use std::f64::consts::FRAC_PI_2;

use serde_json::{Value, json};
use solidcraft_geom::Vec3;

use crate::Session;

pub(super) fn run(s: &mut Session, id: &str, p: Value) -> Value {
    match s.execute(id, &p) {
        Ok(v) => v,
        Err(e) => panic!("{id} {p}: {e}"),
    }
}

pub(super) fn occ(s: &Session, component: &str) -> u64 {
    let c = s.doc.find_component(component).unwrap_or(0);
    s.doc.occurrence_of(c).map(|o| o.id).unwrap_or(0)
}

pub(super) fn place(s: &Session, component: &str, p: Vec3) -> Vec3 {
    solidcraft_doc::apply_point(&solidcraft_doc::joints::occurrence_world(&s.doc, occ(s, component)), p)
}

fn near(a: Vec3, b: Vec3) -> bool {
    a.dist(b) < 1e-6
}

/// A hinge leaf (oracle 63's knuckle geometry): a 40 x 30 x 3 plate and an r4 knuckle along X
/// at y = 33, z = 4.
fn leaf(s: &mut Session, name: &str) {
    run(s, "component.activate", json!({"component": "root"}));
    run(s, "component.create", json!({"name": name}));
    run(s, "solid.box", json!({"length": 40, "width": 30, "height": 3, "corner": [0, 0, 0]}));
    run(s, "solid.cylinder", json!({"base": [0, 33, 4], "axis": [1, 0, 0], "radius": 4, "height": 40, "operation": "new"}));
}

#[test]
fn circle_given_by_its_centre_takes_that_round_end() {
    // #393: `circle` at the centre of a round end, as the parameters document, was refused with
    // "no cylindrical face there" (no face lies at a centre).
    let mut s = Session::default();
    run(&mut s, "component.create", json!({"name": "Plate"}));
    run(&mut s, "solid.box", json!({"length": 30, "width": 20, "height": 6, "corner": [-15, -10, 0]}));
    run(&mut s, "component.activate", json!({"component": "root"}));
    run(&mut s, "component.create", json!({"name": "Knob"}));
    run(&mut s, "solid.cylinder", json!({"base": [0, 0, 6], "axis": [0, 0, 1], "radius": 10, "height": 10, "operation": "new"}));
    let r = run(
        &mut s,
        "joint.create",
        json!({"type": "cylindrical", "a": {"occurrence": "Plate", "face": [0, 0, 6]}, "b": {"occurrence": "Knob", "circle": [0, 0, 6]}, "name": "J"}),
    );
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    // The knob's bottom circle already sits on the plate's top: its axis stays put (it may turn
    // about it, to line up the two frames' x).
    for z in [6.0, 16.0] {
        assert!(near(place(&s, "Knob", Vec3::new(0.0, 0.0, z)), Vec3::new(0.0, 0.0, z)), "{:?}", place(&s, "Knob", Vec3::new(0.0, 0.0, z)));
    }
    // The top end's centre: its axis points up, out of the knob.
    run(&mut s, "joint.origin", json!({"occurrence": "Knob", "circle": [0, 0, 16], "name": "Top"}));
    let top = s.doc.assembly.origins.iter().find(|o| o.name == "Top").map(|o| o.origin.snap.clone());
    assert!(
        matches!(top, Some(solidcraft_doc::joints::Snap::Point { point, z: Some(z) }) if near(point, Vec3::new(0.0, 0.0, 16.0)) && near(z, Vec3::Z)),
        "{top:?}"
    );
    // Off the axis is still refused, and so is a coupling size (it follows a face).
    assert!(s.execute("joint.origin", &json!({"occurrence": "Knob", "circle": [3, 0, 6]})).is_err());
    let e = s.execute("joint.screw", &json!({"joint": "J", "pitch": {"occurrence": "Knob", "circle": [0, 0, 6]}})).unwrap_err();
    assert!(e.to_string().contains("not its centre"), "{e}");
}

#[test]
fn revolute_hinge_turns_about_the_knuckle() {
    let mut s = Session::default();
    leaf(&mut s, "LeafA");
    leaf(&mut s, "LeafB");
    let o = occ(&s, "LeafA");
    run(&mut s, "occurrence.ground", json!({"occurrence": o, "grounded": true}));
    let r = run(
        &mut s,
        "joint.create",
        json!({
        "type": "revolute", "a": {"occurrence": "LeafA", "circle": [1, 37, 4]}, "b": {"occurrence": "LeafB", "circle": [1, 37, 4]}, "flip": true, "name": "Hinge"}),
    );
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    // Same frames: B stays put at angle 0.
    assert!(near(place(&s, "LeafB", Vec3::new(20.0, 0.0, 0.0)), Vec3::new(20.0, 0.0, 0.0)));
    let l = run(&mut s, "joint.list", json!({}));
    let dof = l["dof"].as_array().unwrap().iter().find(|d| d["occurrence"] == occ(&s, "LeafB")).unwrap()["dof"].clone();
    assert_eq!(dof, 1, "{l}");
    // Drive 90°: B turns about the knuckle axis (through (0, 33, 4), along the frame's z = −X).
    run(&mut s, "joint.drive", json!({"joint": "Hinge", "value": 90}));
    let want = solidcraft_doc::rigid(Vec3::ZERO, Vec3::new(0.0, 33.0, 4.0), Vec3::new(-1.0, 0.0, 0.0), FRAC_PI_2);
    let p = Vec3::new(20.0, 0.0, 0.0);
    assert!(near(place(&s, "LeafB", p), solidcraft_doc::apply_point(&want, p)), "{:?}", place(&s, "LeafB", p));
    assert!(near(place(&s, "LeafB", p), Vec3::new(20.0, 29.0, 37.0)));
    // LeafA did not move; the knuckle axis is fixed.
    assert!(near(place(&s, "LeafA", p), p));
    assert!(near(place(&s, "LeafB", Vec3::new(10.0, 33.0, 4.0)), Vec3::new(10.0, 33.0, 4.0)));
    // Expressions drive too, and undo puts it back.
    run(&mut s, "joint.drive", json!({"joint": "Hinge", "value": "pi rad"}));
    assert!(near(place(&s, "LeafB", p), Vec3::new(20.0, 66.0, 8.0)));
    run(&mut s, "edit.undo", json!({}));
    assert!(near(place(&s, "LeafB", p), Vec3::new(20.0, 29.0, 37.0)));
}

/// Two 10 mm cubes in components A (grounded) and B.
fn two_cubes() -> Session {
    let mut s = Session::default();
    for (name, x) in [("A", 0), ("B", 20)] {
        run(&mut s, "component.activate", json!({"component": "root"}));
        run(&mut s, "component.create", json!({"name": name}));
        run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [x, 0, 0]}));
    }
    let o = occ(&s, "A");
    run(&mut s, "occurrence.ground", json!({"occurrence": o, "grounded": true}));
    s
}

#[test]
fn slider_limits_clamp() {
    let mut s = two_cubes();
    // B's bottom face onto A's top face (faces meet), sliding along their common normal.
    let r = run(
        &mut s,
        "joint.create",
        json!({"type": "slider", "a": {"face": [5, 5, 10]}, "b": {"face": [25, 5, 0]}, "limits": [[0, 10]], "name": "Rail"}),
    );
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    // B now sits on A.
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 10.0)), "{:?}", place(&s, "B", Vec3::new(25.0, 5.0, 0.0)));
    let r = run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 25}));
    assert_eq!((&r["values"][0]["value"], &r["values"][0]["unit"]), (&json!(10.0), &json!("mm")), "{r}");
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 20.0)));
    run(&mut s, "joint.drive", json!({"joint": "Rail", "value": -5}));
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 10.0)));
    // Changing the limits clamps the current value.
    run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 8}));
    run(&mut s, "joint.limits", json!({"joint": "Rail", "min": 0, "max": 4}));
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 14.0)));
    // Joints follow edits: A gets taller, B rides on its new top.
    let h = s
        .doc
        .features
        .iter()
        .find(|f| matches!(f.kind, solidcraft_doc::FeatureKind::Box { .. }))
        .and_then(|f| f.param_names.get(2).cloned())
        .unwrap_or_default();
    run(&mut s, "parameters.change", json!({"name": h, "expression": "15"}));
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 19.0)), "{:?}", place(&s, "B", Vec3::new(25.0, 5.0, 0.0)));
}

#[test]
fn rigid_cycles_solve_and_conflicts_report() {
    let mut s = two_cubes();
    run(&mut s, "component.activate", json!({"component": "root"}));
    run(&mut s, "component.create", json!({"name": "C"}));
    run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [40, 0, 0]}));
    run(&mut s, "component.activate", json!({"component": "root"}));
    // A rigid group and a closing as-built joint: a consistent loop.
    run(&mut s, "joint.rigid_group", json!({"occurrences": ["A", "B", "C"]}));
    let r = run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "B", "b": "C"}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    assert!(near(place(&s, "C", Vec3::new(40.0, 0.0, 0.0)), Vec3::new(40.0, 0.0, 0.0)));
    let l = run(&mut s, "joint.list", json!({}));
    assert!(l["dof"].as_array().unwrap().iter().all(|d| d["dof"] == 0), "{l}");
    // A joint that wants C elsewhere conflicts and says so.
    let r = run(
        &mut s,
        "joint.create",
        json!({"type": "rigid", "a": {"occurrence": "A", "point": [0, 0, 0]}, "b": {"occurrence": "C", "point": [40, 0, 0]}, "name": "Wrong"}),
    );
    let c = r["conflicts"].as_array().cloned().unwrap_or_default();
    assert_eq!(c.len(), 1, "{r}");
    assert!(c[0]["why"].as_str().unwrap_or("").contains("off by"), "{r}");
    // Suppressing it clears the conflict.
    let r = run(&mut s, "joint.edit", json!({"joint": "Wrong", "suppressed": true}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0));
    assert!(
        s.execute(
            "joint.create",
            &json!({"type": "rigid", "a": {"occurrence": "A", "point": [0, 0, 0]}, "b": {"occurrence": "A", "point": [1, 0, 0]}})
        )
        .is_err()
    );
    assert!(s.execute("joint.create", &json!({"type": "hinge"})).is_err());
}

/// A 30 x 30 x 3 plate with a through slot whose x = 20 wall carries one rib (0.3 tall, 0.8
/// wide), and a peg in the slot with 0.15 clearance all round.
fn ribbed_slot_and_peg(s: &mut Session, peg_x1: f64) {
    run(s, "sketch.create", json!({"plane": "XY"}));
    run(s, "sketch.rectangle.two_point", json!({"p0": [0, 0], "p1": [30, 30]}));
    run(s, "sketch.finish", json!({}));
    run(s, "solid.extrude", json!({"distance": 3, "body_name": "Plate"}));
    run(s, "sketch.create", json!({"plane": "XY", "offset": -1}));
    let slot = json!([[10, 5], [20, 5], [20, 14.6], [19.7, 14.6], [19.7, 15.4], [20, 15.4], [20, 25], [10, 25]]);
    run(s, "sketch.line", json!({"points": slot, "closed": true}));
    run(s, "sketch.finish", json!({}));
    run(s, "solid.extrude", json!({"distance": 5, "operation": "cut", "targets": ["Plate"]}));
    run(s, "sketch.create", json!({"plane": "XY"}));
    run(s, "sketch.rectangle.two_point", json!({"p0": [10.15, 5.15], "p1": [peg_x1, 24.85]}));
    run(s, "sketch.finish", json!({}));
    run(s, "solid.extrude", json!({"distance": 3, "operation": "new", "body_name": "Peg"}));
}

/// The peg overlaps only the rib: 0.15 x 0.8 x 3 = 0.36 mm³ (#442).
#[test]
fn interference_finds_a_peg_overlapping_a_small_rib() {
    let mut s = Session::default();
    ribbed_slot_and_peg(&mut s, 19.85);
    let i = run(&mut s, "inspect.interference", json!({}));
    assert_eq!(i["count"], 1, "{i}");
    assert!((i["interferences"][0]["volume_mm3"].as_f64().unwrap_or(0.0) - 0.36).abs() < 1e-6, "{i}");
    let (lo, hi) = (&i["interferences"][0]["bbox"]["min"], &i["interferences"][0]["bbox"]["max"]);
    assert!((lo[0].as_f64().unwrap_or(0.0) - 19.7).abs() < 1e-6 && (hi[0].as_f64().unwrap_or(0.0) - 19.85).abs() < 1e-6, "{i}");
}

/// An arc revolved up to a post ends on the post's wall, where the two bodies can't be
/// intersected: the pair is listed as unchecked instead of passing as clear.
#[test]
fn interference_lists_a_pair_it_could_not_check() {
    let mut s = Session::default();
    run(&mut s, "solid.cylinder", json!({"base": [0, 14, -5], "radius": 4, "height": 15, "body_name": "Post"}));
    run(&mut s, "sketch.create", json!({"name": "Profile", "plane": "XZ"}));
    run(&mut s, "sketch.rectangle.two_point", json!({"p0": [10, 0], "p1": [15, 5]}));
    run(&mut s, "sketch.finish", json!({}));
    run(&mut s, "solid.revolve", json!({"sketch": "Profile", "axis": {"origin": [0, 0, 0], "dir": [0, 0, 1]}, "to": [4, 14, 2], "body_name": "Arc"}));
    let i = run(&mut s, "inspect.interference", json!({}));
    assert_eq!(i["count"], 0, "{i}");
    let unchecked = i["unchecked"].as_array().cloned().unwrap_or_default();
    assert_eq!(unchecked.len(), 1, "{i}");
    assert!(unchecked[0]["reason"].as_str().is_some_and(|r| r.starts_with("not verified") && !r.contains("displacement")), "{i}");
    // Bodies that are clear of each other, or overlap plainly, leave the list empty.
    let mut s = two_cubes();
    let i = run(&mut s, "inspect.interference", json!({}));
    assert_eq!(i["unchecked"].as_array().map(Vec::len), Some(0), "{i}");
}

#[test]
fn motion_links_and_interference() {
    let mut s = two_cubes();
    run(&mut s, "joint.create", json!({"type": "cylindrical", "a": {"face": [5, 5, 10]}, "b": {"face": [25, 5, 0]}, "name": "Screw"}));
    run(&mut s, "joint.drive", json!({"joint": "Screw", "values": [0, 0]}));
    // No overlap while B sits on A; then push B 4 mm into A.
    let i = run(&mut s, "inspect.interference", json!({}));
    assert_eq!(i["count"], 0, "{i}");
    run(&mut s, "joint.drive", json!({"joint": "Screw", "values": [0, -4]}));
    let i = run(&mut s, "inspect.interference", json!({}));
    assert_eq!(i["count"], 1, "{i}");
    assert!((i["interferences"][0]["volume_mm3"].as_f64().unwrap_or(0.0) - 400.0).abs() < 1e-3, "{i}");
    // A motion link: a second joint's value follows.
    run(&mut s, "component.activate", json!({"component": "root"}));
    run(&mut s, "component.create", json!({"name": "D"}));
    run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [60, 0, 0]}));
    run(
        &mut s,
        "joint.create",
        json!({"type": "slider", "a": {"occurrence": "A", "face": [5, 5, 10]}, "b": {"occurrence": "D", "face": [65, 5, 0]}, "name": "Follower"}),
    );
    run(&mut s, "joint.motion_link", json!({"a": "Screw", "ia": 1, "b": "Follower", "ratio": 2}));
    run(&mut s, "joint.drive", json!({"joint": "Screw", "values": [0, 3]}));
    assert!(near(place(&s, "D", Vec3::new(65.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 16.0)), "{:?}", place(&s, "D", Vec3::new(65.0, 5.0, 0.0)));
    // Saved and reopened, joints come back.
    let back = solidcraft_doc::Document::from_json(&s.doc.to_json()).unwrap();
    assert_eq!(back.assembly, s.doc.assembly);
    let mut t = Session::new(back);
    let l = run(&mut t, "joint.list", json!({}));
    assert_eq!(l["joints"].as_array().map(Vec::len), Some(2));
}

/// Two faces joined mate: B's bottom face lands on A's top face, B on top of A (not inside
/// it); Flip turns B over instead.
#[test]
fn faces_mate_by_default() {
    let mut s = two_cubes();
    run(&mut s, "joint.create", json!({"type": "rigid", "a": {"face": [5, 5, 10]}, "b": {"face": [25, 5, 0]}, "name": "Stack"}));
    // B's bottom centre (25, 5, 0) at A's top centre, B above it.
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 10.0)));
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 10.0)), Vec3::new(5.0, 5.0, 20.0)), "{:?}", place(&s, "B", Vec3::new(25.0, 5.0, 10.0)));
    run(&mut s, "joint.edit", json!({"joint": "Stack", "flip": true}));
    assert!(near(place(&s, "B", Vec3::new(25.0, 5.0, 10.0)), Vec3::new(5.0, 5.0, 0.0)), "{:?}", place(&s, "B", Vec3::new(25.0, 5.0, 10.0)));
}

/// #1239: two parts as bodies of one component (a multi-body STEP import). The refusal names the
/// way out, and after Create Components from Bodies the same origins make the joint.
#[test]
fn bodies_of_one_component_get_components_first() {
    let mut s = Session::default();
    run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10}));
    run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [20, 0, 0]}));
    let p = json!({"type": "rigid", "a": {"face": [5, 5, 10]}, "b": {"face": [25, 5, 0]}});
    let e = s.execute("joint.create", &p).map(|_| ()).unwrap_err().to_string();
    assert!(e.contains("two different occurrences") && e.contains("component.from_bodies"), "{e}");
    run(&mut s, "component.from_bodies", json!({"bodies": ["Body1", "Body2"]}));
    run(&mut s, "joint.create", p);
    // The first joint's A side stays; B lands on top of it.
    assert!(near(place(&s, "Body2", Vec3::new(25.0, 5.0, 0.0)), Vec3::new(5.0, 5.0, 10.0)));
}

/// #527: an assembly with its fasteners passes 200 bodies quickly; the clash check must still
/// cover the whole design. 201 separate 1 mm cubes 2 mm apart, plus one cube pushed half-way
/// into the first: exactly that pair overlaps, by 0.5 mm³.
#[test]
fn interference_checks_designs_with_more_than_200_bodies() {
    let mut s = Session::default();
    for i in 0..201 {
        run(&mut s, "solid.box", json!({"length": 1, "width": 1, "height": 1, "corner": [2 * i, 0, 0], "operation": "new"}));
    }
    run(&mut s, "solid.box", json!({"length": 1, "width": 1, "height": 1, "corner": [0.5, 0, 0], "operation": "new", "body_name": "Clash"}));
    assert_eq!(s.model.state().bodies.len(), 202);
    let i = run(&mut s, "inspect.interference", json!({}));
    assert_eq!(i["checked"], 202, "{i}");
    assert_eq!(i["count"], 1, "{i}");
    let hit = &i["interferences"][0];
    let mut pair = [hit["a"].as_str().unwrap_or(""), hit["b"].as_str().unwrap_or("")];
    pair.sort_unstable();
    assert_eq!(pair, ["Body1", "Clash"], "{i}");
    assert!((hit["volume_mm3"].as_f64().unwrap_or(0.0) - 0.5).abs() < 1e-6, "{i}");
}

/// The bounding-box sweep behind `inspect.interference` finds exactly the pairs a check of every
/// pair finds (touching boxes count), and reports how many it left out past its limit.
#[test]
fn interference_box_sweep_matches_every_pair_check() {
    use solidcraft_geom::Aabb3;
    let cube = |x: f64, y: f64, z: f64, e: f64| Aabb3 { min: Vec3::new(x, y, z), max: Vec3::new(x + e, y + e, z + e) };
    // A deterministic scatter: overlapping, touching, and apart in only one axis.
    let boxes: Vec<Aabb3> = (0..60)
        .map(f64::from)
        .map(|i| cube((i * 7.3) % 20.0, (i * 3.1) % 9.0, (i * 5.7) % 4.0, 1.0 + (i % 3.0)))
        .chain([cube(30.0, 0.0, 0.0, 1.0), cube(31.0, 0.0, 0.0, 1.0)])
        .collect();
    let mut every = Vec::new();
    for (i, a) in boxes.iter().enumerate() {
        for (j, b) in boxes.iter().enumerate().skip(i + 1) {
            let apart = a.max.x < b.min.x || b.max.x < a.min.x || a.max.y < b.min.y || b.max.y < a.min.y || a.max.z < b.min.z || b.max.z < a.min.z;
            if !apart {
                every.push((i, j));
            }
        }
    }
    assert!(every.contains(&(60, 61)), "touching boxes are a candidate pair");
    let (pairs, skipped) = super::overlapping_pairs(&boxes, usize::MAX);
    assert_eq!((pairs, skipped), (every.clone(), 0));
    let (pairs, skipped) = super::overlapping_pairs(&boxes, 10);
    assert_eq!((pairs.len(), skipped), (10, every.len() - 10));
}

/// A small block in a new component: a part of a linkage, where only its joints matter.
pub(super) fn part(s: &mut Session, name: &str, corner: [f64; 3]) {
    run(s, "component.activate", json!({"component": "root"}));
    run(s, "component.create", json!({"name": name}));
    run(s, "solid.box", json!({"length": 2, "width": 2, "height": 2, "corner": corner}));
}

/// A joint between two parts as they are, at a world point with its z along `z`.
pub(super) fn pin(s: &mut Session, kind: &str, name: &str, a: &str, b: &str, p: Vec3, z: Vec3) {
    let at = |o: &str| json!({"occurrence": o, "point": [p.x, p.y, p.z], "z": [z.x, z.y, z.z]});
    let r = run(s, "joint.create", json!({"type": kind, "a": at(a), "b": at(b), "flip": true, "name": name}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
}

/// Where circles about `p` (radius `r`) and `q` (radius `s`) in the XY plane meet.
pub(super) fn meet(p: Vec3, r: f64, q: Vec3, s: f64) -> [Vec3; 2] {
    let d = q - p;
    let l = d.len();
    let a = (r * r - s * s + l * l) / (2.0 * l);
    let m = p + d * (a / l);
    let n = Vec3::new(-d.y, d.x, 0.0) * ((r * r - a * a).max(0.0).sqrt() / l);
    [m + n, m - n]
}

/// A crank-rocker four-bar about +Z: ground pivots O2 = (0, 0) and O4 = (45, 0), crank 20,
/// coupler 50, rocker 40, assembled with the crank at 90°. Returns the crank pin P0 and the
/// rocker pin Q0 (the upper, open assembly).
pub(super) fn four_bar() -> (Session, Vec3, Vec3) {
    let mut s = Session::default();
    let (o2, o4, p0) = (Vec3::ZERO, Vec3::new(45.0, 0.0, 0.0), Vec3::new(0.0, 20.0, 0.0));
    let [q0, _] = meet(p0, 50.0, o4, 40.0);
    for (name, c) in [("Ground", o2), ("Crank", p0), ("Coupler", (p0 + q0) * 0.5), ("Rocker", q0)] {
        part(&mut s, name, [c.x, c.y, -5.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Crank", "Ground", "Crank", o2, Vec3::Z);
    pin(&mut s, "revolute", "Crank pin", "Crank", "Coupler", p0, Vec3::Z);
    pin(&mut s, "revolute", "Rocker pin", "Coupler", "Rocker", q0, Vec3::Z);
    pin(&mut s, "revolute", "Rocker", "Ground", "Rocker", o4, Vec3::Z);
    (s, p0, q0)
}

/// The four-bar's rocker pin with the crank driven to `to`°, followed a degree at a time from
/// `from`° (where it is at `q`), so it stays on its branch.
fn rocker_pin(from: f64, to: f64, mut q: Vec3) -> Vec3 {
    let n = ((to - from).abs().ceil() as usize).max(1);
    for k in 1..=n {
        let th = (90.0 + from + (to - from) * k as f64 / n as f64).to_radians();
        let [m1, m2] = meet(Vec3::new(20.0 * th.cos(), 20.0 * th.sin(), 0.0), 50.0, Vec3::new(45.0, 0.0, 0.0), 40.0);
        q = if m1.dist(q) <= m2.dist(q) { m1 } else { m2 };
    }
    q
}

#[test]
fn four_bar_follows_its_crank() {
    let (mut s, p0, q0) = four_bar();
    let mut q = q0;
    let mut at_330 = q0;
    for k in 1..=12 {
        let v = 30.0 * f64::from(k);
        let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": v}));
        assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{v}°: {r}");
        assert!(r["stopped_by_loop"].is_null(), "{v}°: {r}");
        // The driven joint keeps exactly the value asked for, answered in degrees as asked.
        assert!((r["values"][0]["value"].as_f64().unwrap_or(f64::NAN) - v).abs() < 1e-9 && r["values"][0]["unit"] == "deg", "{r}");
        q = rocker_pin(v - 30.0, v, q);
        let th = (90.0 + v).to_radians();
        let p = Vec3::new(20.0 * th.cos(), 20.0 * th.sin(), 0.0);
        for (part, local, want) in [("Crank", p0, p), ("Coupler", p0, p), ("Coupler", q0, q), ("Rocker", q0, q)] {
            assert!(near(place(&s, part, local), want), "{v}°: {part} {:?} wants {want:?}", place(&s, part, local));
        }
        if k == 11 {
            at_330 = q;
        }
    }
    // Back where it started after a full turn, and undo steps back.
    assert!(near(q, q0));
    run(&mut s, "edit.undo", json!({}));
    assert!(near(place(&s, "Rocker", q0), at_330), "{:?}", place(&s, "Rocker", q0));
    // One 180° drive lands on the same (open) branch as the stepped path.
    let (mut s, _, q0) = four_bar();
    let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 180}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    assert!(near(place(&s, "Rocker", q0), rocker_pin(0.0, 180.0, q0)), "{:?}", place(&s, "Rocker", q0));
    // A motion study playing the crank places the rocker the same way.
    run(&mut s, "motion.study", json!({"name": "Turn", "steps": 10, "keys": [{"joint": "Crank", "points": [[0, 0], [10, 120]]}]}));
    let r = run(&mut s, "motion.play", json!({"study": "Turn", "step": 5}));
    assert!(r["stopped_by_loop"].is_null(), "{r}");
    assert!(near(place(&s, "Rocker", q0), rocker_pin(180.0, 60.0, rocker_pin(0.0, 180.0, q0))), "{:?}", place(&s, "Rocker", q0));
}

/// The rocker swings between its toggle positions, where crank and coupler line up (|Q| = 70
/// and |Q| = 30, about 69.3° and 139.2° from the ground line); driving it further stops where
/// the loop still closes.
#[test]
fn four_bar_rocker_stops_where_the_loop_cannot_close() {
    let (mut s, _, q0) = four_bar();
    let start = q0.y.atan2(q0.x - 45.0).to_degrees();
    let r = run(&mut s, "joint.drive", json!({"joint": "Rocker", "value": 100}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    let reached = r["values"][0]["value"].as_f64().unwrap_or(f64::NAN);
    // |Q|² = 45² + 40² + 2·45·40·cos φ = 30².
    let limit = ((900.0f64 - 3625.0) / 3600.0).acos().to_degrees() - start;
    assert!(reached > limit - 5.0 && reached <= limit, "stopped at {reached}°, the limit is {limit}°");
    // Inside its swing it moves freely, and the crank follows.
    let r = run(&mut s, "joint.drive", json!({"joint": "Rocker", "value": -10}));
    assert!(r["stopped_by_loop"].is_null() && r["conflicts"].as_array().map(Vec::len) == Some(0), "{r}");
    let q = place(&s, "Rocker", q0);
    assert!((q.y.atan2(q.x - 45.0).to_degrees() - (start - 10.0)).abs() < 1e-6, "{q:?}");
    assert!(place(&s, "Coupler", q0).dist(q) < 1e-6);
    // A full turn would end where it started, but the rocker can't get there.
    let (mut s, _, _) = four_bar();
    let r = run(&mut s, "joint.drive", json!({"joint": "Rocker", "value": 360}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    assert!(r["values"][0]["value"].as_f64().unwrap_or(f64::NAN) <= limit, "{r}");
}

/// A loop value a motion link sets follows through the start of its link chain: a dial outside
/// the loop turns a gear, which sets the rocker's angle, so turning the crank turns the dial.
#[test]
fn four_bar_turns_the_source_of_a_linked_loop_value() {
    let linked = || {
        let (mut s, _, q0) = four_bar();
        for (name, x) in [("Dial", 80.0), ("Gear", 100.0)] {
            part(&mut s, name, [x, 0.0, -5.0]);
            pin(&mut s, "revolute", name, "Ground", name, Vec3::new(x, 0.0, 0.0), Vec3::Z);
        }
        run(&mut s, "joint.motion_link", json!({"a": "Dial", "b": "Gear", "ratio": 1}));
        run(&mut s, "joint.motion_link", json!({"a": "Gear", "b": "Rocker", "ratio": 0.5}));
        (s, q0)
    };
    let (mut s, q0) = linked();
    let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 60}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    let q = rocker_pin(0.0, 60.0, q0);
    assert!(near(place(&s, "Rocker", q0), q), "{:?} wants {q:?}", place(&s, "Rocker", q0));
    let turn = q.y.atan2(q.x - 45.0) - q0.y.atan2(q0.x - 45.0);
    let dial = s.doc.assembly.joints.iter().find(|j| j.name == "Dial").and_then(|j| j.values.first().copied()).unwrap_or(f64::NAN);
    assert!((dial - 2.0 * turn).abs() < 1e-9, "dial {dial}, rocker turned {turn}");
    // Driving the dial drives the rocker through the chain: two turns of the dial would turn
    // the rocker a full turn, which it can't make.
    let (mut s, _) = linked();
    let r = run(&mut s, "joint.drive", json!({"joint": "Dial", "value": 720}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
}

/// Values left out of a drive are free to follow in a loop: a plate on a planar joint whose
/// travel a diagonal slider limits. Driving only the planar joint's x moves its y along.
#[test]
fn values_left_out_of_a_drive_follow_the_loop() {
    let mut s = Session::default();
    part(&mut s, "Ground", [-1.0, -1.0, -5.0]);
    part(&mut s, "Plate", [-1.0, -1.0, 0.0]);
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    let frame = |o: &str, z: [f64; 3], x: [f64; 3]| json!({"occurrence": o, "frame": {"origin": [0, 0, 0], "z": z, "x": x}});
    let flat = |o: &str| frame(o, [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]);
    let r = run(&mut s, "joint.create", json!({"type": "planar", "a": flat("Ground"), "b": flat("Plate"), "flip": true, "name": "Table"}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    let diagonal = |o: &str| frame(o, [1.0, 1.0, 0.0], [0.0, 0.0, 1.0]);
    let r = run(&mut s, "joint.create", json!({"type": "slider", "a": diagonal("Ground"), "b": diagonal("Plate"), "flip": true, "name": "Rail"}));
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    let r = run(&mut s, "joint.drive", json!({"joint": "Table", "values": [10]}));
    assert!(r["stopped_by_loop"].is_null() && r["conflicts"].as_array().map(Vec::len) == Some(0), "{r}");
    assert!(near(place(&s, "Plate", Vec3::ZERO), Vec3::new(10.0, 10.0, 0.0)), "{:?}", place(&s, "Plate", Vec3::ZERO));
}

/// A slider-crank: crank 15 about the origin, rod 40, a piston sliding along X. Returns the crank
/// pin and the wrist pin.
fn slider_crank() -> (Session, Vec3, Vec3) {
    let mut s = Session::default();
    let (o, p0) = (Vec3::ZERO, Vec3::new(0.0, 15.0, 0.0));
    let s0 = Vec3::new((40.0f64 * 40.0 - 15.0 * 15.0).sqrt(), 0.0, 0.0);
    for (name, c) in [("Ground", o), ("Crank", p0), ("Rod", s0 * 0.5), ("Piston", s0)] {
        part(&mut s, name, [c.x, c.y, -5.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Crank", "Ground", "Crank", o, Vec3::Z);
    pin(&mut s, "revolute", "Crank pin", "Crank", "Rod", p0, Vec3::Z);
    pin(&mut s, "revolute", "Wrist pin", "Rod", "Piston", s0, Vec3::Z);
    pin(&mut s, "slider", "Bore", "Ground", "Piston", s0, Vec3::X);
    (s, p0, s0)
}

/// The piston sits at a·cos θ + √(b² − (a·sin θ)²).
#[test]
fn slider_crank_moves_the_piston() {
    let (mut s, p0, s0) = slider_crank();
    for v in [40.0, 135.0, 270.0] {
        let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": v}));
        assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{v}°: {r}");
        let th = (90.0f64 + v).to_radians();
        let x = 15.0 * th.cos() + (40.0f64.powi(2) - (15.0 * th.sin()).powi(2)).sqrt();
        assert!(near(place(&s, "Piston", s0), Vec3::new(x, 0.0, 0.0)), "{v}°: {:?} wants x = {x}", place(&s, "Piston", s0));
        assert!(near(place(&s, "Rod", p0), Vec3::new(15.0 * th.cos(), 15.0 * th.sin(), 0.0)));
    }
}

/// A joint frame on an occurrence, by origin and axes.
fn framed(o: &str, origin: [f64; 3], z: [f64; 3], x: [f64; 3]) -> Value {
    json!({"occurrence": o, "frame": {"origin": origin, "z": z, "x": x}})
}

/// A loop open from the start closes from where it is: an arm on a revolute joint, and a rigid
/// joint that wants it turned 90°.
#[test]
fn an_open_loop_closes_from_where_it_is() {
    let mut s = Session::default();
    part(&mut s, "Ground", [-1.0, -1.0, -5.0]);
    part(&mut s, "Arm", [0.0, -1.0, 0.0]);
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Pivot", "Ground", "Arm", Vec3::ZERO, Vec3::Z);
    let r = run(
        &mut s,
        "joint.create",
        json!({"type": "rigid", "a": framed("Ground", [0.0; 3], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]),
            "b": framed("Arm", [0.0; 3], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]), "flip": true, "name": "Lock"}),
    );
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
    assert!(near(place(&s, "Arm", Vec3::new(10.0, 0.0, 0.0)), Vec3::new(0.0, 10.0, 0.0)), "{:?}", place(&s, "Arm", Vec3::new(10.0, 0.0, 0.0)));
}

/// A loop that can't close does not hold up another one: the four-bar still drives beside a
/// block whose rigid joint wants it where its pivot can't take it.
#[test]
fn a_broken_loop_does_not_stop_another() {
    let (mut s, _, q0) = four_bar();
    part(&mut s, "Block", [200.0, -1.0, -5.0]);
    pin(&mut s, "revolute", "Block pivot", "Ground", "Block", Vec3::new(200.0, 0.0, 0.0), Vec3::Z);
    run(
        &mut s,
        "joint.create",
        json!({"type": "rigid", "a": {"occurrence": "Ground", "point": [200, 0, 0]}, "b": {"occurrence": "Block", "point": [210, 0, 0]}, "flip": true, "name": "Wrong"}),
    );
    let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 60}));
    let names: Vec<&str> = r["conflicts"].as_array().into_iter().flatten().filter_map(|c| c["name"].as_str()).collect();
    assert_eq!(names, ["Wrong"], "{r}");
    assert!(r["stopped_by_loop"].is_null(), "{r}");
    assert!(near(place(&s, "Rocker", q0), rocker_pin(0.0, 60.0, q0)), "{:?}", place(&s, "Rocker", q0));
}

/// A loop locked rigid can't move at all: driving its crank stops at once.
#[test]
fn a_locked_loop_does_not_move() {
    let (mut s, _, _) = four_bar();
    run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "Ground", "b": "Rocker", "name": "Lock"}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 360}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    assert!(r["values"][0]["value"].as_f64().unwrap_or(f64::NAN).to_radians().abs() < 1e-3, "{r}");
}

/// A link that turns the rocker 100 times as far as its dial: a small turn of the dial is a full
/// turn of the rocker, which it can't make.
#[test]
fn a_geared_down_loop_value_is_followed_all_the_way() {
    let (mut s, _, _) = four_bar();
    part(&mut s, "Dial", [80.0, 0.0, -5.0]);
    pin(&mut s, "revolute", "Dial", "Ground", "Dial", Vec3::new(80.0, 0.0, 0.0), Vec3::Z);
    run(&mut s, "joint.motion_link", json!({"a": "Dial", "b": "Rocker", "ratio": 100}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Dial", "value": 3.6}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
}

/// A suppressed dial still turns the rocker through its motion link, and a rocker whose value
/// the file leaves out starts from 0: both are followed all the way, so a full turn stops.
#[test]
fn a_full_turn_stops_from_a_suppressed_dial_or_a_missing_value() {
    let (mut s, _, _) = four_bar();
    part(&mut s, "Dial", [80.0, 0.0, -5.0]);
    pin(&mut s, "revolute", "Dial", "Ground", "Dial", Vec3::new(80.0, 0.0, 0.0), Vec3::Z);
    run(&mut s, "joint.motion_link", json!({"a": "Dial", "b": "Rocker", "ratio": 0.5}));
    run(&mut s, "joint.edit", json!({"joint": "Dial", "suppressed": true}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Dial", "value": 720}));
    assert!(r["stopped_by_loop"].is_object() && r["moved"] == true && r.get("reason").is_none(), "{r}");
    // Undriven, the suppressed dial still follows the rocker when the crank turns.
    run(&mut s, "joint.drive", json!({"joint": "Dial", "value": 0}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 60}));
    assert!(r["stopped_by_loop"].is_null() && r["conflicts"].as_array().map(Vec::len) == Some(0), "{r}");
    let (mut s, _, _) = four_bar();
    if let Some(j) = s.doc_mut().assembly.joints.iter_mut().find(|j| j.name == "Rocker") {
        j.values.clear();
    }
    let r = run(&mut s, "joint.drive", json!({"joint": "Rocker", "value": 360}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
}

/// Loops that only share a rigid joint are independent: an arm whose lock can't close does not
/// stop another arm, beside it on the same rigidly mounted base, from closing its own loop.
#[test]
fn loops_sharing_only_a_rigid_joint_are_solved_apart() {
    let mut s = Session::default();
    for (name, x) in [("Ground", -1.0), ("Base", -1.0), ("Arm", 0.0), ("Other", 100.0)] {
        part(&mut s, name, [x, -1.0, 0.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "Ground", "b": "Base", "name": "Mount"}));
    pin(&mut s, "revolute", "Pivot", "Base", "Arm", Vec3::ZERO, Vec3::Z);
    pin(&mut s, "revolute", "Other pivot", "Base", "Other", Vec3::new(100.0, 0.0, 0.0), Vec3::Z);
    run(
        &mut s,
        "joint.create",
        json!({"type": "rigid", "a": {"occurrence": "Ground", "point": [100, 0, 0]}, "b": {"occurrence": "Other", "point": [110, 0, 0]}, "flip": true, "name": "Wrong"}),
    );
    let r = run(
        &mut s,
        "joint.create",
        json!({"type": "rigid", "a": framed("Ground", [0.0; 3], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]),
            "b": framed("Arm", [0.0; 3], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]), "flip": true, "name": "Lock"}),
    );
    // The broken loop is reported (on whichever of its joints closes it), the arm's is not.
    let names: Vec<&str> = r["conflicts"].as_array().into_iter().flatten().filter_map(|c| c["name"].as_str()).collect();
    assert!(names.len() == 1 && ["Wrong", "Other pivot"].contains(&names[0]), "{r}");
    assert!(near(place(&s, "Arm", Vec3::new(10.0, 0.0, 0.0)), Vec3::new(0.0, 10.0, 0.0)), "{:?}", place(&s, "Arm", Vec3::new(10.0, 0.0, 0.0)));
}

/// Two links writing one value: whichever carries a driven dial's turn into the loop, the turn
/// is followed (here dial A turns gear B, which turns the rocker, before dial D rewrites B).
#[test]
fn a_turn_carried_in_by_any_link_is_followed() {
    let (mut s, _, _) = four_bar();
    for (name, x) in [("A", 80.0), ("B", 100.0), ("D", 120.0)] {
        part(&mut s, name, [x, 0.0, -5.0]);
        pin(&mut s, "revolute", name, "Ground", name, Vec3::new(x, 0.0, 0.0), Vec3::Z);
    }
    run(&mut s, "joint.motion_link", json!({"a": "A", "b": "B", "ratio": 1}));
    run(&mut s, "joint.motion_link", json!({"a": "B", "b": "Rocker", "ratio": 0.5}));
    run(&mut s, "joint.motion_link", json!({"a": "D", "b": "B", "ratio": 1}));
    let r = run(&mut s, "joint.drive", json!({"joint": "A", "value": 720}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
}

/// Several links writing one value: every value a link chain starts from can move to close the
/// loop, whichever of them the link order lets through (here dial A's, before dial B rewrites
/// the gear).
#[test]
fn a_loop_value_moves_through_whichever_link_carries_it() {
    let (mut s, _, q0) = four_bar();
    for (name, x) in [("A", 80.0), ("G", 100.0), ("B", 120.0)] {
        part(&mut s, name, [x, 0.0, -5.0]);
        pin(&mut s, "revolute", name, "Ground", name, Vec3::new(x, 0.0, 0.0), Vec3::Z);
    }
    run(&mut s, "joint.motion_link", json!({"a": "A", "b": "G", "ratio": 1}));
    run(&mut s, "joint.motion_link", json!({"a": "G", "b": "Rocker", "ratio": 1}));
    run(&mut s, "joint.motion_link", json!({"a": "B", "b": "G", "ratio": 1}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 60}));
    assert!(r["stopped_by_loop"].is_null() && r["conflicts"].as_array().map(Vec::len) == Some(0), "{r}");
    assert!(near(place(&s, "Rocker", q0), rocker_pin(0.0, 60.0, q0)), "{:?}", place(&s, "Rocker", q0));
}

/// Two values of one joint can feed two independent loops: a puck's x drives a pair of parallel
/// slides, its y a slide whose rigid lock can't close. Driving x moves the healthy pair.
#[test]
fn values_of_one_joint_feed_independent_loops() {
    let mut s = Session::default();
    for (name, y) in [("Ground", -10.0), ("Puck", -20.0), ("Car", 50.0), ("Other", 100.0)] {
        part(&mut s, name, [-1.0, y, 0.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    let flat = |o: &str| framed(o, [0.0, -20.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]);
    run(&mut s, "joint.create", json!({"type": "planar", "a": flat("Ground"), "b": flat("Puck"), "flip": true, "name": "Table"}));
    pin(&mut s, "slider", "Rail", "Ground", "Car", Vec3::new(0.0, 50.0, 0.0), Vec3::X);
    pin(&mut s, "slider", "Guide", "Ground", "Car", Vec3::new(10.0, 50.0, 0.0), Vec3::X);
    pin(&mut s, "slider", "Lift", "Ground", "Other", Vec3::new(0.0, 100.0, 0.0), Vec3::Y);
    run(
        &mut s,
        "joint.create",
        json!({"type": "rigid", "a": {"occurrence": "Ground", "point": [0, 100, 0]}, "b": {"occurrence": "Other", "point": [10, 100, 0]}, "flip": true, "name": "Wrong"}),
    );
    run(&mut s, "joint.motion_link", json!({"a": "Table", "ia": 0, "b": "Rail", "ratio": 1}));
    run(&mut s, "joint.motion_link", json!({"a": "Table", "ia": 1, "b": "Lift", "ratio": 1}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Table", "values": [10]}));
    assert!(r["stopped_by_loop"].is_null(), "{r}");
    let names: Vec<&str> = r["conflicts"].as_array().into_iter().flatten().filter_map(|c| c["name"].as_str()).collect();
    assert_eq!(names, ["Wrong"], "{r}");
    assert!(near(place(&s, "Car", Vec3::new(0.0, 50.0, 0.0)), Vec3::new(10.0, 50.0, 0.0)), "{:?}", place(&s, "Car", Vec3::new(0.0, 50.0, 0.0)));
}

/// Two loops can move different values of one joint: each keeps what it moved. A table's x
/// feeds one pair of parallel slides and its y another; a study drives both pairs.
#[test]
fn loops_moving_different_values_of_one_joint_keep_both() {
    let mut s = Session::default();
    for (name, y) in [("Ground", -10.0), ("Puck", -20.0), ("CarA", 50.0), ("CarB", 100.0)] {
        part(&mut s, name, [-1.0, y, 0.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    let flat = |o: &str| framed(o, [0.0, -20.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]);
    run(&mut s, "joint.create", json!({"type": "planar", "a": flat("Ground"), "b": flat("Puck"), "flip": true, "name": "Table"}));
    for (car, y) in [("CarA", 50.0), ("CarB", 100.0)] {
        pin(&mut s, "slider", &format!("{car} rail"), "Ground", car, Vec3::new(0.0, y, 0.0), Vec3::X);
        pin(&mut s, "slider", &format!("{car} guide"), "Ground", car, Vec3::new(10.0, y, 0.0), Vec3::X);
    }
    run(&mut s, "joint.motion_link", json!({"a": "Table", "ia": 0, "b": "CarA rail", "ratio": 1}));
    run(&mut s, "joint.motion_link", json!({"a": "Table", "ia": 1, "b": "CarB rail", "ratio": 1}));
    let keys = json!([{"joint": "CarA guide", "points": [[0, 0], [10, 10]]}, {"joint": "CarB guide", "points": [[0, 0], [10, 20]]}]);
    run(&mut s, "motion.study", json!({"name": "Both", "steps": 10, "keys": keys}));
    let r = run(&mut s, "motion.play", json!({"study": "Both", "step": 10}));
    assert!(r["stopped_by_loop"].is_null(), "{r}");
    let table = s.doc.assembly.joints.iter().find(|j| j.name == "Table").map(|j| j.values.clone()).unwrap_or_default();
    assert!(table.len() == 3 && (table[0] - 10.0).abs() < 1e-6 && (table[1] - 20.0).abs() < 1e-6, "{table:?}");
    // A solve with nothing driven leaves them where they are.
    run(&mut s, "joint.solve", json!({}));
    assert!(near(place(&s, "CarA", Vec3::new(0.0, 50.0, 0.0)), Vec3::new(10.0, 50.0, 0.0)), "{:?}", place(&s, "CarA", Vec3::new(0.0, 50.0, 0.0)));
    assert!(near(place(&s, "CarB", Vec3::new(0.0, 100.0, 0.0)), Vec3::new(20.0, 100.0, 0.0)), "{:?}", place(&s, "CarB", Vec3::new(0.0, 100.0, 0.0)));
}

/// A clamped link can jump: a 100:1 link to a rocker limited to a full turn reaches its limit
/// after the dial's first few degrees, back where it started. Each step is checked, so the drive
/// still stops where the rocker can't go.
#[test]
fn a_clamped_link_is_followed_step_by_step() {
    let (mut s, _, _) = four_bar();
    part(&mut s, "Dial", [80.0, 0.0, -5.0]);
    pin(&mut s, "revolute", "Dial", "Ground", "Dial", Vec3::new(80.0, 0.0, 0.0), Vec3::Z);
    run(&mut s, "joint.limits", json!({"joint": "Rocker", "min": 0, "max": 360}));
    run(&mut s, "joint.motion_link", json!({"a": "Dial", "b": "Rocker", "ratio": 100}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Dial", "value": 360}));
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{r}");
}

/// Each occurrence's degrees of freedom as `joint.list` reports them.
fn dof_of(s: &mut Session, component: &str) -> u64 {
    let o = occ(s, component);
    let l = run(s, "joint.list", json!({}));
    l["dof"].as_array().into_iter().flatten().find(|d| d["occurrence"] == o).and_then(|d| d["dof"].as_u64()).unwrap_or(99)
}

/// Loops take degrees of freedom away: a four-bar's moving parts have one between them (its
/// mobility), a part hinged to the coupler one more, a slider-crank one, a parallelogram one, and a
/// four-bar locked rigid none.
#[test]
fn loops_report_their_mobility() {
    let (mut s, p0, q0) = four_bar();
    for (part, want) in [("Ground", 0), ("Crank", 1), ("Coupler", 1), ("Rocker", 1)] {
        assert_eq!(dof_of(&mut s, part), want, "four-bar {part}");
    }
    // Still one after a drive moved it.
    run(&mut s, "joint.drive", json!({"joint": "Crank", "value": 70}));
    assert_eq!(dof_of(&mut s, "Coupler"), 1);
    // A flag hinged to the coupler half-way along: one more.
    let mid = (p0 + q0) * 0.5;
    part(&mut s, "Flag", [mid.x, mid.y, 5.0]);
    run(&mut s, "joint.as_built", json!({"type": "revolute", "a": "Coupler", "b": "Flag", "name": "Flag hinge"}));
    assert_eq!(dof_of(&mut s, "Flag"), 2);
    // Still two when a rotor elsewhere turns the flag's hinge through a motion link.
    part(&mut s, "Rotor", [100.0, 0.0, -5.0]);
    pin(&mut s, "revolute", "Rotor", "Ground", "Rotor", Vec3::new(100.0, 0.0, 0.0), Vec3::Z);
    run(&mut s, "joint.motion_link", json!({"a": "Rotor", "b": "Flag hinge", "ratio": 1}));
    assert_eq!(dof_of(&mut s, "Flag"), 2);
    // A rotor locked by a loop of its own leaves the flag only the mechanism's one.
    run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "Ground", "b": "Rotor", "name": "Rotor lock"}));
    assert_eq!(dof_of(&mut s, "Flag"), 1);
    // Locked: nothing moves.
    let (mut s, _, _) = four_bar();
    run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "Ground", "b": "Rocker", "name": "Lock"}));
    for part in ["Crank", "Coupler", "Rocker"] {
        assert_eq!(dof_of(&mut s, part), 0, "locked {part}");
    }
    // A rotor whose turn a motion link carries into the locked crank can't turn either.
    part(&mut s, "Rotor", [100.0, 0.0, -5.0]);
    pin(&mut s, "revolute", "Rotor", "Ground", "Rotor", Vec3::new(100.0, 0.0, 0.0), Vec3::Z);
    run(&mut s, "joint.motion_link", json!({"a": "Rotor", "b": "Crank", "ratio": 1}));
    assert_eq!(dof_of(&mut s, "Rotor"), 0);
    let (mut s, _, _) = slider_crank();
    for part in ["Crank", "Rod", "Piston"] {
        assert_eq!(dof_of(&mut s, part), 1, "slider-crank {part}");
    }
    // A parallelogram (crank and rocker 20, ground and coupler 45), away from its folded poses.
    let mut s = Session::default();
    let (o2, o4) = (Vec3::ZERO, Vec3::new(45.0, 0.0, 0.0));
    let (p, q) = (Vec3::new(12.0, 16.0, 0.0), Vec3::new(57.0, 16.0, 0.0));
    for (name, c) in [("Ground", o2), ("Crank", p), ("Coupler", (p + q) * 0.5), ("Rocker", q)] {
        part(&mut s, name, [c.x, c.y, -5.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Crank", "Ground", "Crank", o2, Vec3::Z);
    pin(&mut s, "revolute", "Crank pin", "Crank", "Coupler", p, Vec3::Z);
    pin(&mut s, "revolute", "Rocker pin", "Coupler", "Rocker", q, Vec3::Z);
    pin(&mut s, "revolute", "Rocker", "Ground", "Rocker", o4, Vec3::Z);
    for part in ["Crank", "Coupler", "Rocker"] {
        assert_eq!(dof_of(&mut s, part), 1, "parallelogram {part}");
    }
}

/// An actuator in line with the path of its tip pin, as modelled: a panel hinged at the origin,
/// its tip pin at (30, 0) moving along Y, and a barrel and rod along Y from a root pin at
/// (30, -40). There the rod only extends and the barrel's turn is zero to first order, but the
/// barrel turns as soon as the panel does: it has one degree of freedom, at that pose too.
#[test]
fn a_part_at_a_dead_point_of_its_loop_keeps_its_mobility() {
    let mut s = Session::default();
    let (tip, root) = (Vec3::new(30.0, 0.0, 0.0), Vec3::new(30.0, -40.0, 0.0));
    for (name, c) in [("Ground", Vec3::new(0.0, -40.0, 0.0)), ("Panel", tip), ("Barrel", root), ("Rod", (tip + root) * 0.5)] {
        part(&mut s, name, [c.x, c.y, -5.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Hinge", "Ground", "Panel", Vec3::ZERO, Vec3::Z);
    pin(&mut s, "revolute", "Root pin", "Ground", "Barrel", root, Vec3::Z);
    pin(&mut s, "slider", "Stroke", "Barrel", "Rod", root, Vec3::Y);
    pin(&mut s, "revolute", "Tip pin", "Rod", "Panel", tip, Vec3::Z);
    for part in ["Panel", "Barrel", "Rod"] {
        assert_eq!(dof_of(&mut s, part), 1, "dead point: {part}");
    }
    run(&mut s, "joint.drive", json!({"joint": "Hinge", "value": 5}));
    for part in ["Panel", "Barrel", "Rod"] {
        assert_eq!(dof_of(&mut s, part), 1, "driven: {part}");
    }
}

/// A design file path in a fresh temporary folder (removed by the caller).
fn temp_design(tag: &str, ext: &str) -> (std::path::PathBuf, String) {
    let dir = std::env::temp_dir().join(format!("solidcraft-joint-visibility-{tag}-{}", std::process::id()));
    let _ = std::fs::remove_dir_all(&dir);
    std::fs::create_dir_all(&dir).unwrap();
    let path = dir.join(format!("design.{ext}")).to_string_lossy().to_string();
    (dir, path)
}

/// Two hinge leaves joined by a revolute "Hinge" and a rigid "Glue" to a third part.
fn hinged() -> Session {
    let mut s = Session::default();
    leaf(&mut s, "LeafA");
    leaf(&mut s, "LeafB");
    part(&mut s, "Tag", [60.0, 0.0, 0.0]);
    let o = occ(&s, "LeafA");
    run(&mut s, "occurrence.ground", json!({"occurrence": o, "grounded": true}));
    run(
        &mut s,
        "joint.create",
        json!({"type": "revolute", "a": {"occurrence": "LeafA", "circle": [1, 37, 4]}, "b": {"occurrence": "LeafB", "circle": [1, 37, 4]}, "flip": true, "name": "Hinge"}),
    );
    pin(&mut s, "rigid", "Glue", "LeafA", "Tag", Vec3::new(61.0, 1.0, 0.0), Vec3::new(0.0, 0.0, 1.0));
    s
}

fn joint(s: &Session, name: &str) -> u64 {
    s.doc.assembly.joints.iter().find(|j| j.name == name).map(|j| j.id).unwrap()
}

/// #1160: hiding a joint hides only its glyph. It is saved with the design (not an undo step,
/// like other visibility), the hinge still drives its leaf while hidden, and the folder hides
/// and shows every joint at once.
#[test]
fn hidden_joints_still_drive_and_are_saved_with_the_design() {
    let (dir, path) = temp_design("saved", "json");
    let mut s = hinged();
    let (hinge, glue) = (joint(&s, "Hinge"), joint(&s, "Glue"));
    run(&mut s, "file.save", json!({"path": path}));
    let undo = s.undo.len();
    let r = run(&mut s, "browser.visibility", json!({"joints": ["Hinge"], "visible": false}));
    assert_eq!(r["changed"], 1, "{r}");
    assert!(!s.joint_visible(hinge) && s.joint_visible(glue));
    assert_eq!(s.undo.len(), undo, "hiding is not an undo step");
    assert!(s.is_dirty(), "hiding leaves unsaved changes");
    let l = run(&mut s, "joint.list", json!({}));
    assert_eq!(l["joints"].as_array().unwrap().iter().map(|j| j["visible"].clone()).collect::<Vec<_>>(), [json!(false), json!(true)]);

    // Hidden, the hinge still constrains and moves its leaf; undoing the drive keeps it hidden.
    let p = Vec3::new(20.0, 0.0, 0.0);
    run(&mut s, "joint.drive", json!({"joint": "Hinge", "value": 90}));
    assert!(near(place(&s, "LeafB", p), Vec3::new(20.0, 29.0, 37.0)), "{:?}", place(&s, "LeafB", p));
    run(&mut s, "edit.undo", json!({}));
    assert!(near(place(&s, "LeafB", p), p));
    assert!(!s.joint_visible(hinge), "undo keeps the hiding");
    run(&mut s, "edit.redo", json!({}));
    assert!(near(place(&s, "LeafB", p), Vec3::new(20.0, 29.0, 37.0)));

    // Saved and opened again, the hinge stays hidden.
    run(&mut s, "file.save", json!({}));
    run(&mut s, "file.new", json!({}));
    run(&mut s, "doc.open", json!({"path": path}));
    let (hinge, glue) = (joint(&s, "Hinge"), joint(&s, "Glue"));
    assert!(!s.joint_visible(hinge) && s.joint_visible(glue), "{:?}", s.visibility);
    assert!(!s.is_dirty());
    let saved: Value = serde_json::from_slice(&std::fs::read(&path).unwrap()).unwrap();
    assert_eq!(saved["visibility"]["hidden_joints"], json!([hinge]));

    // The folder: all hidden, then all shown (and saved without any hidden joints).
    run(&mut s, "browser.visibility", json!({"folder": "joints", "visible": false}));
    assert!(!s.joint_visible(hinge) && !s.joint_visible(glue));
    run(&mut s, "browser.visibility", json!({"folder": "joints", "visible": true}));
    assert!(s.joint_visible(hinge) && s.joint_visible(glue));
    // By name among other items, too.
    run(&mut s, "browser.visibility", json!({"items": ["Glue"], "visible": false}));
    assert!(!s.joint_visible(glue));
    run(&mut s, "browser.visibility", json!({"items": ["Glue"], "visible": true}));
    run(&mut s, "file.save", json!({}));
    let saved: Value = serde_json::from_slice(&std::fs::read(&path).unwrap()).unwrap();
    assert!(saved.get("visibility").is_none_or(|v| v.get("hidden_joints").is_none()), "{saved}");

    // Bad requests change nothing.
    let before = s.visibility.clone();
    for p in [
        json!({"joints": ["Nope"], "visible": false}),
        json!({"joints": [], "visible": false}),
        json!({"joints": "Hinge", "visible": false}),
        json!({"joints": ["Hinge"], "folder": "joints", "visible": false}),
        json!({"joints": ["Hinge"], "items": ["Glue"], "visible": false}),
    ] {
        assert!(s.execute("browser.visibility", &p).is_err(), "{p}");
    }
    assert_eq!(s.visibility, before);
    let _ = std::fs::remove_dir_all(&dir);
}

/// #1160: a design saved before joints could be hidden (format 19, no `hidden_joints`) opens
/// with every joint shown; and a new joint that takes a deleted hidden joint's id starts shown.
#[test]
fn older_designs_show_every_joint_and_new_joints_start_shown() {
    let (dir, path) = temp_design("legacy", "json");
    let mut s = hinged();
    let mut legacy: Value = serde_json::from_slice(&solidcraft_io::write_design(&s.doc)).unwrap();
    legacy["format"] = json!("solidcraft/19");
    legacy["visibility"] =
        json!({"hidden_bodies": [], "hidden_occurrences": [], "hidden_origin": ["XY"], "hidden_sketches": [], "shown_sketches": []});
    std::fs::write(&path, serde_json::to_vec(&legacy).unwrap()).unwrap();
    run(&mut s, "file.new", json!({}));
    run(&mut s, "doc.open", json!({"path": path}));
    assert_eq!(s.doc.assembly.joints.len(), 2);
    assert!(s.doc.assembly.joints.iter().all(|j| s.joint_visible(j.id)));
    assert_eq!(s.visibility.hidden_origin, ["XY"]);

    let glue = joint(&s, "Glue");
    run(&mut s, "browser.visibility", json!({"joints": [glue], "visible": false}));
    run(&mut s, "joint.delete", json!({"joint": glue}));
    pin(&mut s, "rigid", "Glue2", "LeafA", "Tag", Vec3::new(61.0, 1.0, 0.0), Vec3::new(0.0, 0.0, 1.0));
    let again = joint(&s, "Glue2");
    assert!(s.joint_visible(again), "id {again} reused from {glue}");
    let _ = std::fs::remove_dir_all(&dir);
}

/// Dials R0…R4 on revolute joints to ground, linked R0 → R1 → … → `last` (ratio 1), the links
/// stored from the end of the chain to its start.
fn reverse_link_chain(s: &mut Session, last: &str) {
    for k in 0..5 {
        let x = 100.0 + 10.0 * f64::from(k);
        part(s, &format!("R{k}"), [x, 0.0, -5.0]);
        pin(s, "revolute", &format!("R{k}"), "Ground", &format!("R{k}"), Vec3::new(x, 0.0, 0.0), Vec3::Z);
    }
    for k in (0..5).rev() {
        let b = if k == 4 { last.to_string() } else { format!("R{}", k + 1) };
        run(s, "joint.motion_link", json!({"a": format!("R{k}"), "b": b, "ratio": 1}));
    }
}

/// A motion link chain carries a value through all its links, however they are stored: five
/// links stored from the end still turn the last joint with the first.
#[test]
fn a_link_chain_stored_backwards_carries_its_value_through() {
    let (mut s, _, _) = four_bar();
    part(&mut s, "Last", [200.0, 0.0, -5.0]);
    pin(&mut s, "revolute", "Last", "Ground", "Last", Vec3::new(200.0, 0.0, 0.0), Vec3::Z);
    reverse_link_chain(&mut s, "Last");
    run(&mut s, "joint.drive", json!({"joint": "R0", "value": 10}));
    let l = run(&mut s, "joint.list", json!({}));
    let last = l["joints"].as_array().into_iter().flatten().find(|j| j["name"] == "Last").map(|j| j["values"][0]["value"].clone());
    assert!((last.and_then(|v| v.as_f64()).unwrap_or(f64::NAN) - 10.0).abs() < 1e-9, "{l}");
}

/// Driving the start of such a chain into a four-bar's crank turns the mechanism, and never
/// reports its loop as opened.
#[test]
fn a_link_chain_stored_backwards_drives_a_loop() {
    let (mut s, _, q0) = four_bar();
    reverse_link_chain(&mut s, "Crank");
    for v in [1.0, 30.0] {
        let r = run(&mut s, "joint.drive", json!({"joint": "R0", "value": v}));
        assert_eq!(r["conflicts"].as_array().map(Vec::len), Some(0), "{v}: {r}");
        assert!(r["stopped_by_loop"].is_null(), "{v}: {r}");
        assert!(near(place(&s, "Rocker", q0), rocker_pin(0.0, v, q0)), "{v}: {:?}", place(&s, "Rocker", q0));
    }
}

/// A turret on a pedestal joined to nothing grounded (Rover v7's turret): the solver places
/// neither, so driving the turret moves nothing. The drive, a motion study and joint.list say
/// so, naming the pedestal, instead of answering as if it worked.
#[test]
fn a_turret_on_a_floating_pedestal_says_it_moves_nothing() {
    let mut s = Session::default();
    for (name, corner) in [("Chassis", [0.0, 0.0, 0.0]), ("Arm", [10.0, 0.0, 0.0]), ("Pedestal", [50.0, 0.0, 0.0]), ("Turret", [50.0, 0.0, 2.0])] {
        part(&mut s, name, corner);
    }
    let g = occ(&s, "Chassis");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Shoulder", "Chassis", "Arm", Vec3::new(10.0, 1.0, 1.0), Vec3::Y);
    pin(&mut s, "revolute", "Azimuth", "Pedestal", "Turret", Vec3::new(51.0, 1.0, 2.0), Vec3::Z);
    let corner = Vec3::new(52.0, 0.0, 2.0);
    let start = place(&s, "Turret", corner);
    let r = run(&mut s, "joint.drive", json!({"joint": "Azimuth", "value": 30, "quiet": true}));
    assert_eq!((&r["moved"], &r["unconnected"]), (&json!(false), &json!("Pedestal:1")), "{r}");
    assert!(r["reason"].as_str().is_some_and(|w| w.starts_with("Pedestal:1 is not connected to anything grounded")), "{r}");
    assert!(r.get("dof").is_none() && r.get("fixed").is_none(), "quiet: {r}");
    // The value is set and answered in degrees, as asked; the turret stays where it was.
    assert!((r["values"][0]["value"].as_f64().unwrap_or(f64::NAN) - 30.0).abs() < 1e-9 && r["values"][0]["unit"] == "deg", "{r}");
    assert!(near(place(&s, "Turret", corner), start));
    let l = run(&mut s, "joint.list", json!({}));
    assert_eq!(l["floating"], json!([{"occurrences": ["Pedestal:1", "Turret:1"], "joints": ["Azimuth"]}]), "{l}");
    // A study keying both joints moves the arm and says the turret can't move.
    let keys = json!([{"joint": "Azimuth", "points": [[0, 0], [10, 90]]}, {"joint": "Shoulder", "points": [[0, 0], [10, 45]]}]);
    run(&mut s, "motion.study", json!({"name": "Scan", "steps": 10, "keys": keys}));
    let r = run(&mut s, "motion.play", json!({"study": "Scan", "step": 10, "quiet": true}));
    assert_eq!(r["moved"], true, "{r}");
    let unmoved = r["unmoved"].as_array().cloned().unwrap_or_default();
    assert!(unmoved.len() == 1 && unmoved[0]["name"] == "Azimuth" && unmoved[0]["reason"].as_str().is_some_and(|w| w.contains("Pedestal:1")), "{r}");
    // Quiet: only the arm, which moved, has its pose in the answer.
    assert_eq!(r["positions"].as_array().map(|p| p.iter().map(|x| x["occurrence"].clone()).collect::<Vec<_>>()), Some(vec![json!("Arm:1")]), "{r}");
    // Fixed to the chassis, the pedestal is placed and the turret turns.
    run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "Chassis", "b": "Pedestal", "name": "Mount"}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Azimuth", "value": 60}));
    assert!(r["moved"] == true && r.get("reason").is_none() && r.get("unconnected").is_none() && r["dof"].is_array(), "{r}");
    assert!(!near(place(&s, "Turret", corner), start));
    assert_eq!(run(&mut s, "joint.list", json!({}))["floating"], json!([]));
}

/// `quiet: true` leaves the per-occurrence lists out of joint answers, and `moved` says whether
/// a drive moved anything: driving a joint to where it is moves nothing, with no reason given.
#[test]
fn quiet_joint_answers_and_a_drive_to_where_it_is() {
    let mut s = two_cubes();
    let r =
        run(&mut s, "joint.create", json!({"type": "slider", "a": {"face": [5, 5, 10]}, "b": {"face": [25, 5, 0]}, "name": "Rail", "quiet": true}));
    assert!(r.get("dof").is_none() && r.get("fixed").is_none() && r["conflicts"].is_array(), "{r}");
    let r = run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 5, "quiet": true}));
    assert!(r.get("dof").is_none() && r["moved"] == true, "{r}");
    let r = run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 5}));
    assert!(r["dof"].is_array() && r["moved"] == false && r.get("reason").is_none(), "{r}");
    // A suppressed joint with no motion link moves nothing, and says why.
    run(&mut s, "joint.edit", json!({"joint": "Rail", "suppressed": true}));
    let r = run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 8}));
    assert!(r["moved"] == false && r["reason"] == "Rail is suppressed" && r.get("unconnected").is_none(), "{r}");
}

/// An as-built joint takes a name and limits like any other joint.
#[test]
fn as_built_takes_a_name_and_limits() {
    let mut s = two_cubes();
    let r = run(&mut s, "joint.as_built", json!({"type": "slider", "a": "A", "b": "B", "name": "Rail", "limits": [[0, 5]]}));
    assert_eq!(r["name"], "Rail", "{r}");
    let r = run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 20}));
    assert_eq!((&r["values"][0]["value"], &r["values"][0]["limits"]), (&json!(5.0), &json!([0.0, 5.0])), "{r}");
    assert!(near(place(&s, "B", Vec3::new(20.0, 0.0, 0.0)), Vec3::new(20.0, 0.0, 5.0)), "{:?}", place(&s, "B", Vec3::new(20.0, 0.0, 0.0)));
}

/// `value` drives a joint's first value only: the others keep theirs, as with a shorter `values`.
#[test]
fn a_single_value_keeps_the_joints_other_values() {
    let mut s = two_cubes();
    run(&mut s, "joint.as_built", json!({"type": "cylindrical", "a": "A", "b": "B", "name": "Spindle"}));
    run(&mut s, "joint.drive", json!({"joint": "Spindle", "values": [30, 5]}));
    let at = |r: &Value| [0, 1].map(|i| r["values"][i]["value"].as_f64().unwrap_or(f64::NAN));
    let r = run(&mut s, "joint.drive", json!({"joint": "Spindle", "value": 45}));
    assert!((at(&r)[0] - 45.0).abs() < 1e-9 && (at(&r)[1] - 5.0).abs() < 1e-9, "{r}");
    let r = run(&mut s, "joint.drive", json!({"joint": "Spindle", "values": [60]}));
    assert!((at(&r)[0] - 60.0).abs() < 1e-9 && (at(&r)[1] - 5.0).abs() < 1e-9, "{r}");
}

/// A motion link's offset is in the linked value's units, like joint values and limits: degrees
/// for an angle, mm for a distance, or an expression. `joint.list` answers it the same way, it is
/// stored in radians as before, and a saved link opens with the offset it had.
#[test]
fn a_link_offset_is_in_the_linked_values_units() {
    let mut s = Session::default();
    for (name, x) in [("Ground", 0.0), ("Dial", 80.0), ("Gear", 100.0), ("Car", 120.0), ("Cart", 140.0)] {
        part(&mut s, name, [x, 0.0, -5.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    for (kind, name, x) in [("revolute", "Dial", 80.0), ("revolute", "Gear", 100.0), ("slider", "Car", 120.0), ("slider", "Cart", 140.0)] {
        pin(&mut s, kind, name, "Ground", name, Vec3::new(x, 0.0, 0.0), Vec3::Z);
    }
    run(&mut s, "joint.motion_link", json!({"a": "Dial", "b": "Gear", "ratio": 1, "offset": 10}));
    run(&mut s, "joint.motion_link", json!({"a": "Car", "b": "Cart", "ratio": 1, "offset": "5 mm"}));
    run(&mut s, "joint.drive", json!({"joint": "Dial", "value": 20}));
    run(&mut s, "joint.drive", json!({"joint": "Car", "value": 3}));
    let value = |l: &Value, name: &str| {
        l["joints"].as_array().into_iter().flatten().find(|j| j["name"] == name).and_then(|j| j["values"][0]["value"].as_f64()).unwrap_or(f64::NAN)
    };
    let l = run(&mut s, "joint.list", json!({}));
    assert!((value(&l, "Gear") - 30.0).abs() < 1e-9 && (value(&l, "Cart") - 8.0).abs() < 1e-9, "{l}");
    let links: Vec<(f64, &str)> =
        l["links"].as_array().into_iter().flatten().map(|k| (k["offset"].as_f64().unwrap_or(f64::NAN), k["unit"].as_str().unwrap_or(""))).collect();
    assert!(
        links.len() == 2 && (links[0].0 - 10.0).abs() < 1e-9 && links[0].1 == "deg" && (links[1].0 - 5.0).abs() < 1e-9 && links[1].1 == "mm",
        "{l}"
    );
    assert!((s.doc.assembly.links[0].offset - 10f64.to_radians()).abs() < 1e-12);
    // A design saved before offsets took degrees stored 0.1 rad, and opens turning Gear 5.73° past Dial.
    s.doc_mut().assembly.links[0].offset = 0.1;
    let (dir, path) = temp_design("link-offset", "solidcraft");
    run(&mut s, "file.save", json!({"path": path}));
    run(&mut s, "file.new", json!({}));
    run(&mut s, "doc.open", json!({"path": path}));
    let l = run(&mut s, "joint.list", json!({}));
    assert!((value(&l, "Gear") - value(&l, "Dial") - 0.1f64.to_degrees()).abs() < 1e-9, "{l}");
    let _ = std::fs::remove_dir_all(&dir);
}

/// A link between an angle and a distance takes its ratio in b's units per a's, like its offset:
/// a pinion moves its rack 0.5 mm per degree, and a car turns its dial 2 degrees per mm.
/// `joint.list` answers the ratios the same way; they are stored per radian, as before.
#[test]
fn a_link_ratio_between_an_angle_and_a_distance_is_per_degree() {
    let mut s = Session::default();
    for (name, x) in [("Ground", 0.0), ("Pinion", 80.0), ("Rack", 100.0), ("Car", 120.0), ("Dial", 140.0)] {
        part(&mut s, name, [x, 0.0, -5.0]);
    }
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    for (kind, name, x) in [("revolute", "Pinion", 80.0), ("slider", "Rack", 100.0), ("slider", "Car", 120.0), ("revolute", "Dial", 140.0)] {
        pin(&mut s, kind, name, "Ground", name, Vec3::new(x, 0.0, 0.0), Vec3::Z);
    }
    run(&mut s, "joint.motion_link", json!({"a": "Pinion", "b": "Rack", "ratio": 0.5}));
    run(&mut s, "joint.motion_link", json!({"a": "Car", "b": "Dial", "ratio": 2}));
    run(&mut s, "joint.drive", json!({"joint": "Pinion", "value": 20}));
    run(&mut s, "joint.drive", json!({"joint": "Car", "value": 3}));
    let l = run(&mut s, "joint.list", json!({}));
    let value = |name: &str| {
        l["joints"].as_array().into_iter().flatten().find(|j| j["name"] == name).and_then(|j| j["values"][0]["value"].as_f64()).unwrap_or(f64::NAN)
    };
    assert!((value("Rack") - 10.0).abs() < 1e-9 && (value("Dial") - 6.0).abs() < 1e-9, "{l}");
    let ratios: Vec<f64> = l["links"].as_array().into_iter().flatten().map(|k| k["ratio"].as_f64().unwrap_or(f64::NAN)).collect();
    assert!(ratios.len() == 2 && (ratios[0] - 0.5).abs() < 1e-9 && (ratios[1] - 2.0).abs() < 1e-9, "{l}");
    let stored: Vec<f64> = s.doc.assembly.links.iter().map(|k| k.ratio).collect();
    assert!((stored[0] - 0.5f64 / 1f64.to_radians()).abs() < 1e-9 && (stored[1] - 2f64.to_radians()).abs() < 1e-12, "{stored:?}");
}

/// A new joint starts at its values inside its limits. Limits that leave out 0 (or the values
/// given) start it at the nearer limit, which it keeps, and the answer says the part moved there.
#[test]
fn a_new_joint_starts_inside_its_limits_and_says_so() {
    let mut s = two_cubes();
    let r = run(&mut s, "joint.as_built", json!({"type": "slider", "a": "A", "b": "B", "name": "Rail", "limits": [[2, 5]]}));
    let w = r["warnings"].as_array().cloned().unwrap_or_default();
    assert!(
        w.len() == 1 && w[0].as_str().is_some_and(|w| w.starts_with("Rail distance starts at 2 mm, inside its limits [2, 5], not at 0 mm")),
        "{r}"
    );
    assert!(near(place(&s, "B", Vec3::new(20.0, 0.0, 0.0)), Vec3::new(20.0, 0.0, 2.0)), "{:?}", place(&s, "B", Vec3::new(20.0, 0.0, 0.0)));
    assert_eq!(s.doc.assembly.joints[0].values, [2.0]);
    // Values given outside the limits start at the nearer one too; angles are answered in degrees.
    let mut s = two_cubes();
    let r = run(
        &mut s,
        "joint.create",
        json!({"type": "revolute", "a": {"face": [5, 5, 10]}, "b": {"face": [25, 5, 0]}, "values": [90], "limits": [[0, 60]], "name": "Hinge"}),
    );
    let w = r["warnings"].as_array().cloned().unwrap_or_default();
    assert!(w.len() == 1 && w[0].as_str().is_some_and(|w| w.contains("starts at 60 deg") && w.contains("not at 90 deg")), "{r}");
    // Inside the limits, nothing to say.
    let mut s = two_cubes();
    let r = run(&mut s, "joint.as_built", json!({"type": "cylindrical", "a": "A", "b": "B", "name": "Spindle", "limits": [[-30, 30], [0, 5]]}));
    assert!(r.get("warnings").is_none(), "{r}");
}

/// The trace's points as world points.
fn traced(r: &Value) -> Vec<Vec3> {
    r["points"].as_array().into_iter().flatten().filter_map(crate::params::vec3).collect()
}

/// A point rigidly carried from segment (a0, b0) to segment (a, b) in the XY plane.
fn carried(p0: Vec3, a0: Vec3, b0: Vec3, a: Vec3, b: Vec3) -> Vec3 {
    let turn = (b.y - a.y).atan2(b.x - a.x) - (b0.y - a0.y).atan2(b0.x - a0.x);
    let d = p0 - a0;
    a + Vec3::new(d.x * turn.cos() - d.y * turn.sin(), d.x * turn.sin() + d.y * turn.cos(), d.z)
}

/// A point on the four-bar's coupler, 10 mm off the line between its pins, traces the coupler
/// curve: the crank pin on its circle, the rocker pin where the coupler and rocker circles meet
/// (on the open branch), and the point carried with the pins. A motion study turning the crank
/// traces the same curve, and the design is left as it was.
#[test]
fn four_bar_coupler_point_traces_its_closed_form_curve() {
    let (mut s, p0, q0) = four_bar();
    let d = (q0 - p0) * (1.0 / q0.dist(p0));
    let c0 = (p0 + q0) * 0.5 + Vec3::new(-d.y, d.x, 0.0) * 10.0;
    let before = s.doc.clone();
    let p = json!({"occurrence": "Coupler", "point": [c0.x, c0.y, c0.z], "joint": "Crank", "from": 0, "to": 360, "samples": 73});
    let r = run(&mut s, "motion.trace", p);
    assert_eq!(*s.doc, *before, "a trace leaves the design as it was");
    assert!(r["stopped_at"].is_null() && r["samples"] == 73, "{r}");
    let pts = traced(&r);
    assert_eq!(pts.len(), 73);
    let mut q = q0;
    for (k, got) in pts.iter().enumerate() {
        let v = 5.0 * k as f64;
        if k > 0 {
            q = rocker_pin(v - 5.0, v, q);
        }
        let th = (90.0 + v).to_radians();
        let want = carried(c0, p0, q0, Vec3::new(20.0 * th.cos(), 20.0 * th.sin(), 0.0), q);
        assert!(near(*got, want), "{v}°: {got:?} wants {want:?}");
    }
    assert!(pts.first().zip(pts.last()).is_some_and(|(a, b)| near(*a, *b)), "a full turn closes the curve");
    run(&mut s, "motion.study", json!({"name": "Turn", "steps": 72, "keys": [{"joint": "Crank", "points": [[0, 0], [72, 360]]}]}));
    let r = run(&mut s, "motion.trace", json!({"occurrence": "Coupler", "point": [c0.x, c0.y, c0.z], "study": "Turn"}));
    let from_study = traced(&r);
    assert_eq!(from_study.len(), 73, "{r}");
    assert!(from_study.iter().zip(&pts).all(|(a, b)| near(*a, *b)), "{r}");
}

/// The middle of a slider-crank's rod: halfway between the crank pin on its circle and the wrist
/// pin at a·cos θ + √(b² − (a·sin θ)²).
#[test]
fn slider_crank_rod_traces_its_closed_form_curve() {
    let (mut s, p0, s0) = slider_crank();
    let m0 = (p0 + s0) * 0.5;
    let r =
        run(&mut s, "motion.trace", json!({"occurrence": "Rod", "point": [m0.x, m0.y, m0.z], "joint": "Crank", "from": 0, "to": 360, "samples": 37}));
    let pts = traced(&r);
    assert_eq!(pts.len(), 37, "{r}");
    for (k, got) in pts.iter().enumerate() {
        let th = (90.0 + 10.0 * k as f64).to_radians();
        let x = 15.0 * th.cos() + (40.0f64.powi(2) - (15.0 * th.sin()).powi(2)).sqrt();
        let want = (Vec3::new(15.0 * th.cos(), 15.0 * th.sin(), 0.0) + Vec3::new(x, 0.0, 0.0)) * 0.5;
        assert!(near(*got, want), "{}°: {got:?} wants {want:?}", 10 * k);
    }
}

/// Driving the rocker past its swing stops where the loop can't close: the trace ends there.
#[test]
fn a_trace_ends_where_the_loop_stops_the_motion() {
    let (mut s, _, q0) = four_bar();
    let start = q0.y.atan2(q0.x - 45.0).to_degrees();
    let r = run(
        &mut s,
        "motion.trace",
        json!({"occurrence": "Rocker", "point": [q0.x, q0.y, q0.z], "joint": "Rocker", "from": 0, "to": 100, "samples": 21}),
    );
    assert!(r["stopped_by_loop"].is_object(), "{r}");
    let k = r["stopped_at"].as_u64().unwrap_or(u64::MAX) as usize;
    let pts = traced(&r);
    assert!(k > 0 && k < 20 && pts.len() == k + 1 && r["samples"] == k + 1, "{r}");
    let angle = |p: &Vec3| p.y.atan2(p.x - 45.0).to_degrees();
    for (i, p) in pts.iter().take(k).enumerate() {
        assert!((angle(p) - (start + 5.0 * i as f64)).abs() < 1e-6, "sample {i}: {}", angle(p));
    }
    let limit = ((900.0f64 - 3625.0) / 3600.0).acos().to_degrees();
    let last = pts.last().map(angle).unwrap_or(f64::NAN);
    assert!(last > limit - 5.0 && last <= limit + 1e-9, "stopped at {last}°, the limit is {limit}°");
}

/// Keep makes a 3D sketch spline through the trace, in one undo step.
#[test]
fn a_kept_trace_is_a_3d_sketch_spline() {
    let (mut s, p0, q0) = four_bar();
    let c0 = (p0 + q0) * 0.5;
    let p = json!({"occurrence": "Coupler", "point": [c0.x, c0.y, c0.z], "joint": "Crank", "from": 0, "to": 180, "samples": 19});
    let pts = traced(&run(&mut s, "motion.trace", p.clone()));
    let features = s.doc.features.len();
    let r = run(&mut s, "motion.trace.keep", p);
    assert_eq!((r["name"].as_str(), r["points"].as_u64()), (Some("Motion Trace1"), Some(19)), "{r}");
    assert!(s.active_sketch.is_none(), "the sketch is left");
    let id = r["sketch"].as_u64().unwrap_or(0);
    let sk = s.doc.sketch(id).cloned().unwrap_or_default();
    assert!(sk.view.three_d && sk.wires.len() == 1, "{r}");
    let fit = sk.wires.first().map(|w| w.fit.clone()).unwrap_or_default();
    assert!(fit.len() == pts.len() && fit.iter().zip(&pts).all(|(a, b)| a.dist(*b) < 1e-9), "{fit:?}");
    let again = json!({"occurrence": "Coupler", "point": [0, 0, 0], "joint": "Crank", "from": 0, "to": 90});
    assert_eq!(run(&mut s, "motion.trace.keep", again)["name"], "Motion Trace2");
    run(&mut s, "edit.undo", json!({}));
    run(&mut s, "edit.undo", json!({}));
    assert_eq!(s.doc.features.len(), features);
    // A point on the ground does not move: there is nothing to keep.
    let e = s.execute("motion.trace.keep", &json!({"occurrence": "Ground", "point": [0, 0, 0], "joint": "Crank", "from": 0, "to": 90})).unwrap_err();
    assert!(e.to_string().contains("does not move"), "{e}");
}

/// A full turn kept closes exactly on its start, also when the sample before the end lies a hair
/// from it (a study keyed to 359.99999° one step before 360°).
#[test]
fn a_kept_full_turn_closes_on_its_start() {
    let mut s = Session::default();
    part(&mut s, "Ground", [-1.0, -1.0, -5.0]);
    part(&mut s, "Arm", [0.0, -1.0, 0.0]);
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    pin(&mut s, "revolute", "Pivot", "Ground", "Arm", Vec3::ZERO, Vec3::Z);
    run(&mut s, "motion.study", json!({"name": "Turn", "steps": 5, "keys": [{"joint": "Pivot", "points": [[0, 0], [4, 359.99999], [5, 360]]}]}));
    let r = run(&mut s, "motion.trace.keep", json!({"occurrence": "Arm", "point": [1, 0, 0], "study": "Turn"}));
    let id = r["sketch"].as_u64().unwrap_or(0);
    let fit = s.doc.sketch(id).ok().and_then(|sk| sk.wires.first().map(|w| w.fit.clone())).unwrap_or_default();
    assert_eq!(fit.len(), 5, "{fit:?}");
    assert_eq!(fit.first(), fit.last(), "{fit:?}");
}

/// Kept while a component is active and shown moved (a move not captured yet): the spline goes
/// in the root, where no joint moves it, through the traced points; the component stays active.
#[test]
fn a_trace_kept_in_a_moved_component_stays_on_the_path() {
    let (mut s, p0, q0) = four_bar();
    let crank = occ(&s, "Crank");
    let c0 = (p0 + q0) * 0.5;
    let p = json!({"occurrence": "Coupler", "point": [c0.x, c0.y, c0.z], "joint": "Crank", "from": 0, "to": 90, "samples": 4});
    let pts = traced(&run(&mut s, "motion.trace", p.clone()));
    run(&mut s, "component.activate", json!({"component": "Crank", "occurrence": crank, "path": [crank]}));
    run(&mut s, "occurrence.move", json!({"occurrence": crank, "translate": [0, 0, 100], "capture": false}));
    let active = (s.active_component, s.active_occurrence_path.clone());
    let r = run(&mut s, "motion.trace.keep", p);
    assert_eq!((s.active_component, s.active_occurrence_path.clone()), active);
    let id = r["sketch"].as_u64().unwrap_or(0);
    assert_eq!(s.doc.feature(id).map(|f| f.component), Some(0), "{r}");
    let fit = s.doc.sketch(id).ok().and_then(|sk| sk.wires.first().map(|w| w.fit.clone())).unwrap_or_default();
    assert!(fit.len() == pts.len() && fit.iter().zip(&pts).all(|(a, b)| near(*a, *b)), "{fit:?} wants {pts:?}");
}

/// A part inside a sub-assembly placed twice: the occurrence path picks the instance traced. The
/// second Arm turns about its pivot and its Tip goes round; the first Arm, and so the Tip at its
/// first placement, stays put.
#[test]
fn a_trace_follows_the_instance_its_path_names() {
    let mut s = Session::default();
    part(&mut s, "Ground", [-1.0, -1.0, -5.0]);
    let g = occ(&s, "Ground");
    run(&mut s, "occurrence.ground", json!({"occurrence": g, "grounded": true}));
    run(&mut s, "component.activate", json!({"component": "root"}));
    let arm = run(&mut s, "component.create", json!({"name": "Arm"}));
    run(&mut s, "component.create", json!({"name": "Tip"}));
    run(&mut s, "solid.box", json!({"length": 2, "width": 2, "height": 2, "corner": [10, 0, 0]}));
    run(&mut s, "component.activate", json!({"component": "root"}));
    let second = run(&mut s, "occurrence.copy", json!({"component": arm["component"], "translate": [0, 50, 0]}))["occurrence"].as_u64().unwrap_or(0);
    let at = |o: Value| json!({"occurrence": o, "point": [0, 50, 0], "z": [0, 0, 1]});
    run(&mut s, "joint.create", json!({"type": "revolute", "a": at(json!(g)), "b": at(json!(second)), "flip": true, "name": "Pivot"}));
    let tip = occ(&s, "Tip");
    let trace = |s: &mut Session, o: Value| {
        traced(&run(s, "motion.trace", json!({"occurrence": o, "point": [11, 51, 1], "joint": "Pivot", "from": 0, "to": 90, "samples": 3})))
    };
    let turned = trace(&mut s, json!([second, tip]));
    let pivot = Vec3::new(0.0, 50.0, 1.0);
    assert!(turned.iter().all(|p| (p.dist(pivot) - 122f64.sqrt()).abs() < 1e-6), "{turned:?}");
    assert!(turned.first().zip(turned.last()).is_some_and(|(a, b)| (a.dist(*b) - 244f64.sqrt()).abs() < 1e-6), "a quarter turn: {turned:?}");
    let first = trace(&mut s, json!(tip));
    assert!(first.iter().all(|p| p.dist(Vec3::new(11.0, 51.0, 1.0)) < 1e-9), "{first:?}");
    assert!(s.execute("motion.trace", &json!({"occurrence": [tip, second], "point": [0, 0, 0], "joint": "Pivot", "from": 0, "to": 90})).is_err());
    assert!(s.execute("motion.trace", &json!({"occurrence": vec![second; 65], "point": [0, 0, 0], "joint": "Pivot", "from": 0, "to": 90})).is_err());
}

/// Trace params come from scripts and the control channel: bad ones are refused, never a panic.
#[test]
fn hostile_trace_params_are_refused() {
    let (mut s, _, _) = four_bar();
    run(&mut s, "motion.study", json!({"name": "Turn", "steps": 4, "keys": [{"joint": "Crank", "points": [[0, 0], [4, 90]]}]}));
    let base = json!({"occurrence": "Coupler", "point": [0, 0, 0], "joint": "Crank", "from": 0, "to": 90});
    let with = |k: &str, v: Value| {
        let mut p = base.clone();
        p[k] = v;
        p
    };
    let without = |k: &str| {
        let mut p = base.clone();
        p.as_object_mut().map(|o| o.remove(k));
        p
    };
    for p in [
        with("samples", json!(0)),
        with("samples", json!(1)),
        with("samples", json!(501)),
        with("samples", json!(1e300)),
        with("samples", json!(-3)),
        with("samples", json!("many")),
        with("point", json!([f64::MAX, 0, 0])),
        with("point", json!([0, 0])),
        with("point", json!("here")),
        without("point"),
        with("occurrence", json!("Nowhere")),
        without("occurrence"),
        with("joint", json!("Nowhere")),
        with("index", json!(1)),
        with("index", json!(-1)),
        with("from", json!("nonsense +")),
        with("to", json!(1e300)),
        without("from"),
        without("to"),
        with("study", json!("Turn")),
        with("study", json!(null)),
        without("joint"),
    ] {
        for cmd in ["motion.trace", "motion.trace.keep"] {
            assert!(s.execute(cmd, &p).is_err(), "{cmd} {p}");
        }
    }
    run(&mut s, "joint.as_built", json!({"type": "rigid", "a": "Ground", "b": "Crank", "name": "Lock"}));
    assert!(s.execute("motion.trace", &with("joint", json!("Lock"))).is_err(), "a rigid joint does not move");
}

#[path = "joints_coupling_tests.rs"]
mod coupling;

#[path = "joints_cam_tests.rs"]
mod cam;