diff --git a/ROADMAP.md b/ROADMAP.md
index ab001dbd..ad930f54 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -67,6 +67,9 @@ headline counts in-scope tabs only and lists the deferred ones separately.
   Type a value and press Enter to commit one undo step; rejected values remain editable and
   cancellation leaves the sketch unchanged. Fit keeps geometry clear of the Sketch Palette
   and navigation controls, including enlarged displays and nested pending placements.
+- Curvature and Polygon constraints accept complete preselected operands. Fix/Unfix
+  consumes complete point/curve selections consistently; mixed or ambiguous selections
+  retain the picking workflow. Rejected constraints preserve selection and undo history.
 - Contextual error reporting: a **Create Issue** action beside feature errors opens a
   reviewable GitHub issue draft with the error, operation settings, build diagnostics and
   useful reproduction context. The draft is editable, with optional capture of the actual
diff --git a/crates/ui-egui/src/lib.rs b/crates/ui-egui/src/lib.rs
index f5d09ced..df8a8319 100644
--- a/crates/ui-egui/src/lib.rs
+++ b/crates/ui-egui/src/lib.rs
@@ -519,22 +519,6 @@ impl SolveApp {
             let edges = self.session.selection.iter().any(|s| matches!(s, solvecraft_engine::Sel::Edge { .. }));
             return self.start(if edges { "solid.fillet" } else { "solid.extrude" });
         }
-        // Fix/Unfix: the selected sketch points and curves change at once, otherwise pick them.
-        if id == "sketch.constraint.fix" {
-            let ents: Vec<String> = self
-                .session
-                .selection
-                .iter()
-                .filter_map(|s| match s {
-                    solvecraft_engine::Sel::SketchCurve { id } | solvecraft_engine::Sel::SketchPoint { id } => Some(id.clone()),
-                    _ => None,
-                })
-                .collect();
-            if !ents.is_empty() {
-                let _ = self.run(id, json!({ "entities": ents }));
-                return;
-            }
-        }
         // Construction toggle: selected sketch curves switch at once, otherwise pick them.
         // Construction (X): convert the selection, or switch construction mode; no pick tool.
         if id == "sketch.construction" {
diff --git a/crates/ui-egui/src/tools.rs b/crates/ui-egui/src/tools.rs
index 14d2aaae..012c38ba 100644
--- a/crates/ui-egui/src/tools.rs
+++ b/crates/ui-egui/src/tools.rs
@@ -326,7 +326,25 @@ fn run_shape(app: &mut SolveApp, t: &Tool) -> Result<Vec<String>, String> {
 /// Only consume a complete, unambiguous selection; command validation owns geometry.
 pub(crate) fn constraint_preselection(command: &str, selection: &[solvecraft_engine::Sel]) -> Option<Value> {
     use solvecraft_engine::Sel::{SketchCurve, SketchPoint};
+    let selected_ids = |curves_only: bool, minimum: usize| -> Option<Vec<&str>> {
+        if !(minimum..=200).contains(&selection.len()) {
+            return None;
+        }
+        let ids: Vec<&str> = selection
+            .iter()
+            .map(|s| match s {
+                SketchCurve { id } => Some(id.as_str()),
+                SketchPoint { id } if !curves_only => Some(id.as_str()),
+                _ => None,
+            })
+            .collect::<Option<_>>()?;
+        let unique: std::collections::BTreeSet<_> = ids.iter().copied().collect();
+        (unique.len() == ids.len()).then_some(ids)
+    };
     match (command, selection) {
+        ("sketch.constraint.fix", _) => selected_ids(false, 1).map(|ids| json!({"entities":ids})),
+        ("sketch.constraint.polygon", _) => selected_ids(true, 3).map(|ids| json!({"lines":ids})),
+        ("sketch.constraint.curvature", [SketchCurve { id: a }, SketchCurve { id: b }]) if a != b => Some(json!({"a":a,"b":b})),
         ("sketch.constraint.horizontal_vertical", [SketchCurve { id }]) => Some(json!({"line":id})),
         ("sketch.constraint.horizontal_vertical", [SketchPoint { id: a }, SketchPoint { id: b }]) if a != b => Some(json!({"points":[a,b]})),
         ("sketch.constraint.coincident", [a, b]) => {
diff --git a/crates/ui-egui/tests/constraint_preselection.rs b/crates/ui-egui/tests/constraint_preselection.rs
index 6787aee7..891240e5 100644
--- a/crates/ui-egui/tests/constraint_preselection.rs
+++ b/crates/ui-egui/tests/constraint_preselection.rs
@@ -146,3 +146,106 @@ fn rejected_preselection_preserves_document_and_error() {
     assert!(!h.app.status.as_ref().is_some_and(|(_, _, error)| *error));
     assert!(h.app.session.selection.is_empty());
 }
+
+#[test]
+fn curvature_polygon_and_fix_consume_clicked_operands_atomically() {
+    for command in ["fix", "curvature", "polygon"] {
+        let mut h = Harness::new();
+        h.app.run("sketch.create", json!({"plane":"XY"})).unwrap();
+        let picks = match command {
+            "curvature" => {
+                h.app.run("sketch.line", json!({"points":[[10,10],[30,10]],"infer":false})).unwrap();
+                h.app.run("sketch.spline.control_point", json!({"points":["l1.end",[40,12],[50,16],[60,25]]})).unwrap();
+                vec![[20., 10.], [45., 14.875]]
+            }
+            "polygon" => {
+                h.app.run("sketch.line", json!({"points":[[10,10],[40,10],[40,30],[10,30]],"closed":true,"infer":false})).unwrap();
+                vec![[25., 10.], [40., 20.], [25., 30.], [10., 20.]]
+            }
+            _ => {
+                h.app.run("sketch.line", json!({"points":[[10,10],[40,10]],"infer":false})).unwrap();
+                h.app.run("sketch.point", json!({"point":[20,25],"id":"p"})).unwrap();
+                vec![[25., 10.], [20., 25.]]
+            }
+        };
+        h.call("ui.view", json!({"view":"top"}));
+        h.app.cam.distance = 80.0;
+        h.app.cam.target = solvecraft_engine::geom::Vec3::new(30.0, 15.0, 0.0);
+        h.settle();
+        for (i, p) in picks.iter().enumerate() {
+            h.step(&json!({"click":{"sketch":p},"shift":i>0})).unwrap();
+        }
+        assert_eq!(h.app.session.selection.len(), picks.len(), "{command}: {:?}", h.app.session.selection);
+        let before = h.app.session.doc.to_json();
+        let undo = h.app.session.undo.len();
+        h.step(&json!({"start":format!("sketch.constraint.{command}")})).unwrap();
+        assert!(!h.app.status.as_ref().is_some_and(|(_, _, error)| *error), "{command}: {:?}", h.app.status);
+        assert!(h.app.tool.is_none());
+        assert!(h.app.session.selection.is_empty());
+        assert_eq!(h.app.session.undo.len(), undo + 1);
+        let st = h.app.session.world_state();
+        let sk = &st.sketch(h.app.session.active_sketch.unwrap()).unwrap().sketch;
+        assert!(sk.constraints.iter().any(|c| match command {
+            "fix" => matches!(c.kind, ConstraintKind::Fix { .. }),
+            "curvature" => matches!(c.kind, ConstraintKind::Smooth { .. }),
+            _ => matches!(c.kind, ConstraintKind::Equal { .. }),
+        }));
+        match command {
+            "fix" => {
+                assert!(sk.curve_locked(sk.curve_index("l1").unwrap()));
+                assert!(sk.point_locked(sk.resolve_point("p").unwrap()));
+            }
+            "curvature" => {
+                let spline = sk.curves.iter().find(|c| c.id != "l1").unwrap();
+                let pts: Vec<_> = spline.kind.point_ids().iter().map(|i| sk.point(*i).unwrap()).collect();
+                let line = sk.polyline(sk.curve_index("l1").unwrap());
+                let direction = (line[1] - line[0]).normalized().unwrap();
+                assert!((pts[1] - pts[0]).cross(direction).abs() < 1e-5);
+                assert!((pts[2] - pts[1]).cross(pts[1] - pts[0]).abs() < 1e-3);
+            }
+            _ => {
+                let lengths: Vec<_> = ["l1", "l2", "l3", "l4"]
+                    .iter()
+                    .map(|id| {
+                        let pts = sk.polyline(sk.curve_index(id).unwrap());
+                        pts[0].dist(pts[1])
+                    })
+                    .collect();
+                assert!(lengths[0] > 1.0);
+                assert!(lengths.iter().all(|l| (l - lengths[0]).abs() < 1e-6));
+            }
+        }
+        assert!(st.sketch(h.app.session.active_sketch.unwrap()).unwrap().report.ok());
+        let after = h.app.session.doc.to_json();
+        h.app.run("edit.undo", json!({})).unwrap();
+        assert_eq!(h.app.session.doc.to_json(), before);
+        h.app.run("edit.redo", json!({})).unwrap();
+        assert_eq!(h.app.session.doc.to_json(), after);
+    }
+}
+
+#[test]
+fn remaining_constraints_preserve_mixed_selections_and_rejected_geometry() {
+    for command in ["fix", "curvature", "polygon"] {
+        let mut h = lines();
+        let before = h.app.session.doc.to_json();
+        let undo = h.app.session.undo.len();
+        let mixed = vec![Sel::SketchCurve { id: "l1".into() }, Sel::Body { name: "missing".into() }];
+        h.app.session.selection = mixed.clone();
+        h.step(&json!({"start":format!("sketch.constraint.{command}")})).unwrap();
+        assert!(h.app.tool.is_some());
+        assert_eq!(h.app.session.selection, mixed);
+        assert_eq!(h.app.session.doc.to_json(), before);
+        assert_eq!(h.app.session.undo.len(), undo);
+    }
+    let mut h = lines();
+    let selection = vec![Sel::SketchCurve { id: "l1".into() }, Sel::SketchCurve { id: "missing".into() }];
+    h.app.session.selection = selection.clone();
+    let before = h.app.session.doc.to_json();
+    let undo = h.app.session.undo.len();
+    h.step(&json!({"start":"sketch.constraint.curvature"})).unwrap();
+    assert!(h.app.status.as_ref().is_some_and(|(_, _, error)| *error));
+    assert_eq!(h.app.session.selection, selection);
+    assert_eq!(h.app.session.doc.to_json(), before);
+    assert_eq!(h.app.session.undo.len(), undo);
+}