Loft: surfaces follow sections by distance along them (#1084)

Loft faces between sections are spaced by chord length instead of by parameter, so uneven sections no longer twist the surface. Fixes #968.

crates/engine/src/tests.rs

@@ -279,6 +279,7 @@ mod boolean_diagnostics;
 mod component_frames;
 mod large_step_import;
 mod loft_cut;
+mod loft_spacing;
 mod mirror_planes;
 mod path_scope;
 mod primitive_points;

crates/engine/src/tests/loft_spacing.rs

@@ -0,0 +1,77 @@
+//! Lofted round tubes through sections that are not evenly spaced.
+//!
+//! A loft's surface used to pass through its sections at uniform parameters, so a section close to
+//! its neighbour (a bore that runs 5 mm past the end of a tube whose other sections are 12 mm
+//! apart, or 60 mm in a snail) made the surface overshoot between the others, by several times the
+//! tube's radius. The overshoot also made booleans with the tube fail for some section counts and
+//! not for their neighbours.
+
+use std::f64::consts::PI;
+
+use super::*;
+
+/// `sections` circles of radius `radius` centred on an arc of radius `path` turning `angle`
+/// (radians), in planes normal to the arc, lofted into the body `body`; `over` extends the
+/// sections past both ends along the tangent.
+fn tube(s: &mut Session, body: &str, radius: f64, path: f64, angle: f64, sections: usize, over: f64) {
+    let mut stations: Vec<[f64; 4]> = (0..sections)
+        .map(|i| {
+            let t = angle * i as f64 / (sections - 1) as f64;
+            [path * t.cos(), path * t.sin(), -t.sin(), t.cos()]
+        })
+        .collect();
+    if over > 0.0 {
+        let (a, b) = (stations[0], stations[sections - 1]);
+        stations.insert(0, [a[0] - over * a[2], a[1] - over * a[3], a[2], a[3]]);
+        stations.push([b[0] + over * b[2], b[1] + over * b[3], b[2], b[3]]);
+    }
+    let mut list = Vec::new();
+    for (i, [x, y, tx, ty]) in stations.iter().enumerate() {
+        let name = format!("{body}{i}");
+        run(s, "sketch.create", json!({"plane": {"origin": [x, y, 0], "x_dir": [0, 0, 1], "y_dir": [ty, -tx, 0]}, "name": name}));
+        run(s, "sketch.circle.center", json!({"center": [0, 0], "radius": radius}));
+        run(s, "sketch.finish", json!({}));
+        list.push(json!({"sketch": name}));
+    }
+    run(s, "solid.loft", json!({"sections": list, "operation": "new", "name": format!("Loft{body}"), "body_name": body}));
+}
+
+fn bounds(s: &mut Session, body: &str) -> ([f64; 3], [f64; 3]) {
+    let m = run(s, "inspect.measure", json!({}));
+    let b = m["bodies"].as_array().unwrap().iter().find(|b| b["name"] == body).unwrap();
+    let get = |k: &str| -> [f64; 3] {
+        let v = b["bbox"][k].as_array().unwrap();
+        [v[0].as_f64().unwrap(), v[1].as_f64().unwrap(), v[2].as_f64().unwrap()]
+    };
+    (get("min"), get("max"))
+}
+
+#[test]
+fn a_bore_with_a_short_overrun_stays_inside_its_tube() {
+    // 14 sections 12 mm apart, and one more 5 mm beyond each end: the bore is a tube of radius 18
+    // around the arc (z within 18 of the arc's plane), and used to reach z = 88.
+    let mut s = Session::default();
+    tube(&mut s, "Bore", 18.0, 100.0, PI / 2.0, 14, 5.0);
+    let (lo, hi) = bounds(&mut s, "Bore");
+    assert!(hi[2] < 18.0 + 0.1 && lo[2] > -18.0 - 0.1, "z from {} to {}", lo[2], hi[2]);
+    let want = PI * 18.0 * 18.0 * (100.0 * PI / 2.0 + 10.0);
+    let got = volume(&mut s);
+    assert!(rel(got, want) < 2e-3, "{got} vs {want}");
+}
+
+#[test]
+fn a_hollow_elbow_is_cut_for_any_number_of_sections() {
+    let (path, outer, inner) = (100.0, 30.0, 18.0);
+    // Each of these gave "no result" (the first six) or failed in another way.
+    for (degrees, sections) in [(60.0, 5), (60.0, 7), (90.0, 10), (90.0, 14), (120.0, 7), (120.0, 13)] {
+        let angle = degrees * PI / 180.0;
+        let mut s = Session::default();
+        tube(&mut s, "Outer", outer, path, angle, sections, 0.0);
+        tube(&mut s, "Inner", inner, path, angle, sections, 5.0);
+        run(&mut s, "solid.combine", json!({"target": "Outer", "tools": ["Inner"], "operation": "cut", "name": "Hollow"}));
+        assert_eq!(s.model.state().bodies.len(), 1, "{degrees} degrees, {sections} sections");
+        let want = PI * (outer * outer - inner * inner) * path * angle;
+        let got = volume(&mut s);
+        assert!(rel(got, want) < 3e-3, "{degrees} degrees, {sections} sections: {got} vs {want}");
+    }
+}

crates/kernel/src/build.rs

@@ -1398,18 +1398,52 @@ pub(crate) fn ruled_loft_faces(wires: &[mt::Wire], edge_sources: &[Vec<Vec<usize
     Ok(sides)
 }
 
-/// Points across the sections (one per section, in order) as a smooth B-spline: cubic through
-/// four or more, quadratic through three.
-fn across(pts: &[Vec3]) -> Option<mt::BSplineCurve<mt::Point3>> {
+/// Points across the sections (one per section, in order) as a smooth B-spline through them at the
+/// parameters `u` (rising from 0 to 1, one per section): cubic through four or more, quadratic
+/// through three.
+fn across(pts: &[Vec3], u: &[f64]) -> Option<mt::BSplineCurve<mt::Point3>> {
     match pts {
         [a, b, c] => {
-            let m = *b * 2.0 - (*a + *c) * 0.5;
+            // The quadratic Bezier through `b` at t = u[1].
+            let t = *u.get(1)?;
+            if !(t > 0.0 && t < 1.0) {
+                return None;
+            }
+            let m = (*b - *a * ((1.0 - t) * (1.0 - t)) - *c * (t * t)) * (1.0 / (2.0 * t * (1.0 - t)));
             mt::BSplineCurve::try_new(mt::KnotVec::bezier_knot(2), vec![p3(*a), p3(m), p3(*c)]).ok()
         }
-        _ => interpolate_cubic(pts),
+        _ => interpolate_cubic_at(pts, u),
     }
 }
 
+/// The parameters of the sections along a loft: in proportion to the distance between them (the
+/// mean over the wires' vertices), so that unevenly spaced sections get a surface that follows
+/// them. At a uniform parameter a section close to its neighbour makes the surface overshoot
+/// between the others (by several times the section's size when the spacing differs tenfold).
+/// Evenly spaced sections give the uniform parameters.
+fn section_parameters(edges: &[Vec<mt::Edge>]) -> Vec<f64> {
+    let m = edges.len();
+    let uniform = || (0..m).map(|i| i as f64 / (m.max(2) - 1) as f64).collect::<Vec<f64>>();
+    let corners: Vec<Vec<Vec3>> = edges.iter().map(|es| es.iter().map(|e| from_p3(e.front().point())).collect()).collect();
+    let mut u = vec![0.0];
+    for w in corners.windows(2) {
+        let (Some(a), Some(b)) = (w.first(), w.get(1)) else { return uniform() };
+        let n = a.len().min(b.len());
+        if n == 0 {
+            return uniform();
+        }
+        let step = a.iter().zip(b).map(|(p, q)| p.dist(*q)).sum::<f64>() / n as f64;
+        u.push(u.last().copied().unwrap_or(0.0) + step);
+    }
+    let Some(total) = u.last().copied().filter(|t| t.is_finite() && *t > 0.0) else { return uniform() };
+    let u: Vec<f64> = u.iter().map(|x| x / total).collect();
+    // A section on top of its neighbour: no parameter for it, so the uniform ones.
+    if u.windows(2).any(|w| w.get(1).zip(w.first()).is_none_or(|(b, a)| b - a < 1e-6)) {
+        return uniform();
+    }
+    u
+}
+
 /// A loft whose side faces are B-spline surfaces through every section (smooth across the
 /// middle sections, which leave no edges). Every section wire comes from `uniform_wire`, so the
 /// k-th edges of all sections share one knot vector and their control points pair up. Face k
@@ -1432,6 +1466,7 @@ pub(crate) fn smooth_loft_faces(wires: &[mt::Wire], numbers: &[Vec<Vec<usize>>],
         }
     };
     let (Some(first), Some(last)) = (edges.first(), edges.last()) else { return Err(fail("sections")) };
+    let along = section_parameters(&edges);
     // Seams: through the k-th vertex of every section (an open wire's last one at the end of
     // its last edge).
     let vertex = |e: &mt::Edge, end: bool| if end { e.back().clone() } else { e.front().clone() };
@@ -1440,7 +1475,7 @@ pub(crate) fn smooth_loft_faces(wires: &[mt::Wire], numbers: &[Vec<Vec<usize>>],
     for k in 0..seam_count {
         let (at, end) = if k < n { (k, false) } else { (n - 1, true) };
         let pts: Vec<Vec3> = edges.iter().filter_map(|es| es.get(at).map(|e| from_p3(vertex(e, end).point()))).collect();
-        let c = across(&pts).ok_or_else(|| fail("seam"))?;
+        let c = across(&pts, &along).ok_or_else(|| fail("seam"))?;
         let (Some(a), Some(b)) = (first.get(at), last.get(at)) else { return Err(fail("seam")) };
         seams.push(mt::Edge::new(&vertex(a, end), &vertex(b, end), mt::Curve::BSplineCurve(c)));
     }
@@ -1458,7 +1493,7 @@ pub(crate) fn smooth_loft_faces(wires: &[mt::Wire], numbers: &[Vec<Vec<usize>>],
         let mut vk = None;
         for j in 0..m {
             let pts: Vec<Vec3> = curves.iter().filter_map(|c| c.control_points().get(j).map(|p| from_p3(*p))).collect();
-            let c = across(&pts).ok_or_else(|| fail("surface"))?;
+            let c = across(&pts, &along).ok_or_else(|| fail("surface"))?;
             vk = Some(c.knot_vec().clone());
             ctrl.push(c.control_points().clone());
         }