim::Seg(s) => vec![*s],
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Prim::Circle(c) => vec![Segment::Arc { arc: cadcraft_geom::Arc::new(c.center, c.radius, 0.0, 0.0), ccw: true }],
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Prim::Infinite { base, dir, .. } => vec![Segment::Line(cadcraft_geom::Line::new(*base - *dir * 1e7, *base + *dir * 1e7))],
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Prim::Ellipse(e) => {
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let mut pts = Vec::new();
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e.tessellate(e.major.len() * 1e-3, &mut pts);
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pts.windows(2).filter_map(|w| Some(Segment::Line(cadcraft_geom::Line::new(*w.first()?, *w.get(1)?)))).collect()
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}
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Prim::Spline(s) => {
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let pts = s.tessellate(1e-3);
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pts.windows(2).filter_map(|w| Some(Segment::Line(cadcraft_geom::Line::new(*w.first()?, *w.get(1)?)))).collect()
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}
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Prim::Fill(f) => {
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let n = f.len();
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(0..n).filter_map(|i| Some(Segment::Line(cadcraft_geom::Line::new(*f.get(i)?, *f.get((i + 1) % n)?)))).collect()
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}
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Prim::Point(_) => Vec::new(),
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}
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}
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/// Find the best object snap near `cursor` within `aperture` (world units).
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///
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/// Tangent and perpendicular snaps need the base point (the other end of the line). With no
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/// base and `deferred` set (the prompt says it can resolve them, `Prompt.deferred`),
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/// they snap as *deferred*: the hit carries the curve and is resolved once the other end is
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/// known. Deferred hits only win where no other snap does (they are as unspecific as Nearest).
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pub fn osnap(d: &Drawing, space: &Space, cursor: Vec2, aperture: f64, osmode: u32, base: Option<Vec2>, deferred: bool) -> Option<SnapHit> {
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if osmode == 0 || osmode & mode::OFF != 0 {
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return None;
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}
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let ix = crate::spatial::index(d, space);
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osnap_with(d, space, &ix, cursor, aperture, osmode, base, deferred)
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}
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#[allow(clippy::too_many_arguments)]
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pub(crate) fn osnap_with(
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d: &Drawing,
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space: &Space,
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ix: &Option<std::sync::Arc<crate::spatial::SpatialIndex>>,
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cursor: Vec2,
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aperture: f64,
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osmode: u32,
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base: Option<Vec2>,
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deferred: bool,
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) -> Option<SnapHit> {
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osnap_with_neighborhood(d, space, ix, cursor, aperture, osmode, base, deferred).0
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}
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/// Find the best object snap and retain the local-space primitives gathered for that query.
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#[allow(clippy::too_many_arguments)]
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pub(crate) fn osnap_with_neighborhood(
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d: &Drawing,
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space: &Space,
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ix: &Option<std::sync::Arc<crate::spatial::SpatialIndex>>,
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cursor: Vec2,
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aperture: f64,
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osmode: u32,
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base: Option<Vec2>,
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deferred: bool,
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) -> (Option<SnapHit>, Option<Vec<Prim>>) {
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if osmode == 0 || osmode & mode::OFF != 0 || !cursor.is_finite() || !(aperture.is_finite() && aperture > 0.0) {
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return (None, None);
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}
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let (mut best, near_prims) = match osnap_in_with_prims(d, space, ix, cursor, aperture, osmode, base, deferred, &[], None) {
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Some((hit, prims)) => (hit, Some(prims)),
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None => (None, None),
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};
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let views = viewport::near(d, space, cursor, aperture);
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if views.is_empty() {
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return (best, near_prims);
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}
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let model = Space::Model;
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let model_ix = crate::spatial::index(d, &model);
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for view in views {
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let model_cursor = view.to_model(cursor);
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let model_aperture = aperture / view.scale;
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let model_base = base.map(|p| view.to_model(p));
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if !model_cursor.is_finite() || !(model_aperture.is_finite() && model_aperture > 0.0) || model_base.is_some_and(|p| !p.is_finite()) {
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continue;
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}
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let hit = osnap_in(
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d,
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&model,
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&model_ix,
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model_cursor,
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model_aperture,
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osmode,
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model_base,
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deferred,
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&view.viewport.frozen_layers,
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Some(view.model_clip),
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)
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.and_then(|h| view.hit(h));
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if let Some(hit) = hit
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&& best.as_ref().is_none_or(|b| snap_score(hit.mode, hit.point, cursor, aperture) < snap_score(b.mode, b.point, cursor, aperture))
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{
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best = Some(hit);
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}
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}
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(best, near_prims)
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}
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#[allow(clippy::too_many_arguments)]
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fn osnap_in(
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d: &Drawing,
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space: &Space,
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ix: &Option<std::sync::Arc<crate::spatial::SpatialIndex>>,
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cursor: Vec2,
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aperture: f64,
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osmode: u32,
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base: Option<Vec2>,
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deferred: bool,
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frozen: &[String],
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clip: Option<Bounds2>,
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) -> Option<SnapHit> {
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osnap_in_with_prims(d, space, ix, cursor, aperture, osmode, base, deferred, frozen, clip).and_then(|(hit, _)| hit)
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}
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#[allow(clippy::too_many_arguments)]
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fn osnap_in_with_prims(
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d: &Drawing,
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space: &Space,
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ix: &Option<std::sync::Arc<crate::spatial::SpatialIndex>>,
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cursor: Vec2,
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aperture: f64,
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osmode: u32,
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base: Option<Vec2>,
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deferred: bool,
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frozen: &[String],
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clip: Option<Bounds2>,
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) -> Option<(Option<SnapHit>, Vec<Prim>)> {
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let (mut cands, near_prims) = gather_in(d, space, ix, cursor, aperture, osmode, frozen)?;
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// Intersections between nearby primitives; Apparent Intersection also where their extensions
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// meet (lines extended, arcs as full circles: in 2D, the "apparent" crossing of objects
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// that don't reach each other).
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if osmode & (mode::INT | mode::APP) != 0 {
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let mut segs: Vec<Vec<Segment>> = near_prims.iter().take(200).map(prim_segments).collect();
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let probe = finite_intersection_probe(cursor, aperture);
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for (i, segments) in segs.iter_mut().enumerate() {
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let preserves_app = osmode & mode::APP != 0 && near_prims.get(i).is_some_and(extendable);
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if !preserves_app {
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segments.retain(|segment| segment_may_intersect_probe(segment, probe.as_ref()));
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}
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}
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let real = if osmode & mode::INT != 0 { mode::INT } else { mode::APP };
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for i in 0..segs.len() {
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for j in i + 1..segs.len() {
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// Extending a tessellated ellipse or spline chord means nothing.
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let extend = osmode & mode::APP != 0 && [i, j].iter().all(|k| near_prims.get(*k).is_some_and(extendable));
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for a in segs.get(i).into_iter().flatten() {
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for b in segs.get(j).into_iter().flatten() {
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for x in intersect_ext(&fix_circle(a), &fix_circle(b), false) {
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if x.dist(cursor) <= aperture {
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cands.push((real, x));
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}
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}
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if extend {
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for x in intersect_ext(a, b, true) {
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if x.is_finite() && x.dist(cursor) <= aperture {
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cands.push((mode::APP, x));
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}
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}
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}
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}
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}
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}
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}
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}
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let hit = finish(cands, &near_prims, cursor, aperture, osmode, base, deferred, clip);
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Some((hit, near_prims))
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}
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fn finite_intersection_probe(cursor: Vec2, aperture: f64) -> Option<Bounds2> {
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if !(cursor.is_finite() && aperture.is_finite() && aperture > 0.0) {
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return None;
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}
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let probe = Bounds2::new(cursor, cursor).expand(aperture);
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if !finite_bounds(&probe) {
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return None;
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}
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// The finite line intersection accepts a 1e-9 parameter slack; retain that slack in the broad phase.
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let scale = cursor.x.abs().max(cursor.y.abs()).max(aperture).max(1.0);
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let padded = probe.expand(EPS * scale);
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finite_bounds(&padded).then_some(padded)
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}
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fn segment_may_intersect_probe(segment: &Segment, probe: Option<&Bounds2>) -> bool {
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let Some(probe) = probe else { return true };
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let bounds = segment.bounds();
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if !finite_bounds(&bounds) {
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return true;
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}
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let width = bounds.width();
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let height = bounds.height();
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if !(width.is_finite() && height.is_finite()) {
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return true;
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}
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let scale = bounds.min.x.abs().max(bounds.min.y.abs()).max(bounds.max.x.abs()).max(bounds.max.y.abs()).max(width).max(height).max(1.0);
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let padded = bounds.expand(EPS * scale);
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!finite_bounds(&padded) || padded.intersects(probe)
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}
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fn finite_bounds(bounds: &Bounds2) -> bool {
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!bounds.is_empty() && bounds.min.is_finite() && bounds.max.is_finite()
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}
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/// Whether a primitive has a meaningful extension (a line, an arc, a circle, an xline or ray).
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pub(crate) fn extendable(p: &Prim) -> bool {
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matches!(p, Prim::Seg(_) | Prim::Circle(_) | Prim::Infinite { .. })
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}
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/// The snap candidates of `osmode` and the primitives within `aperture` of `cursor`; `None`
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/// when the drawing can't be searched.
|
|
pub(crate) fn gather(
|
|
d: &Drawing,
|
|
space: &Space,
|
|
ix: &Option<std::sync::Arc<crate::spatial::SpatialIndex>>,
|
|
cursor: Vec2,
|
|
aperture: f64,
|
|
osmode: u32,
|
|
) -> Option<(Vec<(u32, Vec2)>, Vec<Prim>)> {
|
|
gather_in(d, space, ix, cursor, aperture, osmode, &[])
|
|
}
|
|
|
|
fn gather_in(
|
|
d: &Drawing,
|
|
space: &Space,
|
|
ix: &Option<std::sync::Arc<crate::spatial::SpatialIndex>>,
|
|
cursor: Vec2,
|
|
aperture: f64,
|
|
osmode: u32,
|
|
frozen: &[String],
|
|
) -> Option<(Vec<(u32, Vec2)>, Vec<Prim>)> {
|
|
let probe = Bounds2::new(cursor, cursor).expand(aperture);
|
|
let mut cands: Vec<(u32, Vec2)> = Vec::new();
|
|
let mut near_prims: Vec<Prim> = Vec::new();
|
|
let mut count = 0usize;
|
|
let mut budget = MAX_BLOCK_LEAVES;
|
|
for (e, known) in crate::select::candidates(d, space, ix, &probe.expand(aperture), true, false)? {
|
|
if !d.is_visible(e) || frozen.iter().any(|l| l.eq_ignore_ascii_case(&e.common.layer)) {
|
|
continue;
|
|
}
|
|
let inf = crate::select::is_infinite(e);
|
|
if !inf && !crate::select::bounds_of(d, e, known).expand(aperture).intersects(&probe) {
|
|
continue;
|
|
}
|
|
count += 1;
|
|
if count > 2000 {
|
|
break;
|
|
}
|
|
if osmode & mode::INS != 0 {
|
|
match &e.kind {
|
|
EntityKind::Text(t) => cands.push((mode::INS, t.justify_point())),
|
|
EntityKind::MText(t) => cands.push((mode::INS, t.insert.xy())),
|
|
EntityKind::Tolerance(t) => cands.push((mode::INS, t.insert.xy())),
|
|
EntityKind::Insert(i) => {
|
|
cands.push((mode::INS, i.insert.xy()));
|
|
cands.extend(i.attribs.iter().filter(|a| !a.invisible).map(|a| (mode::INS, a.text.justify_point())));
|
|
}
|
|
EntityKind::AttDef(a) => cands.push((mode::INS, a.text.justify_point())),
|
|
// A multileader: its text's insertion point, or its block content's.
|
|
EntityKind::MLeader(m) => {
|
|
cands.extend(m.text.iter().map(|t| (mode::INS, t.insert.xy())));
|
|
cands.extend(m.block.iter().map(|b| (mode::INS, b.insert.xy())));
|
|
}
|
|
_ => {}
|
|
}
|
|
}
|
|
let mut sink = Sink { osmode, aperture, probe, cands: &mut cands, near: &mut near_prims };
|
|
sink.object(&e.kind, None);
|
|
// A block reference snaps to the objects inside it, placed by its transform.
|
|
if let EntityKind::Insert(ins) = &e.kind {
|
|
block_leaves(d, ins, &Mat3::IDENTITY, 0, &mut budget, frozen, &mut |k, m| sink.object(k, Some(m)));
|
|
}
|
|
if let EntityKind::Dimension(dm) = &e.kind {
|
|
sink.dimension(d, dm, &mut budget, frozen);
|
|
}
|
|
}
|
|
Some((cands, near_prims))
|
|
}
|
|
|
|
/// Picks the best of the gathered candidates, adding the base-dependent and deferred snaps.
|
|
#[allow(clippy::too_many_arguments)]
|
|
fn finish(
|
|
mut cands: Vec<(u32, Vec2)>,
|
|
near_prims: &[Prim],
|
|
cursor: Vec2,
|
|
aperture: f64,
|
|
osmode: u32,
|
|
base: Option<Vec2>,
|
|
deferred: bool,
|
|
clip: Option<Bounds2>,
|
|
) -> Option<SnapHit> {
|
|
// Perpendicular / tangent from the base point.
|
|
if let Some(bp) = base {
|
|
for p in near_prims {
|
|
if osmode & mode::PER != 0 {
|
|
match p {
|
|
Prim::Seg(Segment::Line(l)) => cands.push((mode::PER, l.project(bp))),
|
|
// Both antipodes, filtered to the arc's sweep: a perpendicular in the gap is
|
|
// not offered, and the far side is still found.
|
|
Prim::Seg(Segment::Arc { arc, .. }) => {
|
|
let curve = SnapCurve::Arc { center: arc.center, radius: arc.radius, start: arc.start, end: arc.end };
|
|
cands.extend(curve.perpendiculars(bp, bp).into_iter().map(|q| (mode::PER, q)));
|
|
}
|
|
Prim::Circle(c) => cands.push((mode::PER, c.closest(bp))),
|
|
Prim::Infinite { base: b0, dir, .. } => cands.push((mode::PER, *b0 + *dir * (bp - *b0).dot(*dir))),
|
|
Prim::Ellipse(e) => cands.extend(curves::ellipse_perpendiculars(e, bp).into_iter().map(|q| (mode::PER, q))),
|
|
Prim::Spline(s) => cands.extend(curves::spline_perpendiculars(s, bp).into_iter().map(|q| (mode::PER, q))),
|
|
_ => {}
|
|
}
|
|
}
|
|
if osmode & mode::TAN != 0 {
|
|
let pts = match p {
|
|
// Only the tangent points that lie on the arc itself (not its circle).
|
|
Prim::Seg(Segment::Arc { arc, .. }) => Circle::new(arc.center, arc.radius)
|
|
.tangent_points(bp)
|
|
.into_iter()
|
|
.filter(|t| arc.contains_angle(arc.center.angle_to(*t)))
|
|
.collect(),
|
|
Prim::Circle(c) => c.tangent_points(bp),
|
|
Prim::Ellipse(e) => curves::ellipse_tangents(e, bp),
|
|
Prim::Spline(s) => curves::spline_tangents(s, bp),
|
|
_ => Vec::new(),
|
|
};
|
|
cands.extend(pts.into_iter().map(|t| (mode::TAN, t)));
|
|
}
|
|
}
|
|
}
|
|
let visible = |p: Vec2| p.is_finite() && clip.is_none_or(|c| c.contains(p));
|
|
let best = cands.iter().filter(|(_, p)| visible(*p) && p.dist(cursor) <= aperture).min_by(|a, b| {
|
|
// Prefer more specific modes when nearly equidistant.
|
|
let da = snap_score(a.0, a.1, cursor, aperture);
|
|
let db = snap_score(b.0, b.1, cursor, aperture);
|
|
da.total_cmp(&db)
|
|
});
|
|
if let Some((m, p)) = best {
|
|
return Some(SnapHit { point: *p, mode: *m, name: name_of(*m), viewport: None, deferred: None });
|
|
}
|
|
if base.is_none()
|
|
&& deferred
|
|
&& let Some(h) = deferred_hit(near_prims, cursor, aperture, osmode, clip)
|
|
{
|
|
return Some(h);
|
|
}
|
|
if osmode & mode::NEA != 0 {
|
|
// The closest point of all nearby objects, whatever their drawing order.
|
|
let mut nb: Option<(f64, Vec2)> = None;
|
|
let mut consider = |c: Vec2| {
|
|
let dd = c.dist(cursor);
|
|
if visible(c) && dd <= aperture && nb.is_none_or(|(bd, _)| dd < bd) {
|
|
nb = Some((dd, c));
|
|
}
|
|
};
|
|
for p in near_prims {
|
|
for s in prim_segments(p) {
|
|
consider(fix_circle(&s).closest(cursor));
|
|
}
|
|
if let Prim::Circle(c) = p {
|
|
consider(c.closest(cursor));
|
|
}
|
|
}
|
|
if let Some((_, p)) = nb {
|
|
return Some(SnapHit { point: p, mode: mode::NEA, name: "Nearest", viewport: None, deferred: None });
|
|
}
|
|
}
|
|
None
|
|
}
|
|
|
|
fn snap_score(mode: u32, point: Vec2, cursor: Vec2, aperture: f64) -> f64 {
|
|
point.dist(cursor) - if mode == mode::INT || mode == mode::END { aperture * 0.15 } else { 0.0 }
|
|
}
|
|
|
|
/// Upper bound on the block-reference objects one snap query looks at (hostile files).
|
|
const MAX_BLOCK_LEAVES: usize = 20_000;
|
|
|
|
/// Collects snap candidates and the primitives near the cursor.
|
|
struct Sink<'a> {
|
|
osmode: u32,
|
|
aperture: f64,
|
|
probe: Bounds2,
|
|
cands: &'a mut Vec<(u32, Vec2)>,
|
|
near: &'a mut Vec<Prim>,
|
|
}
|
|
|
|
impl Sink<'_> {
|
|
/// The snap points of one object; `xf` places an object from inside a block reference
|
|
/// (whose primitives far from the cursor are skipped).
|
|
fn object(&mut self, kind: &EntityKind, xf: Option<&Mat3>) {
|
|
let osmode = self.osmode;
|
|
// OSNAPHATCH = 0: hatches are left out.
|
|
if osmode & mode::HATCH == 0 && matches!(kind, EntityKind::Hatch(_)) {
|
|
return;
|
|
}
|
|
let at = |p: Vec2| xf.map_or(p, |m| m.apply(p));
|
|
if osmode & mode::END != 0
|
|
&& let EntityKind::Solid(s) | EntityKind::Trace(s) = kind
|
|
{
|
|
self.cands.extend(s.corners.iter().map(|c| (mode::END, at(c.xy()))));
|
|
}
|
|
for p in kind.prims() {
|
|
let p = match xf {
|
|
Some(m) => {
|
|
let p = xform_prim(&p, m);
|
|
if !prim_near(&p, &self.probe, self.aperture) {
|
|
continue;
|
|
}
|
|
p
|
|
}
|
|
None => p,
|
|
};
|
|
let cands = &mut *self.cands;
|
|
match &p {
|
|
Prim::Seg(s) => {
|
|
if osmode & mode::END != 0 {
|
|
cands.push((mode::END, s.start()));
|
|
cands.push((mode::END, s.end()));
|
|
}
|
|
if osmode & mode::MID != 0 {
|
|
cands.push((mode::MID, s.mid()));
|
|
}
|
|
if let Segment::Arc { arc, .. } = s {
|
|
if osmode & mode::CEN != 0 {
|
|
cands.push((mode::CEN, arc.center));
|
|
}
|
|
if osmode & mode::QUA != 0 {
|
|
for k in 0..4 {
|
|
let a = k as f64 * PI / 2.0;
|
|
if arc.contains_angle(a) {
|
|
cands.push((mode::QUA, Vec2::polar(arc.center, arc.radius, a)));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
Prim::Circle(c) => {
|
|
if osmode & mode::CEN != 0 {
|
|
cands.push((mode::CEN, c.center));
|
|
}
|
|
if osmode & mode::QUA != 0 {
|
|
for k in 0..4 {
|
|
cands.push((mode::QUA, Vec2::polar(c.center, c.radius, k as f64 * PI / 2.0)));
|
|
}
|
|
}
|
|
}
|
|
Prim::Ellipse(el) => {
|
|
if osmode & mode::CEN != 0 {
|
|
cands.push((mode::CEN, el.center));
|
|
}
|
|
if osmode & mode::QUA != 0 {
|
|
// Only the quadrant points the arc passes through.
|
|
for k in 0..4 {
|
|
let t = k as f64 * PI / 2.0;
|
|
if cadcraft_geom::angle_in_sweep(t, el.start, el.end) {
|
|
cands.push((mode::QUA, el.at_param(t)));
|
|
}
|
|
}
|
|
}
|
|
if osmode & mode::END != 0 && !el.is_full() {
|
|
cands.push((mode::END, el.at_param(el.start)));
|
|
cands.push((mode::END, el.at_param(el.end)));
|
|
}
|
|
if osmode & mode::MID != 0
|
|
&& let Some(m) = curves::ellipse_mid(el)
|
|
{
|
|
cands.push((mode::MID, m));
|
|
}
|
|
}
|
|
Prim::Spline(s) => {
|
|
if osmode & mode::END != 0 && !s.closed {
|
|
let (lo, hi) = s.domain();
|
|
cands.push((mode::END, s.eval(lo)));
|
|
cands.push((mode::END, s.eval(hi)));
|
|
}
|
|
if osmode & mode::MID != 0
|
|
&& let Some(m) = curves::spline_mid(s)
|
|
{
|
|
cands.push((mode::MID, m));
|
|
}
|
|
}
|
|
Prim::Point(pt) => {
|
|
if osmode & mode::NOD != 0 && matches!(kind, EntityKind::Point(_)) {
|
|
cands.push((mode::NOD, *pt));
|
|
}
|
|
}
|
|
Prim::Infinite { base, .. } => {
|
|
if osmode & mode::END != 0 && matches!(kind, EntityKind::Ray(_)) {
|
|
cands.push((mode::END, *base));
|
|
}
|
|
}
|
|
Prim::Fill(_) => {}
|
|
}
|
|
self.near.push(p);
|
|
}
|
|
if osmode & mode::GCEN != 0 {
|
|
// The centroid of the area a closed polyline or spline encloses.
|
|
let pts = match kind {
|
|
EntityKind::LwPolyline(pl) if pl.closed => {
|
|
cadcraft_geom::Polyline { vertices: pl.vertices.clone(), closed: true }.tessellate(self.aperture / 10.0)
|
|
}
|
|
EntityKind::Spline(s) if s.closed => s.tessellate(1e-3),
|
|
_ => Vec::new(),
|
|
};
|
|
if let Some(c) = centroid(&pts) {
|
|
self.cands.push((mode::GCEN, at(c)));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
impl Sink<'_> {
|
|
/// A dimension snaps to what it draws, as in AutoCAD (into its block): the objects of its
|
|
/// block when the drawing has one (read from a file), else the lines generated from it
|
|
/// (Endpoint on their ends); Node on its definition points.
|
|
fn dimension(&mut self, d: &Drawing, dm: &cadcraft_doc::Dimension, budget: &mut usize, frozen: &[String]) {
|
|
match dm.block.as_ref().and_then(|n| d.block(n)) {
|
|
Some(blk) => {
|
|
// The block holds world geometry: a reference at its own base point places it as is.
|
|
let ins = Insert {
|
|
block: blk.name.clone(),
|
|
insert: blk.base,
|
|
scale: cadcraft_geom::Vec3::new(1.0, 1.0, 1.0),
|
|
rotation: 0.0,
|
|
attribs: Vec::new(),
|
|
cols: 1,
|
|
rows: 1,
|
|
col_spacing: 0.0,
|
|
row_spacing: 0.0,
|
|
};
|
|
block_leaves(d, &ins, &Mat3::IDENTITY, 0, budget, frozen, &mut |k, m| self.object(k, Some(m)));
|
|
}
|
|
None => {
|
|
let g = cadcraft_render::dimension_in(d, dm);
|
|
for line in &g.lines {
|
|
let (Some(a), Some(b)) = (line.first(), line.last()) else { continue };
|
|
if self.osmode & mode::END != 0 {
|
|
self.cands.extend([(mode::END, *a), (mode::END, *b)]);
|
|
}
|
|
if self.osmode & mode::MID != 0 && line.len() == 2 {
|
|
self.cands.push((mode::MID, (*a + *b) * 0.5));
|
|
}
|
|
for w in line.windows(2) {
|
|
if let [p, q] = w {
|
|
let s = Prim::Seg(Segment::Line(cadcraft_geom::Line::new(*p, *q)));
|
|
if prim_near(&s, &self.probe, self.aperture) {
|
|
self.near.push(s);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if self.osmode & mode::NOD != 0 {
|
|
self.cands.extend(dim_def_points(dm).into_iter().map(|p| (mode::NOD, p)));
|
|
}
|
|
}
|
|
}
|
|
|
|
/// The definition points of a dimension that its kind uses.
|
|
fn dim_def_points(dm: &cadcraft_doc::Dimension) -> Vec<Vec2> {
|
|
use cadcraft_doc::DimKind;
|
|
let pts = match dm.kind {
|
|
DimKind::Linear { .. } | DimKind::Aligned | DimKind::ArcLength => vec![dm.defpt, dm.p13, dm.p14],
|
|
DimKind::Radius | DimKind::Diameter => vec![dm.defpt, dm.p15],
|
|
DimKind::Angular3P => vec![dm.defpt, dm.p13, dm.p14, dm.p15],
|
|
DimKind::Angular => vec![dm.defpt, dm.p13, dm.p14, dm.p15, dm.p16],
|
|
DimKind::Ordinate { .. } => vec![dm.p13, dm.p14],
|
|
};
|
|
pts.into_iter().map(|p| p.xy()).filter(|p| p.is_finite()).collect()
|
|
}
|
|
|
|
/// Calls `f` with each object drawn by a block reference and the transform placing it, nested
|
|
/// references expanded (within [`MAX_BLOCK_DEPTH`] levels and `budget` objects); objects that
|
|
/// aren't drawn (hidden, on a layer that is off or frozen, attribute definitions) are left out.
|
|
fn block_leaves(d: &Drawing, ins: &Insert, m: &Mat3, depth: usize, budget: &mut usize, frozen: &[String], f: &mut dyn FnMut(&EntityKind, &Mat3)) {
|
|
if depth >= MAX_BLOCK_DEPTH {
|
|
return;
|
|
}
|
|
let Some(blk) = d.block(&ins.block) else { return };
|
|
if blk.entities.is_empty() {
|
|
return;
|
|
}
|
|
let (cols, rows) = (ins.cols.clamp(1, 10_000), ins.rows.clamp(1, 10_000));
|
|
for r in 0..rows {
|
|
for c in 0..cols {
|
|
// Each array cell spends budget too, so a huge array of tiny blocks stays bounded.
|
|
if *budget == 0 {
|
|
return;
|
|
}
|
|
*budget -= 1;
|
|
let off = Vec2::new(ins.col_spacing * f64::from(c), ins.row_spacing * f64::from(r)).rotate(ins.rotation);
|
|
let mm = m.then_before(Mat3::translate(off).then_before(ins.transform(blk.base.xy())));
|
|
for be in blk.entities.iter() {
|
|
if *budget == 0 {
|
|
return;
|
|
}
|
|
*budget -= 1;
|
|
// Objects on layer 0 take the reference's layer, which is visible.
|
|
if !be.common.visible
|
|
|| (be.common.layer != "0" && (!d.is_visible(be) || frozen.iter().any(|l| l.eq_ignore_ascii_case(&be.common.layer))))
|
|
{
|
|
continue;
|
|
}
|
|
match &be.kind {
|
|
EntityKind::AttDef(_) => {}
|
|
EntityKind::Insert(inner) => block_leaves(d, inner, &mm, depth + 1, budget, frozen, f),
|
|
k => f(k, &mm),
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/// Whether `p` comes within `aperture` of the box `probe`.
|
|
fn prim_near(p: &Prim, probe: &Bounds2, aperture: f64) -> bool {
|
|
let b = match p {
|
|
Prim::Seg(s) => s.bounds(),
|
|
Prim::Circle(c) => c.bounds(),
|
|
Prim::Ellipse(e) => e.bounds(),
|
|
Prim::Spline(s) => Bounds2::from_points(s.control.iter().copied()),
|
|
Prim::Point(q) => Bounds2::new(*q, *q),
|
|
Prim::Infinite { .. } => return true,
|
|
Prim::Fill(f) => Bounds2::from_points(f.iter().copied()),
|
|
};
|
|
b.expand(aperture).intersects(probe)
|
|
}
|
|
|
|
/// The rotation-and-uniform-scale factor of `m`'s linear part (mirroring allowed), or `None`
|
|
/// when it distorts shapes (non-uniform scale or shear).
|
|
fn similarity_scale(m: &Mat3) -> Option<f64> {
|
|
let (u, v) = (Vec2::new(m.a, m.b), Vec2::new(m.c, m.d));
|
|
let (lu, lv) = (u.len(), v.len());
|
|
let tol = 1e-9 * lu.max(lv);
|
|
((lu - lv).abs() <= tol && u.dot(v).abs() <= tol * lu.max(lv) && lu > 0.0).then_some(lu)
|
|
}
|
|
|
|
/// `p` placed by the affine transform `m`, exactly: circles and arcs under a non-uniform scale
|
|
/// become ellipses and elliptical arcs.
|
|
fn xform_prim(p: &Prim, m: &Mat3) -> Prim {
|
|
let mirror = m.is_mirroring();
|
|
match p {
|
|
Prim::Seg(Segment::Line(l)) => Prim::Seg(Segment::Line(cadcraft_geom::Line::new(m.apply(l.a), m.apply(l.b)))),
|
|
Prim::Seg(Segment::Arc { arc, ccw }) => match similarity_scale(m) {
|
|
Some(s) => {
|
|
let c = m.apply(arc.center);
|
|
let (a0, a1) = (c.angle_to(m.apply(arc.start_point())), c.angle_to(m.apply(arc.end_point())));
|
|
let (start, end) = if mirror { (a1, a0) } else { (a0, a1) };
|
|
Prim::Seg(Segment::Arc { arc: cadcraft_geom::Arc::new(c, arc.radius * s, start, end), ccw: *ccw != mirror })
|
|
}
|
|
None => {
|
|
let e = Ellipse { center: arc.center, major: Vec2::X * arc.radius, ratio: 1.0, start: arc.start, end: arc.end };
|
|
Prim::Ellipse(xform_ellipse(&e, m))
|
|
}
|
|
},
|
|
Prim::Circle(c) => match similarity_scale(m) {
|
|
Some(s) => Prim::Circle(Circle::new(m.apply(c.center), c.radius * s)),
|
|
None => Prim::Ellipse(xform_ellipse(&Ellipse::full(c.center, Vec2::X * c.radius, 1.0), m)),
|
|
},
|
|
Prim::Ellipse(e) => Prim::Ellipse(xform_ellipse(e, m)),
|
|
Prim::Spline(s) => {
|
|
let mut s = s.clone();
|
|
s.control.iter_mut().chain(s.fit.iter_mut()).for_each(|q| *q = m.apply(*q));
|
|
Prim::Spline(s)
|
|
}
|
|
Prim::Point(q) => Prim::Point(m.apply(*q)),
|
|
Prim::Infinite { base, dir, ray } => Prim::Infinite { base: m.apply(*base), dir: m.apply_vec(*dir).normalized(), ray: *ray },
|
|
Prim::Fill(f) => Prim::Fill(f.iter().map(|q| m.apply(*q)).collect()),
|
|
}
|
|
}
|
|
|
|
/// The image of an ellipse (or elliptical arc) under an affine transform: the conjugate
|
|
/// semi-diameters `A·major`, `A·minor` give the new principal axes; parameters shift with them
|
|
/// (and reverse under a mirroring transform).
|
|
fn xform_ellipse(e: &Ellipse, m: &Mat3) -> Ellipse {
|
|
let center = m.apply(e.center);
|
|
let (am, an) = (m.apply_vec(e.major), m.apply_vec(e.minor()));
|
|
// |am·cos t + an·sin t| is largest at t0: the new major axis.
|
|
let t0 = 0.5 * (2.0 * am.dot(an)).atan2(am.dot(am) - an.dot(an));
|
|
let (s0, c0) = t0.sin_cos();
|
|
let (u, v) = (am * c0 + an * s0, an * c0 - am * s0);
|
|
let ratio = if u.len() > 0.0 { (v.len() / u.len()).min(1.0) } else { 1.0 };
|
|
if e.is_full() {
|
|
return Ellipse::full(center, u, ratio);
|
|
}
|
|
let (start, end) = if u.cross(v) >= 0.0 { (e.start - t0, e.end - t0) } else { (t0 - e.end, t0 - e.start) };
|
|
Ellipse { center, major: u, ratio, start: cadcraft_geom::norm_angle(start), end: cadcraft_geom::norm_angle(end) }
|
|
}
|
|
|
|
/// The nearest deferred tangent/perpendicular within `aperture` of `cursor`.
|
|
fn deferred_hit(prims: &[Prim], cursor: Vec2, aperture: f64, osmode: u32, clip: Option<Bounds2>) -> Option<SnapHit> {
|
|
let mut best: Option<(f64, SnapHit)> = None;
|
|
for p in prims {
|
|
let curve = match p {
|
|
Prim::Circle(c) => SnapCurve::Circle { center: c.center, radius: c.radius },
|
|
Prim::Seg(Segment::Arc { arc, .. }) => SnapCurve::Arc { center: arc.center, radius: arc.radius, start: arc.start, end: arc.end },
|
|
Prim::Seg(Segment::Line(l)) => SnapCurve::Line { a: l.a, b: l.b },
|
|
Prim::Infinite { base, dir, .. } => SnapCurve::Line { a: *base, b: *base + *dir },
|
|
_ => continue,
|
|
};
|
|
let (m, name, at) = match curve {
|
|
SnapCurve::Circle { center, radius } if osmode & mode::TAN != 0 => {
|
|
(mode::TAN, "Deferred Tangent", Circle::new(center, radius).closest(cursor))
|
|
}
|
|
SnapCurve::Circle { center, radius } if osmode & mode::PER != 0 => {
|
|
(mode::PER, "Deferred Perpendicular", Circle::new(center, radius).closest(cursor))
|
|
}
|
|
SnapCurve::Arc { center, radius, start, end } if osmode & mode::TAN != 0 => {
|
|
(mode::TAN, "Deferred Tangent", cadcraft_geom::Arc::new(center, radius, start, end).closest(cursor))
|
|
}
|
|
SnapCurve::Arc { center, radius, start, end } if osmode & mode::PER != 0 => {
|
|
(mode::PER, "Deferred Perpendicular", cadcraft_geom::Arc::new(center, radius, start, end).closest(cursor))
|
|
}
|
|
SnapCurve::Line { a, b } if osmode & mode::PER != 0 => {
|
|
// Pick on the drawn extent: a segment's own span, an xline/ray anywhere.
|
|
let l = cadcraft_geom::Line::new(a, b);
|
|
(mode::PER, "Deferred Perpendicular", if matches!(p, Prim::Seg(_)) { l.closest(cursor) } else { l.project(cursor) })
|
|
}
|
|
_ => continue,
|
|
};
|
|
let dd = at.dist(cursor);
|
|
if at.is_finite() && clip.is_none_or(|c| c.contains(at)) && dd <= aperture && best.is_none_or(|(bd, _)| dd < bd) {
|
|
best = Some((dd, SnapHit { point: at, mode: m, name, viewport: None, deferred: Some(Deferred { mode: m, curve, at }) }));
|
|
}
|
|
}
|
|
best.map(|(_, h)| h)
|
|
}
|
|
|
|
/// Solve a line whose ends may be deferred tangent/perpendicular snaps: returns its two
|
|
/// endpoints (in the order given), or `None` when there is no such line (a point inside the
|
|
/// circle it should be tangent to, concentric circles, non-parallel lines both perpendicular to
|
|
/// it, degenerate or non-finite geometry). Among several solutions, the one whose deferred
|
|
/// points lie closest to where the curves were picked wins (as AutoCAD does).
|
|
pub fn resolve_deferred(a: LineEnd, b: LineEnd) -> Option<(Vec2, Vec2)> {
|
|
match (a, b) {
|
|
(LineEnd::Point(p), LineEnd::Point(q)) => (p.is_finite() && q.is_finite()).then_some((p, q)),
|
|
(LineEnd::Point(_), LineEnd::Deferred(_)) => resolve_deferred(b, a).map(|(q, p)| (p, q)),
|
|
(LineEnd::Deferred(d), LineEnd::Point(p)) => {
|
|
if !p.is_finite() {
|
|
return None;
|
|
}
|
|
let cands: Vec<Vec2> = match d.mode {
|
|
mode::TAN => d.curve.tangents(p),
|
|
mode::PER => d.curve.perpendiculars(p, d.at),
|
|
_ => Vec::new(),
|
|
};
|
|
pick_best(cands.into_iter().map(|t| (t, p)), d.at, None)
|
|
}
|
|
(LineEnd::Deferred(d1), LineEnd::Deferred(d2)) => {
|
|
let pairs = deferred_pairs(&d1, &d2).or_else(|| deferred_pairs(&d2, &d1).map(|v| v.into_iter().map(|(q, p)| (p, q)).collect()))?;
|
|
pick_best(pairs.into_iter(), d1.at, Some(d2.at))
|
|
}
|
|
}
|
|
}
|
|
|
|
/// Candidate lines between two deferred snaps (`None` when this order isn't handled; the
|
|
/// caller retries swapped).
|
|
fn deferred_pairs(d1: &Deferred, d2: &Deferred) -> Option<Vec<(Vec2, Vec2)>> {
|
|
use SnapCurve::{Circle as C, Line as L};
|
|
// The math below is on the circle an arc lies on; the sweep is checked afterwards.
|
|
let circle_of = |c: SnapCurve| match c {
|
|
SnapCurve::Circle { center, radius } | SnapCurve::Arc { center, radius, .. } => C { center, radius },
|
|
other => other,
|
|
};
|
|
let pairs = match ((d1.mode, circle_of(d1.curve)), (d2.mode, circle_of(d2.curve))) {
|
|
((mode::TAN, C { center: c1, radius: r1 }), (mode::TAN, C { center: c2, radius: r2 })) => {
|
|
Circle::new(c1, r1).common_tangents(&Circle::new(c2, r2))
|
|
}
|
|
// Perpendicular to a circle = through its center.
|
|
((mode::TAN, C { center, radius }), (mode::PER, C { center: k, radius: rk })) => Circle::new(center, radius)
|
|
.tangent_points(k)
|
|
.into_iter()
|
|
.flat_map(|t| {
|
|
let u = (t - k).normalized();
|
|
[(t, k + u * rk), (t, k - u * rk)]
|
|
})
|
|
.collect(),
|
|
// Perpendicular to a line: the tangent runs along the line's normal.
|
|
((mode::TAN, C { center, radius }), (mode::PER, L { a, b })) => {
|
|
let Some(v) = line_dir(a, b) else { return Some(Vec::new()) };
|
|
let l = cadcraft_geom::Line::new(a, b);
|
|
[center + v * radius, center - v * radius].into_iter().map(|t| (t, l.project(t))).collect()
|
|
}
|
|
((mode::PER, C { center: k1, radius: r1 }), (mode::PER, C { center: k2, radius: r2 })) => {
|
|
let u = (k2 - k1).normalized();
|
|
if u == Vec2::ZERO {
|
|
return Some(Vec::new());
|
|
}
|
|
let mut v = Vec::new();
|
|
for s1 in [1.0, -1.0] {
|
|
for s2 in [1.0, -1.0] {
|
|
v.push((k1 + u * (r1 * s1), k2 + u * (r2 * s2)));
|
|
}
|
|
}
|
|
v
|
|
}
|
|
((mode::PER, C { center: k, radius: rk }), (mode::PER, L { a, b })) => {
|
|
let Some(v) = line_dir(a, b) else { return Some(Vec::new()) };
|
|
let f = cadcraft_geom::Line::new(a, b).project(k);
|
|
let u = if f.dist(k) > cadcraft_geom::EPS { (f - k).normalized() } else { v.perp() };
|
|
vec![(k + u * rk, f), (k - u * rk, f)]
|
|
}
|
|
((mode::PER, L { a: a1, b: b1 }), (mode::PER, L { a: a2, b: b2 })) => {
|
|
// Only parallel lines share a perpendicular; it passes through the first pick.
|
|
let (Some(v1), Some(v2)) = (line_dir(a1, b1), line_dir(a2, b2)) else { return Some(Vec::new()) };
|
|
if v1.cross(v2).abs() > 1e-9 {
|
|
return Some(Vec::new());
|
|
}
|
|
let p = cadcraft_geom::Line::new(a1, b1).project(d1.at);
|
|
vec![(p, cadcraft_geom::Line::new(a2, b2).project(p))]
|
|
}
|
|
_ => return None,
|
|
};
|
|
// A solution on an arc's circle that falls off the arc is no solution: the line would touch
|
|
// the circle, not the arc that was picked.
|
|
Some(pairs.into_iter().filter(|(p, q)| d1.curve.contains(*p) && d2.curve.contains(*q)).collect())
|
|
}
|
|
|
|
/// Unit direction of the line through `a` and `b`, if it has one.
|
|
fn line_dir(a: Vec2, b: Vec2) -> Option<Vec2> {
|
|
let v = (b - a).normalized();
|
|
(v != Vec2::ZERO && v.is_finite()).then_some(v)
|
|
}
|
|
|
|
/// The finite, non-degenerate candidate closest to the picks.
|
|
fn pick_best(cands: impl Iterator<Item = (Vec2, Vec2)>, at1: Vec2, at2: Option<Vec2>) -> Option<(Vec2, Vec2)> {
|
|
cands
|
|
.filter(|(p, q)| p.is_finite() && q.is_finite() && p.dist(*q) > cadcraft_geom::EPS)
|
|
.map(|(p, q)| (p.dist(at1) + at2.map_or(0.0, |a| q.dist(a)), (p, q)))
|
|
.filter(|(cost, _)| cost.is_finite())
|
|
.min_by(|x, y| x.0.total_cmp(&y.0))
|
|
.map(|(_, l)| l)
|
|
}
|
|
|
|
/// Full circles are stored as zero-sweep arcs in `prim_segments`; give them a full sweep.
|
|
fn fix_circle(s: &Segment) -> Segment {
|
|
match *s {
|
|
Segment::Arc { arc, ccw } if (arc.start - arc.end).abs() < 1e-15 => {
|
|
Segment::Arc { arc: cadcraft_geom::Arc { start: 0.0, end: cadcraft_geom::TAU - 1e-12, ..arc }, ccw }
|
|
}
|
|
other => other,
|
|
}
|
|
}
|
|
|
|
fn centroid(pts: &[Vec2]) -> Option<Vec2> {
|
|
let n = pts.len();
|
|
if n < 3 {
|
|
return None;
|
|
}
|
|
let mut a = 0.0;
|
|
let mut c = Vec2::ZERO;
|
|
for i in 0..n {
|
|
let (p, q) = (pts.get(i)?, pts.get((i + 1) % n)?);
|
|
let cr = p.cross(*q);
|
|
a += cr;
|
|
c += (*p + *q) * cr;
|
|
}
|
|
if a.abs() < 1e-12 { None } else { Some(c / (3.0 * a)) }
|
|
}
|
|
|
|
/// Constrain `p` relative to `base` to the nearest multiple of 90° (ortho).
|
|
pub fn ortho(base: Vec2, p: Vec2) -> Vec2 {
|
|
let d = p - base;
|
|
if d.x.abs() >= d.y.abs() { Vec2::new(p.x, base.y) } else { Vec2::new(base.x, p.y) }
|
|
}
|
|
|
|
/// Polar tracking: if the direction base→p is within `tol` radians of a multiple of `inc`,
|
|
/// return the point projected onto that ray and the angle.
|
|
pub fn polar(base: Vec2, p: Vec2, inc: f64, tol: f64) -> Option<(Vec2, f64)> {
|
|
if inc <= 1e-9 {
|
|
return None;
|
|
}
|
|
let d = p - base;
|
|
let len = d.len();
|
|
if len < 1e-12 {
|
|
return None;
|
|
}
|
|
let a = d.angle();
|
|
let k = (a / inc).round();
|
|
let snapped = k * inc;
|
|
if (a - snapped).abs() <= tol {
|
|
let dir = Vec2::from_angle(snapped);
|
|
Some((base + dir * d.dot(dir), cadcraft_geom::norm_angle(snapped)))
|
|
} else {
|
|
None
|
|
}
|
|
}
|
|
|
|
/// Grid snap: the nearest point of the grid of `unit` spacing through `origin`, turned by
|
|
/// `angle` (radians) about it.
|
|
pub fn grid_snap(p: Vec2, unit: Vec2, origin: Vec2, angle: f64) -> Vec2 {
|
|
let angle = if angle.is_finite() { angle } else { 0.0 };
|
|
let q = (p - origin).rotate(-angle);
|
|
let sx = if unit.x > 1e-12 { (q.x / unit.x).round() * unit.x } else { q.x };
|
|
let sy = if unit.y > 1e-12 { (q.y / unit.y).round() * unit.y } else { q.y };
|
|
let s = origin + Vec2::new(sx, sy).rotate(angle);
|
|
if s.is_finite() { s } else { p }
|
|
}
|
|
|
|
/// The snap grid's origin (SNAPBASE) and rotation in radians (SNAPANG, in degrees) of a drawing.
|
|
pub fn grid_frame(d: &Drawing) -> (Vec2, f64) {
|
|
let base = d.header.point("SNAPBASE").map(|p| p.xy()).filter(|p| p.is_finite()).unwrap_or(Vec2::ZERO);
|
|
(base, d.header.f64("SNAPANG", 0.0).to_radians())
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use super::*;
|
|
use cadcraft_doc::{Common, Line};
|
|
use cadcraft_geom::Vec3;
|
|
|
|
fn drawing() -> Drawing {
|
|
let mut d = Drawing::new_imperial();
|
|
let l = |a: (f64, f64), b: (f64, f64)| EntityKind::Line(Line { a: Vec3::new(a.0, a.1, 0.0), b: Vec3::new(b.0, b.1, 0.0) });
|
|
d.add(&Space::Model, Common::default(), l((0.0, 0.0), (10.0, 0.0))).unwrap();
|
|
d.add(&Space::Model, Common::default(), l((5.0, -5.0), (5.0, 5.0))).unwrap();
|
|
d.add(&Space::Model, Common::default(), EntityKind::Circle(cadcraft_doc::Circle { center: Vec3::new(20.0, 0.0, 0.0), radius: 2.0 })).unwrap();
|
|
d
|
|
}
|
|
|
|
#[test]
|
|
fn endpoint_and_mid() {
|
|
let d = drawing();
|
|
let h = osnap(&d, &Space::Model, Vec2::new(9.8, 0.1), 0.5, mode::END | mode::MID, None, false).unwrap();
|
|
assert_eq!(h.point, Vec2::new(10.0, 0.0));
|
|
let m = osnap(&d, &Space::Model, Vec2::new(5.1, 0.1), 0.5, mode::MID, None, false).unwrap();
|
|
assert_eq!(m.point, Vec2::new(5.0, 0.0));
|
|
}
|
|
|
|
#[test]
|
|
fn intersection() {
|
|
let d = drawing();
|
|
let h = osnap(&d, &Space::Model, Vec2::new(5.2, 0.2), 0.5, mode::INT, None, false).unwrap();
|
|
assert!(h.point.near(Vec2::new(5.0, 0.0), 1e-9));
|
|
assert_eq!(h.name, "Intersection");
|
|
}
|
|
|
|
#[test]
|
|
fn center_quadrant_tangent() {
|
|
let d = drawing();
|
|
assert_eq!(osnap(&d, &Space::Model, Vec2::new(20.1, 0.1), 0.5, mode::CEN, None, false).unwrap().point, Vec2::new(20.0, 0.0));
|
|
assert!(osnap(&d, &Space::Model, Vec2::new(20.0, 2.1), 0.5, mode::QUA, None, false).unwrap().point.near(Vec2::new(20.0, 2.0), 1e-9));
|
|
let t = osnap(&d, &Space::Model, Vec2::new(19.9, 1.9), 1.0, mode::TAN, Some(Vec2::new(10.0, 0.0)), false);
|
|
assert!(t.is_some());
|
|
}
|
|
|
|
#[test]
|
|
fn perpendicular_from_base() {
|
|
let d = drawing();
|
|
let h = osnap(&d, &Space::Model, Vec2::new(3.0, 0.2), 0.5, mode::PER, Some(Vec2::new(3.0, 4.0)), false).unwrap();
|
|
assert!(h.point.near(Vec2::new(3.0, 0.0), 1e-9));
|
|
}
|
|
|
|
#[test]
|
|
fn ortho_and_polar() {
|
|
assert_eq!(ortho(Vec2::ZERO, Vec2::new(5.0, 1.0)), Vec2::new(5.0, 0.0));
|
|
assert_eq!(ortho(Vec2::ZERO, Vec2::new(1.0, 5.0)), Vec2::new(0.0, 5.0));
|
|
let (p, a) = polar(Vec2::ZERO, Vec2::new(5.0, 5.1), 45f64.to_radians(), 3f64.to_radians()).unwrap();
|
|
assert!((a - PI / 4.0).abs() < 1e-12);
|
|
assert!((p.x - p.y).abs() < 1e-9);
|
|
assert_eq!(grid_snap(Vec2::new(0.74, 1.26), Vec2::new(0.5, 0.5), Vec2::ZERO, 0.0), Vec2::new(0.5, 1.5));
|
|
}
|
|
|
|
#[test]
|
|
fn off_bit_disables() {
|
|
let d = drawing();
|
|
assert!(osnap(&d, &Space::Model, Vec2::new(9.8, 0.1), 0.5, mode::END | mode::OFF, None, false).is_none());
|
|
}
|
|
|
|
/// Distance from `c` to the infinite line through `p` and `q`.
|
|
fn line_dist(c: Vec2, p: Vec2, q: Vec2) -> f64 {
|
|
((q - p).cross(c - p) / p.dist(q)).abs()
|
|
}
|
|
|
|
fn tan(center: (f64, f64), radius: f64, at: (f64, f64)) -> LineEnd {
|
|
let curve = SnapCurve::Circle { center: Vec2::new(center.0, center.1), radius };
|
|
LineEnd::Deferred(Deferred { mode: mode::TAN, curve, at: Vec2::new(at.0, at.1) })
|
|
}
|
|
|
|
fn pt(x: f64, y: f64) -> LineEnd {
|
|
LineEnd::Point(Vec2::new(x, y))
|
|
}
|
|
|
|
#[test]
|
|
fn deferred_tangent_without_base() {
|
|
let d = drawing();
|
|
let at = Vec2::new(20.0, 2.1);
|
|
// Without a base, tangent snaps only as deferred, and only where the prompt resolves it.
|
|
assert!(osnap(&d, &Space::Model, at, 0.5, mode::TAN, None, false).is_none());
|
|
let h = osnap(&d, &Space::Model, at, 0.5, mode::TAN, None, true).unwrap();
|
|
assert_eq!((h.mode, h.name), (mode::TAN, "Deferred Tangent"));
|
|
assert!(h.point.near(Vec2::new(20.0, 2.0), 1e-9));
|
|
let df = h.deferred.unwrap();
|
|
assert_eq!(df.curve, SnapCurve::Circle { center: Vec2::new(20.0, 0.0), radius: 2.0 });
|
|
assert_eq!(h.input(), crate::Input::Deferred(df));
|
|
// With a base it is an ordinary tangent.
|
|
let t = osnap(&d, &Space::Model, Vec2::new(19.9, 1.9), 1.0, mode::TAN, Some(Vec2::new(10.0, 0.0)), true).unwrap();
|
|
assert!(t.deferred.is_none() && t.name == "Tangent");
|
|
// A specific snap still wins over a deferred one.
|
|
let q = osnap(&d, &Space::Model, at, 0.5, mode::TAN | mode::QUA, None, true).unwrap();
|
|
assert_eq!(q.mode, mode::QUA);
|
|
// Deferred perpendicular on a line.
|
|
let p = osnap(&d, &Space::Model, Vec2::new(2.0, 0.2), 0.5, mode::PER, None, true).unwrap();
|
|
assert_eq!(p.name, "Deferred Perpendicular");
|
|
assert!(p.point.near(Vec2::new(2.0, 0.0), 1e-9));
|
|
}
|
|
|
|
#[test]
|
|
fn resolve_tangent_to_free_point() {
|
|
let (a, b) = resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), pt(20.0, 5.0)).unwrap();
|
|
assert!(b.near(Vec2::new(20.0, 5.0), 1e-12));
|
|
assert!((a.len() - 5.0).abs() < 1e-9 && (line_dist(Vec2::ZERO, a, b) - 5.0).abs() < 1e-9);
|
|
assert!(a.y > 0.0, "the tangent point nearest the pick wins");
|
|
let (a2, _) = resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, -5.0)), pt(20.0, 5.0)).unwrap();
|
|
assert!(a2.y < 0.0);
|
|
// Order of the ends is kept.
|
|
let (p, q) = resolve_deferred(pt(20.0, 5.0), tan((0.0, 0.0), 5.0, (0.0, 5.0))).unwrap();
|
|
assert!(p.near(Vec2::new(20.0, 5.0), 1e-12) && q.near(a, 1e-12));
|
|
}
|
|
|
|
#[test]
|
|
fn resolve_belt_tangent_between_circles() {
|
|
let (c1, r1, c2, r2) = (Vec2::ZERO, 10.0, Vec2::new(30.0, 0.0), 4.0);
|
|
// Both picked on top: the outer (belt) tangent above.
|
|
let (a, b) = resolve_deferred(tan((0.0, 0.0), r1, (0.0, 10.0)), tan((30.0, 0.0), r2, (30.0, 4.0))).unwrap();
|
|
assert!((line_dist(c1, a, b) - r1).abs() < 1e-9 && (line_dist(c2, a, b) - r2).abs() < 1e-9);
|
|
assert!((a.dist(c1) - r1).abs() < 1e-9 && (b.dist(c2) - r2).abs() < 1e-9);
|
|
assert!(a.y > 0.0 && b.y > 0.0);
|
|
// Top of one, bottom of the other: the crossed (inner) tangent.
|
|
let (a, b) = resolve_deferred(tan((0.0, 0.0), r1, (0.0, 10.0)), tan((30.0, 0.0), r2, (30.0, -4.0))).unwrap();
|
|
assert!((line_dist(c1, a, b) - r1).abs() < 1e-9 && (line_dist(c2, a, b) - r2).abs() < 1e-9);
|
|
assert!(a.y > 0.0 && b.y < 0.0);
|
|
}
|
|
|
|
#[test]
|
|
fn resolve_perpendicular_cases() {
|
|
let per_line = |a: (f64, f64), b: (f64, f64), at: (f64, f64)| {
|
|
let curve = SnapCurve::Line { a: Vec2::new(a.0, a.1), b: Vec2::new(b.0, b.1) };
|
|
LineEnd::Deferred(Deferred { mode: mode::PER, curve, at: Vec2::new(at.0, at.1) })
|
|
};
|
|
// Perpendicular from a free point onto a line (its extension counts).
|
|
let (a, b) = resolve_deferred(per_line((0.0, 0.0), (10.0, 0.0), (5.0, 0.0)), pt(15.0, 7.0)).unwrap();
|
|
assert!(a.near(Vec2::new(15.0, 0.0), 1e-9) && b.near(Vec2::new(15.0, 7.0), 1e-12));
|
|
// Tangent to a circle and perpendicular to a line: runs along the line's normal.
|
|
let (a, b) = resolve_deferred(tan((0.0, 10.0), 2.0, (2.0, 10.0)), per_line((0.0, 0.0), (10.0, 0.0), (2.0, 0.0))).unwrap();
|
|
assert!(a.near(Vec2::new(2.0, 10.0), 1e-9) && b.near(Vec2::new(2.0, 0.0), 1e-9));
|
|
// Non-parallel lines have no common perpendicular.
|
|
assert!(resolve_deferred(per_line((0.0, 0.0), (10.0, 0.0), (1.0, 0.0)), per_line((0.0, 0.0), (0.0, 10.0), (0.0, 1.0))).is_none());
|
|
}
|
|
|
|
#[test]
|
|
fn resolve_degenerate_input_is_none_not_panic() {
|
|
// Point inside (or on) the circle: no tangent.
|
|
assert!(resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), pt(1.0, 1.0)).is_none());
|
|
assert!(resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), pt(5.0, 0.0)).is_none());
|
|
// Concentric or nested circles: no common tangent.
|
|
assert!(resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), tan((0.0, 0.0), 2.0, (0.0, 2.0))).is_none());
|
|
assert!(resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), tan((1.0, 0.0), 2.0, (1.0, 2.0))).is_none());
|
|
// Same circle twice.
|
|
assert!(resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), tan((0.0, 0.0), 5.0, (0.0, -5.0))).is_none());
|
|
// Zero radius: degenerates to a line through the point, without panicking.
|
|
let _ = resolve_deferred(tan((0.0, 0.0), 0.0, (0.0, 0.0)), pt(10.0, 0.0));
|
|
let _ = resolve_deferred(tan((0.0, 0.0), 0.0, (0.0, 0.0)), tan((10.0, 0.0), 0.0, (10.0, 0.0)));
|
|
// Non-finite and huge numbers.
|
|
for v in [f64::NAN, f64::INFINITY, -f64::INFINITY, 1e308, -1e308] {
|
|
let _ = resolve_deferred(tan((v, 0.0), 5.0, (0.0, 5.0)), pt(20.0, v));
|
|
let _ = resolve_deferred(tan((0.0, 0.0), v, (v, 5.0)), tan((v, v), 2.0, (0.0, v)));
|
|
let r = resolve_deferred(tan((0.0, 0.0), 5.0, (0.0, 5.0)), pt(v, 0.0));
|
|
assert!(r.is_none_or(|(a, b)| a.is_finite() && b.is_finite()));
|
|
}
|
|
// A degenerate line can't be perpendicular to anything.
|
|
let curve = SnapCurve::Line { a: Vec2::ZERO, b: Vec2::ZERO };
|
|
assert!(resolve_deferred(LineEnd::Deferred(Deferred { mode: mode::PER, curve, at: Vec2::ZERO }), pt(3.0, 3.0)).is_none());
|
|
// Tangent to a line is meaningless.
|
|
let curve = SnapCurve::Line { a: Vec2::ZERO, b: Vec2::X };
|
|
assert!(resolve_deferred(LineEnd::Deferred(Deferred { mode: mode::TAN, curve, at: Vec2::ZERO }), pt(3.0, 3.0)).is_none());
|
|
}
|
|
|
|
/// A drawing with one arc: center (20,0), radius 2, swept CCW from 0° to 90° (the first
|
|
/// quadrant only, so the rest of its circle is the gap).
|
|
fn arc_drawing() -> Drawing {
|
|
let mut d = Drawing::new_imperial();
|
|
d.add(
|
|
&Space::Model,
|
|
Common::default(),
|
|
EntityKind::Arc(cadcraft_doc::Arc { center: Vec3::new(20.0, 0.0, 0.0), radius: 2.0, start: 0.0, end: std::f64::consts::FRAC_PI_2 }),
|
|
)
|
|
.unwrap();
|
|
d
|
|
}
|
|
|
|
fn on_arc(p: Vec2) -> bool {
|
|
let a = Vec2::new(20.0, 0.0).angle_to(p);
|
|
cadcraft_geom::angle_in_sweep(a, 0.0, std::f64::consts::FRAC_PI_2) && (p.dist(Vec2::new(20.0, 0.0)) - 2.0).abs() < 1e-9
|
|
}
|
|
|
|
#[test]
|
|
fn arc_tangent_only_on_the_arc_not_its_circle() {
|
|
let d = arc_drawing();
|
|
// From (20,5), the circle's tangents touch at about ±23.6° from the vertical through the
|
|
// center: one lands at 90+23.6 = 113.6° (the gap), the other at 90-23.6 = 66.4° (on the
|
|
// arc). Only the one on the arc may snap.
|
|
let base = Some(Vec2::new(20.0, 5.0));
|
|
let t = osnap(&d, &Space::Model, Vec2::new(20.0 + 2.0, 0.0), 8.0, mode::TAN, base, false).expect("the arc's tangent");
|
|
assert!(on_arc(t.point), "tangent must lie on the arc, got {:?}", t.point);
|
|
// The other solution is on the circle but off the arc, so it is not offered.
|
|
let off = Vec2::polar(Vec2::new(20.0, 0.0), 2.0, 113.6f64.to_radians());
|
|
assert!(!on_arc(off));
|
|
let none = osnap(&d, &Space::Model, off, 0.05, mode::TAN, base, false);
|
|
assert!(none.is_none(), "a tangent in the arc's gap must not snap, got {none:?}");
|
|
}
|
|
|
|
#[test]
|
|
fn arc_perpendicular_clamps_to_the_arc() {
|
|
let d = arc_drawing();
|
|
// The foot of the perpendicular from below lands at 270°, in the gap. The opposite
|
|
// antipode at (20,2) is on the arc. The cursor is 5 units away from it, so the aperture
|
|
// is a little larger to keep the distance test off the boundary.
|
|
let h = osnap(&d, &Space::Model, Vec2::new(20.0, -3.0), 5.5, mode::PER, Some(Vec2::new(20.0, -6.0)), false)
|
|
.expect("the perpendicular on the arc");
|
|
assert!(on_arc(h.point), "perpendicular must stay on the arc, got {:?}", h.point);
|
|
assert!(h.point.near(Vec2::new(20.0, 2.0), 1e-9), "the opposite antipode on the arc, got {:?}", h.point);
|
|
}
|
|
|
|
#[test]
|
|
fn arc_deferred_tangent_keeps_its_sweep() {
|
|
let d = arc_drawing();
|
|
let at = Vec2::polar(Vec2::new(20.0, 0.0), 2.0, 45f64.to_radians());
|
|
let h = osnap(&d, &Space::Model, at, 0.5, mode::TAN, None, true).expect("deferred tangent on the arc");
|
|
assert_eq!((h.mode, h.name), (mode::TAN, "Deferred Tangent"));
|
|
let df = h.deferred.unwrap();
|
|
// The sweep travels with the curve, so a later solve stays on the arc.
|
|
assert!(matches!(df.curve, SnapCurve::Arc { .. }), "the arc's sweep must be kept: {:?}", df.curve);
|
|
// A deferred tangent solves to a point on the arc, not into its gap.
|
|
let solved = resolve_deferred(LineEnd::Deferred(df), pt(10.0, 10.0)).expect("a tangent from (10,10)");
|
|
// "In the order given": the deferred end solves first.
|
|
assert!(on_arc(solved.0), "resolved tangent must lie on the arc, got {:?}", solved.0);
|
|
}
|
|
|
|
#[test]
|
|
fn deferred_tangent_pairs_with_arcs() {
|
|
// The arc is the top half of a circle at (0,0) r=5.
|
|
let arc = SnapCurve::Arc { center: Vec2::new(0.0, 0.0), radius: 5.0, start: 0.0, end: std::f64::consts::PI };
|
|
// The circle is at (10,0) r=5.
|
|
let circle = SnapCurve::Circle { center: Vec2::new(10.0, 0.0), radius: 5.0 };
|
|
|
|
let d_arc = Deferred { mode: mode::TAN, curve: arc, at: Vec2::new(0.0, 5.0) };
|
|
let d_circle = Deferred { mode: mode::TAN, curve: circle, at: Vec2::new(10.0, 5.0) };
|
|
|
|
// Common tangents of the carrier circles: two outer (y=5 and y=-5) and two inner.
|
|
// The y=-5 tangent touches the arc's circle at (0,-5), which is in the gap.
|
|
// The y=5 tangent touches at (0,5), on the arc.
|
|
// The inner tangents touch the left circle at angles that are also not on the top half.
|
|
// Only the y=5 solution survives the arc's sweep.
|
|
let solved = resolve_deferred(LineEnd::Deferred(d_arc), LineEnd::Deferred(d_circle)).unwrap();
|
|
assert!(solved.0.near(Vec2::new(0.0, 5.0), 1e-9), "expected the belt tangent on the top arc, got {:?}", solved.0);
|
|
assert!(solved.1.near(Vec2::new(10.0, 5.0), 1e-9));
|
|
}
|
|
}
|