Variable-radius fillets through middle points: radii at positions along the edge, straight or smooth between

kernel::fillet_variable_points(body, edge, start, [(position, radius)...], smooth): the radius law is a B-spline of the edge parameter (straight pieces, or C1 cubic pieces with Catmull-Rom slopes), and since every section's arc is affine in its radius the blend is exactly a rational B-spline (degree 2 across, the law's degree along) with B-spline contact curves on the faces. The largest radius along the edge decides whether the blend fits. Fillet type variable takes mid: [[position, radius expr], ...] and smooth; middle radii are parameters of the feature (Mid radius) and follow user parameters. Tests: straight pieces against (1 - pi/4) L (a^2 + ab + b^2) / 3 per piece, smooth against the integrated law, either end as start, refusals; engine test with a parameter-driven middle radius.

Refs #9

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01RjGw4gA5ZvKrU8MQP6sBgT

crates/engine/src/cmd/features.rs

@@ -31,7 +31,7 @@ pub static COMMANDS: &[CommandSpec] = &[
         .at("SOLID", "MODIFY")
         .icon("fillet")
         .key("F")
-        .params("edges: [[x,y,z] point on edge | {body, index}]; radius: expr; body?; type?: constant|chord (radius is the width across)|variable (radius at the end nearest start, radius2 at the other); radius2?; start?: [x,y,z]"),
+        .params("edges: [[x,y,z] point on edge | {body, index}]; radius: expr; body?; type?: constant|chord (radius is the width across)|variable (radius at the end nearest start, radius2 at the other); radius2?; start?: [x,y,z]; mid?: [[position 0…1 from start, radius expr], …] (variable radii between the ends); smooth?: bool (smooth instead of straight between the radii)"),
     CommandSpec::new("solid.chamfer", "Chamfer", chamfer).at("SOLID", "MODIFY").icon("chamfer").params("edges: [[x,y,z] | {body, index}]; distance: expr; distance2?: expr (along the second face) | angle?: expr (from the first face); flip?: bool (which face is first: by default the one facing up most); body?"),
     CommandSpec::new("solid.combine", "Combine", combine).at("SOLID", "MODIFY").icon("combine").params("target: body; tools: [body]; operation?: join|cut|intersect; keep_tools?: bool; new_component?: bool (the result goes into a new component; component_name?)"),
     CommandSpec::new("solid.pattern.rectangular", "Rectangular Pattern", pattern_rect)
@@ -604,7 +604,24 @@ fn fillet(s: &mut Session, p: &Value) -> Result<Value> {
             check_expr(s, &radius2, Kind::Length, cmd, "radius2")?;
             let start =
                 p.get("start").and_then(vec3).ok_or_else(|| bad(cmd, "a variable fillet needs `start`: [x,y,z] near the end that takes `radius`"))?;
-            solvecraft_doc::FilletStyle::Variable { radius2, start }
+            let mut mid = Vec::new();
+            for m in p.get("mid").and_then(Value::as_array).into_iter().flatten().take(100) {
+                let (Some(t), Some(r)) = (m.get(0).and_then(Value::as_f64), m.get(1)) else {
+                    return Err(bad(cmd, "`mid` entries are [position, radius]"));
+                };
+                if !(t.is_finite() && t > 0.0 && t < 1.0) {
+                    return Err(bad(cmd, "`mid` positions lie between 0 and 1 (from the start end)"));
+                }
+                let r = match r {
+                    Value::String(x) => x.clone(),
+                    Value::Number(n) => n.to_string(),
+                    _ => return Err(bad(cmd, "a `mid` radius is a number or an expression")),
+                };
+                check_expr(s, &r, Kind::Length, cmd, "mid radius")?;
+                mid.push((t, r));
+            }
+            let smooth = p.get("smooth").and_then(Value::as_bool).unwrap_or(false);
+            solvecraft_doc::FilletStyle::Variable { radius2, start, mid, smooth }
         }
         Some(o) => return Err(bad(cmd, format!("unknown fillet type `{o}` (constant, chord or variable)"))),
     };

crates/engine/src/tests.rs

@@ -1069,6 +1069,29 @@ fn chord_and_variable_fillets() {
     let removed = (1.0 - PI / 4.0) * 20.0 * (4.0 + 10.0 + 25.0) / 3.0;
     assert!(rel(v, 6000.0 - removed) < 1e-4, "{v}");
     assert!(s.execute("solid.fillet", &json!({"edges": [[10, 10, 30]], "radius": 2, "type": "variable"})).is_err());
+    // A radius through a middle point (a user parameter), straight between: 2 → 4 → 2.
+    let mut s = Session::default();
+    run(&mut s, "solid.box", json!({"length": 10, "width": 20, "height": 30, "body_name": "B"}));
+    run(&mut s, "parameters.add", json!({"name": "waist", "expression": "4 mm"}));
+    run(
+        &mut s,
+        "solid.fillet",
+        json!({"edges": [[10, 10, 30]], "radius": 2, "type": "variable", "radius2": 2, "start": [10, 0, 30], "mid": [[0.5, "waist"]]}),
+    );
+    let vol = |s: &Session| solvecraft_kernel::measure(&s.world_state().body("B").unwrap().body).unwrap().volume;
+    let removed = 2.0 * (1.0 - PI / 4.0) * 10.0 * (4.0 + 8.0 + 16.0) / 3.0;
+    assert!(rel(vol(&s), 6000.0 - removed) < 1e-4, "{}", vol(&s));
+    // The middle radius follows its parameter.
+    run(&mut s, "parameters.change", json!({"name": "waist", "expression": "3 mm"}));
+    let removed = 2.0 * (1.0 - PI / 4.0) * 10.0 * (4.0 + 6.0 + 9.0) / 3.0;
+    assert!(rel(vol(&s), 6000.0 - removed) < 1e-4, "{}", vol(&s));
+    assert!(
+        s.execute(
+            "solid.fillet",
+            &json!({"edges": [[10, 10, 30]], "radius": 2, "type": "variable", "radius2": 2, "start": [10, 0, 30], "mid": [[1.5, 3]]})
+        )
+        .is_err()
+    );
 }
 
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