diff --git a/crates/doc/src/document.rs b/crates/doc/src/document.rs
index db170f99..0e962e81 100644
--- a/crates/doc/src/document.rs
+++ b/crates/doc/src/document.rs
@@ -2361,18 +2361,25 @@ impl Document {
     /// the sketch over is refused. Offsets whose sources moved are refreshed and solved again:
     /// from the stored state again after a refused or failed first solve (the geometry is still
     /// the stored one), from the solved one otherwise.
+    ///
+    /// `moved_from`: the stored sketch, when `sk` is that sketch with its links refreshed. A
+    /// link's points are where their source is now; the sides and turns the solve keeps are
+    /// those of the stored state ([`Sketch::positions_in`]), not the ones read beside a line
+    /// that has moved past a point.
     pub fn solve_sketch(
         &self,
         vals: &std::collections::BTreeMap<String, expr::Value>,
         sk: &mut Sketch,
         stored: &solidcraft_sketch::DrivingValues,
+        moved_from: Option<&Sketch>,
     ) -> Result<solidcraft_sketch::SolveReport> {
         self.apply_dimension_values(vals, sk)?;
-        let mut report = solidcraft_sketch::solve_after_value_edit(sk, stored);
+        let was = |sk: &Sketch| moved_from.and_then(|from| sk.positions_in(from));
+        let mut report = solidcraft_sketch::solve_after_edit(sk, stored, was(sk).as_deref());
         if !sk.offsets.is_empty() || !sk.freeform_offsets.is_empty() {
             // Source dimensions may have moved curves during the solve.
             sk.refresh_offsets()?;
-            report = if report.ok() { solidcraft_sketch::solve(sk) } else { solidcraft_sketch::solve_after_value_edit(sk, stored) };
+            report = if report.ok() { solidcraft_sketch::solve(sk) } else { solidcraft_sketch::solve_after_edit(sk, stored, was(sk).as_deref()) };
         }
         Ok(report)
     }
diff --git a/crates/doc/src/eval.rs b/crates/doc/src/eval.rs
index 7b522bec..9d0bf366 100644
--- a/crates/doc/src/eval.rs
+++ b/crates/doc/src/eval.rs
@@ -3347,9 +3347,10 @@ fn eval_feature(doc: &Document, vals: &BTreeMap<String, Value>, f: &Feature, st:
             if let Some(w) = face_warning {
                 warns.insert(0, w);
             }
-            // The stored sketch is solved for its stored values.
+            // The stored sketch is solved for its stored values, with its links where they
+            // were stored: a link that moved must not change the side a dimension from it is on.
             let stored = sk.driving_values();
-            let report = doc.solve_sketch(vals, &mut sk, &stored)?;
+            let report = doc.solve_sketch(vals, &mut sk, &stored, Some(sketch))?;
             if !report.keeps_orientation() {
                 warns.insert(0, report.failure(|f| format!("the sketch constraints conflict ({f})")));
             }
diff --git a/crates/engine/src/cmd/sketch.rs b/crates/engine/src/cmd/sketch.rs
index f575beb1..45fc0e1b 100644
--- a/crates/engine/src/cmd/sketch.rs
+++ b/crates/engine/src/cmd/sketch.rs
@@ -294,7 +294,7 @@ pub(super) fn edit_solved<T>(
             let unsolved = sk.clone();
             #[cfg(test)]
             solve_counts::record(Analysis::Full);
-            let rep = doc.solve_sketch(&vals, &mut sk, &stored)?;
+            let rep = doc.solve_sketch(&vals, &mut sk, &stored, None)?;
             Some(settle(strict, rep, &mut sk, unsolved)?)
         }
     };
@@ -336,7 +336,7 @@ pub(super) fn counted_solve(
 pub(super) fn solve_current(sk: &mut Sketch, doc: &solidcraft_doc::Document) -> Result<SolveReport> {
     let stored = sk.driving_values();
     let (values, _) = doc.param_values();
-    Ok(doc.solve_sketch(&values, sk, &stored)?)
+    Ok(doc.solve_sketch(&values, sk, &stored, None)?)
 }
 
 /// Solves run on this thread by [`counted_solve`] and the edit's own solve: (all of them, those
diff --git a/crates/engine/src/cmd/sketch_project.rs b/crates/engine/src/cmd/sketch_project.rs
index 723998b7..8e17849e 100644
--- a/crates/engine/src/cmd/sketch_project.rs
+++ b/crates/engine/src/cmd/sketch_project.rs
@@ -166,8 +166,14 @@ fn owner_frame(s: &Session, doc: &Document, comp: u64) -> solidcraft_doc::Mat {
     if comp == s.active_component { s.active_component_frame() } else { doc.component_transform(comp) }
 }
 
-/// Re-resolve the links of a sketch being edited against the model before it, so edits see
-/// current reference geometry. Returns warnings.
+/// Re-resolve the links of a sketch being edited (`sk`, a copy of the stored sketch `id`)
+/// against the model before it, so edits see current reference geometry. Returns warnings.
+///
+/// When a link moved, the rest of the sketch follows it as the evaluation solves it, keeping
+/// the stored sides and turns, so the edit goes on from the sketch the model shows. Left where
+/// it was stored beside a line that has moved past it, a dimensioned point would give the
+/// edit's solve the other side to keep. A sketch that does not solve that way keeps its stored
+/// geometry, with the links moved.
 pub(super) fn refresh(s: &Session, doc: &Document, id: u64, sk: &mut Sketch) -> Vec<String> {
     if sk.links.is_empty() {
         return Vec::new();
@@ -183,10 +189,21 @@ pub(super) fn refresh(s: &Session, doc: &Document, id: u64, sk: &mut Sketch) ->
         return vec!["lost face attachment; reattach explicitly".into()];
     };
     let Ok(plane) = sketch_plane(&doc, id, &st) else { return Vec::new() };
-    match attachment {
+    let warnings = match attachment {
         Some(anchor) => solidcraft_doc::project::refresh_face_anchor_links(&doc, &vals, &st, &plane, sk, anchor),
         None => solidcraft_doc::project::refresh_links(&doc, &vals, &st, &plane, sk),
+    };
+    if let Ok(stored) = doc.sketch(id)
+        && sk.positions_in(stored).is_some()
+    {
+        let mut solved = sk.clone();
+        let follows = solved.refresh_offsets().is_ok()
+            && doc.solve_sketch(&vals, &mut solved, &stored.driving_values(), Some(stored)).is_ok_and(|report| report.keeps_orientation());
+        if follows {
+            *sk = solved;
+        }
     }
+    warnings
 }
 
 /// Add a link for `src` to sketch `id` in `doc` (not stored in the session). Returns the link id.
@@ -547,6 +564,10 @@ pub(super) fn auto_project_face(s: &mut Session, id: u64, _at: Vec3) -> Result<O
 #[path = "sketch_project_tests.rs"]
 mod tests;
 
+#[cfg(test)]
+#[path = "sketch_project_side_tests.rs"]
+mod side_tests;
+
 #[cfg(test)]
 #[path = "sketch_model_plane_tests.rs"]
 mod model_plane_tests;
diff --git a/crates/engine/src/cmd/sketch_project_side_tests.rs b/crates/engine/src/cmd/sketch_project_side_tests.rs
new file mode 100644
index 00000000..4e847b07
--- /dev/null
+++ b/crates/engine/src/cmd/sketch_project_side_tests.rs
@@ -0,0 +1,180 @@
+//! A dimension from linked geometry keeps its side when the link's source moves: a point held
+//! 5 from a projected line stays on the side it was drawn on wherever a parameter takes the
+//! line, also past the place the point is stored at.
+
+use serde_json::{Value, json};
+use solidcraft_geom::Vec2;
+
+use crate::Session;
+
+fn run(s: &mut Session, id: &str, p: Value) -> Value {
+    match s.execute(id, &p) {
+        Ok(v) => v,
+        Err(e) => panic!("{id} {p}: {e}"),
+    }
+}
+
+/// Sketch `A`: the horizontal line `rail`, 100 long, at the height the parameter `height`
+/// (50) gives it.
+fn rail_sketch(s: &mut Session) {
+    run(s, "parameters.add", json!({"name": "height", "expression": "50 mm"}));
+    run(s, "sketch.create", json!({"plane": "XY", "name": "A"}));
+    run(s, "sketch.line", json!({"points": [[0, 50], [100, 50]], "ids": ["rail"]}));
+    run(s, "sketch.constraint.horizontal_vertical", json!({"line": "rail", "mode": "horizontal"}));
+    run(s, "sketch.constraint.horizontal_vertical", json!({"points": ["origin", "rail.start"], "mode": "vertical"}));
+    run(s, "sketch.dimension", json!({"entities": ["origin", "rail.start"], "value": "height"}));
+    run(s, "sketch.dimension", json!({"entities": ["rail"], "value": "100 mm"}));
+    run(s, "sketch.finish", json!({}));
+}
+
+/// Sketch `S` (left open): `rail` brought in by `command`, and the point `p` at (50, `y`),
+/// 50 from the origin horizontally. Returns the linked line.
+fn point_by_the_rail(s: &mut Session, command: &str, y: f64) -> String {
+    rail_sketch(s);
+    run(s, "sketch.create", json!({"plane": "XY", "name": "S"}));
+    let r = run(s, command, json!({"refs": [{"sketch": "A", "curve": "rail"}]}));
+    let rail = r["links"][0]["curves"][0].as_str().unwrap().to_string();
+    run(s, "sketch.point", json!({"point": [50, y], "id": "p"}));
+    run(s, "sketch.dimension", json!({"entities": ["origin", "p"], "type": "horizontal", "value": "50 mm"}));
+    rail
+}
+
+/// `p` held 5 from `line`: the dimension's parameter.
+fn five_from(s: &mut Session, line: &str) -> String {
+    let r = run(s, "sketch.dimension", json!({"entities": ["p", line], "type": "distance", "value": "5 mm"}));
+    r["param"].as_str().unwrap().to_string()
+}
+
+fn set_height(s: &mut Session, height: f64) {
+    run(s, "parameters.change", json!({"name": "height", "expression": format!("{height} mm")}));
+}
+
+/// Where the model has `p` of sketch `S`.
+fn p(s: &Session) -> Vec2 {
+    let st = s.model.state();
+    let sk = &st.sketch(s.doc.find_feature("S").unwrap().id).unwrap().sketch;
+    sk.point(sk.resolve_point("p").unwrap()).unwrap()
+}
+
+/// `p` is at (50, `y`), and the sketch has nothing to report.
+#[track_caller]
+fn assert_p(s: &Session, y: f64, when: &str) {
+    assert!(p(s).dist(Vec2::new(50.0, y)) < 1e-9, "{when}: {:?}", p(s));
+    let feature = s.model.result(s.doc.find_feature("S").unwrap().id).unwrap();
+    assert_eq!((&feature.error, &feature.warning), (&None, &None), "{when}");
+}
+
+/// A line of sketch `A` whose height a parameter drives, projected into sketch `S`, whose point
+/// is dimensioned 5 from the projection.
+#[test]
+fn a_distance_from_a_projected_line_keeps_its_side_when_the_source_moves_past() {
+    let mut s = Session::default();
+    let rail = point_by_the_rail(&mut s, "sketch.project", 45.0);
+    five_from(&mut s, &rail);
+    run(&mut s, "sketch.finish", json!({}));
+    assert_p(&s, 45.0, "drawn");
+    // The source drops below the point's stored place: the point stays below the projection.
+    for height in [20.0, 50.0, 6.0, 400.0] {
+        set_height(&mut s, height);
+        assert_p(&s, height - 5.0, &format!("height {height}"));
+    }
+    // Editing the sketch afterwards refreshes the projection first; the side is the one from before.
+    set_height(&mut s, 20.0);
+    run(&mut s, "sketch.edit", json!({"sketch": "S"}));
+    run(&mut s, "sketch.point", json!({"point": [80, 80]}));
+    run(&mut s, "sketch.finish", json!({}));
+    assert_p(&s, 15.0, "after an edit");
+}
+
+/// The same from the other side: the point above the line, the source rising past it and
+/// coming back; and with the line brought in by Include 3D Geometry.
+#[test]
+fn a_point_above_the_line_stays_above_when_the_source_rises_past_and_returns() {
+    for command in ["sketch.project", "sketch.include_3d"] {
+        let mut s = Session::default();
+        let rail = point_by_the_rail(&mut s, command, 55.0);
+        five_from(&mut s, &rail);
+        run(&mut s, "sketch.finish", json!({}));
+        for height in [80.0, 400.0, 50.0, 6.0, 50.0] {
+            set_height(&mut s, height);
+            assert_p(&s, height + 5.0, &format!("{command}, height {height}"));
+        }
+    }
+}
+
+/// Model geometry in a sketch on XZ (whose y runs down the model's Z): the top of a box whose
+/// height a parameter drives, as a projected edge, as an edge of a projected face and as a
+/// section of the body. The point is 5 below the top, inside the box.
+#[test]
+fn a_distance_from_model_geometry_keeps_its_side_when_the_model_moves_past() {
+    // A projected edge is found again by the point picked on it, so it follows small steps
+    // only; a face (by its name) and a body follow any.
+    let small: &[f64] = &[42.0, 50.0, 58.0, 50.0, 44.0];
+    let large: &[f64] = &[20.0, 50.0, 6.0, 400.0];
+    let cases = [
+        ("sketch.project", json!({"edge": [50, 0, 50]}), 0.0, small),
+        ("sketch.project", json!({"face": [50, 0, 25]}), 0.0, large),
+        ("sketch.intersect", json!({"body": "Body1"}), -20.0, large),
+    ];
+    for (command, link, front, heights) in cases {
+        let mut s = Session::default();
+        run(&mut s, "parameters.add", json!({"name": "height", "expression": "50 mm"}));
+        run(&mut s, "solid.box", json!({"corner": [0, front, 0], "length": 100, "width": 40, "height": "height"}));
+        run(&mut s, "sketch.create", json!({"plane": "XZ", "name": "S"}));
+        run(&mut s, command, json!({"refs": [link]}));
+        let curves = run(&mut s, "sketch.inspect", json!({}))["curves"].clone();
+        let high = |c: &Value, end: &str| (c[end][1].as_f64().unwrap() + 50.0).abs() < 1e-6;
+        let top = curves.as_array().unwrap().iter().find(|c| high(c, "start_at") && high(c, "end_at")).unwrap()["id"].as_str().unwrap().to_string();
+        run(&mut s, "sketch.point", json!({"point": [50, -45], "id": "p"}));
+        run(&mut s, "sketch.dimension", json!({"entities": ["origin", "p"], "type": "horizontal", "value": "50 mm"}));
+        five_from(&mut s, &top);
+        run(&mut s, "sketch.finish", json!({}));
+        // (An edge found again by its picked point says so in a warning.)
+        for height in heights {
+            set_height(&mut s, *height);
+            assert!(p(&s).dist(Vec2::new(50.0, 5.0 - height)) < 1e-9, "{command} {link}, height {height}: {:?}", p(&s));
+        }
+    }
+}
+
+/// Another projection added after the source moved stores the sketch without solving it: the
+/// sketch it stores is the one the model shows.
+#[test]
+fn a_projection_added_after_the_source_moved_leaves_the_side() {
+    let mut s = Session::default();
+    let rail = point_by_the_rail(&mut s, "sketch.project", 45.0);
+    five_from(&mut s, &rail);
+    run(&mut s, "sketch.finish", json!({}));
+    set_height(&mut s, 20.0);
+    run(&mut s, "sketch.edit", json!({"sketch": "S"}));
+    run(&mut s, "sketch.project", json!({"refs": ["origin"]}));
+    run(&mut s, "sketch.finish", json!({}));
+    assert_p(&s, 15.0, "after the projection");
+    set_height(&mut s, 50.0);
+    assert_p(&s, 45.0, "back at 50");
+}
+
+/// The side is still the user's to choose, by where the point is when the dimension is added:
+/// also when the source has moved past the point since it was drawn. That side is kept from
+/// then on, and through an edit of the dimension's value.
+#[test]
+fn a_dimension_added_after_the_source_moved_takes_the_side_its_point_is_on() {
+    let mut s = Session::default();
+    let rail = point_by_the_rail(&mut s, "sketch.project", 45.0);
+    run(&mut s, "sketch.finish", json!({}));
+    // Drawn below the line; the line drops below it.
+    set_height(&mut s, 20.0);
+    assert_p(&s, 45.0, "no distance yet");
+    run(&mut s, "sketch.edit", json!({"sketch": "S"}));
+    let distance = five_from(&mut s, &rail);
+    run(&mut s, "sketch.finish", json!({}));
+    assert_p(&s, 25.0, "dimensioned above the line");
+    for height in [50.0, 6.0, 400.0, 20.0] {
+        set_height(&mut s, height);
+        assert_p(&s, height + 5.0, &format!("height {height}"));
+    }
+    run(&mut s, "parameters.change", json!({"name": distance, "expression": "8 mm"}));
+    assert_p(&s, 28.0, "8 from the line");
+    set_height(&mut s, 6.0);
+    assert_p(&s, 14.0, "8 from the line, height 6");
+}
diff --git a/crates/sketch/src/construct.rs b/crates/sketch/src/construct.rs
index 996abef9..53be92b6 100644
--- a/crates/sketch/src/construct.rs
+++ b/crates/sketch/src/construct.rs
@@ -94,11 +94,13 @@ impl Placement {
 
 /// Place the points the constraints pin down; `given[i]` marks the points that are constants
 /// for this solve. Branches are chosen to match the orientation of `reference` (positions
-/// before an interactive move) where it covers a point, of the sketch's current positions
-/// otherwise; a reference longer than the point list is ignored. `on_curve` holds the sketch's
-/// point-on-curve pairs ([`crate::solver::points_on_curves`]); the decomposition works within
-/// what is left of `budget`, and charges it.
-pub(crate) fn seed(sk: &Sketch, given: &[bool], reference: Option<&[Vec2]>, on_curve: &[(usize, usize)], budget: &mut Budget) -> Seed {
+/// before an interactive move, or the stored ones after linked geometry moved) where it covers
+/// a point, of the sketch's current positions otherwise; a reference longer than the point list
+/// is ignored. `edits`: the solve applies edits; a drag step solves against its reference and
+/// moves only held points. `on_curve` holds the sketch's point-on-curve pairs
+/// ([`crate::solver::points_on_curves`]); the decomposition works within what is left of
+/// `budget`, and charges it.
+pub(crate) fn seed(sk: &Sketch, given: &[bool], reference: Option<&[Vec2]>, edits: bool, on_curve: &[(usize, usize)], budget: &mut Budget) -> Seed {
     let n = sk.points.len();
     let reference = reference.filter(|r| r.len() <= n);
     let before = |i: usize| match reference.and_then(|r| r.get(i)) {
@@ -139,9 +141,6 @@ pub(crate) fn seed(sk: &Sketch, given: &[bool], reference: Option<&[Vec2]>, on_c
     if !switch::decompose_on() {
         return out;
     }
-    // A drag step solves against its reference and moves only held points; any other solve
-    // applies edits.
-    let edits = reference.is_none();
     let mut clusters = Decomposition::new(&reading, &prop.anchors, edits, budget.left());
     if !clusters.built() {
         return out;
diff --git a/crates/sketch/src/construct_rounds_tests.rs b/crates/sketch/src/construct_rounds_tests.rs
index 8be3c0bb..ec7442d9 100644
--- a/crates/sketch/src/construct_rounds_tests.rs
+++ b/crates/sketch/src/construct_rounds_tests.rs
@@ -693,7 +693,7 @@ fn hostile_lines_and_rounds_neither_panic_nor_change_the_report() {
         let mut c = base();
         case(&mut c.sk);
         let sk = edited(&c);
-        let s = seed(&sk, &given(&sk), Some(&[v(f64::NAN, 0.0)]), &points_on_curves(&sk), &mut Budget::full());
+        let s = seed(&sk, &given(&sk), Some(&[v(f64::NAN, 0.0)]), false, &points_on_curves(&sk), &mut Budget::full());
         assert!(s.pos.iter().flatten().all(|p| p.is_finite()), "case {i}: {s:?}");
         assert!(s.radius.iter().flatten().all(|r| r.is_finite() && *r > 0.0), "case {i}: {s:?}");
         let mut t = c.sk.clone();
@@ -751,7 +751,7 @@ fn a_dimensioned_radius_is_seeded_with_nothing_given() {
     let mut sk = Sketch::new();
     let circle = sk.add_circle(v(10.0, 5.0), 10.0, None, None).unwrap();
     push(&mut sk, ConstraintKind::Diameter { c: circle, value: 30.0 });
-    let s = seed(&sk, &vec![false; sk.points.len()], None, &[], &mut Budget::full());
+    let s = seed(&sk, &vec![false; sk.points.len()], None, true, &[], &mut Budget::full());
     assert_eq!(s.radius[circle], Some(15.0));
 }
 
@@ -773,10 +773,10 @@ fn the_touch_point_comes_from_the_point_on_curve_index() {
     push(&mut sk, ConstraintKind::Tangent { a: l, b: circle });
     push(&mut sk, ConstraintKind::PointOnCurve { p: b, c: circle });
     let on_curve = crate::solver::points_on_curves(&sk);
-    let with = seed(&sk, &given(&sk), None, &on_curve, &mut Budget::full());
+    let with = seed(&sk, &given(&sk), None, true, &on_curve, &mut Budget::full());
     assert!(with.placed_by[c].is_some_and(Placement::anchors), "{with:?}");
     assert!(with.pos[c].unwrap().dist(v(40.0, 12.0) + d.perp() * 8.0) < 1e-9, "{with:?}");
-    let without = seed(&sk, &given(&sk), None, &[], &mut Budget::full());
+    let without = seed(&sk, &given(&sk), None, true, &[], &mut Budget::full());
     assert!(!without.placed_by[c].is_some_and(Placement::anchors), "{without:?}");
 }
 
diff --git a/crates/sketch/src/construct_tests.rs b/crates/sketch/src/construct_tests.rs
index 50c1998c..a69d9833 100644
--- a/crates/sketch/src/construct_tests.rs
+++ b/crates/sketch/src/construct_tests.rs
@@ -528,7 +528,7 @@ fn hostile_input_neither_panics_nor_changes_the_report() {
         case(&mut sk, a, b, l);
         let mut mask = given(&sk);
         mask.push(true);
-        let s = seed(&sk, &mask, Some(&[v(f64::NAN, 0.0)]), &points_on_curves(&sk), &mut Budget::full());
+        let s = seed(&sk, &mask, Some(&[v(f64::NAN, 0.0)]), false, &points_on_curves(&sk), &mut Budget::full());
         assert!(s.pos.iter().flatten().all(|p| p.is_finite()), "case {i}: {s:?}");
         let n = sk.points.len();
         for reference in [None, Some(vec![Vec2::ZERO; 1]), Some(vec![v(f64::NAN, f64::INFINITY); n]), Some(vec![Vec2::ZERO; n + 3])] {
@@ -902,7 +902,7 @@ fn given_points_are_never_placed() {
     push(&mut sk, ConstraintKind::Distance { p: a, q: d, value: 36.0 });
     let mask = given(&sk);
     assert!(mask[g]);
-    let out = seed(&sk, &mask, None, &points_on_curves(&sk), &mut Budget::full());
+    let out = seed(&sk, &mask, None, true, &points_on_curves(&sk), &mut Budget::full());
     assert_eq!((out.pos[g], out.placed_by[g]), (None, None), "{out:?}");
     assert_eq!(out.placed_by[d], None, "nothing is built on it: {out:?}");
 }
diff --git a/crates/sketch/src/lib.rs b/crates/sketch/src/lib.rs
index a445f45f..c2313655 100644
--- a/crates/sketch/src/lib.rs
+++ b/crates/sketch/src/lib.rs
@@ -55,7 +55,8 @@ pub use profiles::{
 };
 pub use shape::{Shape, intersections};
 pub use solver::{
-    Analysis, DrivingValues, Hold, SolveReport, SolveStatus, measure_dimension, solve, solve_after_value_edit, solve_holding, solve_with,
+    Analysis, DrivingValues, Hold, SolveReport, SolveStatus, measure_dimension, solve, solve_after_edit, solve_after_value_edit, solve_holding,
+    solve_with,
 };
 pub use text::{MAX_TEXT_CHARS, text_geometry, text_geometry_in};
 pub use wire::{MAX_FIT_POINTS, MAX_WIRE_POINTS, Wire, WireSpace, fit_polyline};
diff --git a/crates/sketch/src/link.rs b/crates/sketch/src/link.rs
index 65826610..de352149 100644
--- a/crates/sketch/src/link.rs
+++ b/crates/sketch/src/link.rs
@@ -852,6 +852,21 @@ impl Sketch {
         Ok(true)
     }
 
+    /// Where this sketch's points were in `stored`, the same sketch before its links were
+    /// moved to where their sources are now ([`Sketch::update_link`]): point by point, as
+    /// [`crate::solve_after_edit`] takes them. Points are matched by id (a rebuilt link has
+    /// new ones); a point `stored` does not have is where it is now. `None` when none moved.
+    pub fn positions_in(&self, stored: &Sketch) -> Option<Vec<Vec2>> {
+        let aligned = self.points.len() == stored.points.len() && self.points.iter().zip(&stored.points).all(|(p, q)| p.id == q.id);
+        let was: Vec<Vec2> = if aligned {
+            stored.points.iter().map(|p| p.pos).collect()
+        } else {
+            let by_id: std::collections::BTreeMap<&str, Vec2> = stored.points.iter().map(|p| (p.id.as_str(), p.pos)).collect();
+            self.points.iter().map(|p| by_id.get(p.id.as_str()).copied().unwrap_or(p.pos)).collect()
+        };
+        self.points.iter().zip(&was).any(|(p, w)| p.pos != *w).then_some(was)
+    }
+
     fn drop_link_entities(&mut self, id: &str) {
         let curves = self.link_curves(id);
         let keep = self.links.clone();
@@ -921,3 +936,7 @@ impl Sketch {
 #[cfg(test)]
 #[path = "link_identity_tests.rs"]
 mod identity_tests;
+
+#[cfg(test)]
+#[path = "link_side_tests.rs"]
+mod side_tests;
diff --git a/crates/sketch/src/link_side_tests.rs b/crates/sketch/src/link_side_tests.rs
new file mode 100644
index 00000000..e5b07738
--- /dev/null
+++ b/crates/sketch/src/link_side_tests.rs
@@ -0,0 +1,122 @@
+//! A dimension from a link keeps its side when the link moves: the solve after the links are
+//! refreshed reads sides and turns where the points were stored ([`Sketch::positions_in`]),
+//! not beside a line that has already moved past them.
+
+use super::*;
+use crate::{ConstraintKind, solve, solve_after_edit};
+
+fn source() -> LinkSource {
+    LinkSource::SketchCurve { sketch: 1, curve: "rail".into() }
+}
+
+fn rail(height: f64) -> Vec<LinkGeom> {
+    vec![LinkGeom::Line(Vec2::new(0.0, height), Vec2::new(80.0, height))]
+}
+
+/// What the evaluation does with a stored sketch whose link's source moved: the link goes
+/// where the source is, then the sketch is solved from its stored state. `kept`: the solve is
+/// given the stored positions.
+fn moved(stored: &Sketch, link: &str, geom: &[LinkGeom], kept: bool) -> Sketch {
+    let mut sk = stored.clone();
+    assert!(!sk.update_link(link, geom).unwrap(), "the link keeps its points");
+    let before = if kept { sk.positions_in(stored) } else { None };
+    assert!(solve_after_edit(&mut sk, &stored.driving_values(), before.as_deref()).keeps_orientation());
+    sk
+}
+
+fn near(at: Vec2, x: f64, y: f64) -> bool {
+    at.dist(Vec2::new(x, y)) < 1e-9
+}
+
+#[test]
+fn a_point_dimensioned_from_a_linked_line_keeps_its_side_when_the_line_moves_past() {
+    let mut sk = Sketch::new();
+    let link = sk.add_link(LinkKind::Project, source(), &rail(50.0)).unwrap();
+    let l = sk.link_curves(&link)[0];
+    let p = sk.add_point(Vec2::new(40.0, 45.0), None).unwrap();
+    sk.add_constraint(ConstraintKind::DistanceX { p: 0, q: p, value: 40.0 }, None).unwrap();
+    sk.add_constraint(ConstraintKind::PointLineDistance { p, l, value: 5.0 }, None).unwrap();
+    assert!(solve(&mut sk).ok());
+    // Past the point (20, 6, 44), away from it (400) and not as far as it (48).
+    for height in [20.0, 6.0, 44.0, 400.0, 48.0] {
+        let at = moved(&sk, &link, &rail(height), true).points[p].pos;
+        assert!(near(at, 40.0, height - 5.0), "{height}: {at:?}");
+    }
+    // Read where the line is now, the stored point is above it: the solution on that side.
+    let at = moved(&sk, &link, &rail(20.0), false).points[p].pos;
+    assert!(near(at, 40.0, 25.0), "{at:?}");
+}
+
+#[test]
+fn a_dimension_along_an_axis_keeps_its_side_of_a_linked_point_that_moves_past() {
+    for upright in [true, false] {
+        let end = |h: f64| vec![LinkGeom::Point(if upright { Vec2::new(80.0, h) } else { Vec2::new(h, 80.0) })];
+        let mut sk = Sketch::new();
+        let link = sk.add_link(LinkKind::Project, LinkSource::SketchPoint { sketch: 1, point: "end".into() }, &end(50.0)).unwrap();
+        let q = sk.link_points(&link)[0];
+        let p = sk.add_point(if upright { Vec2::new(40.0, 45.0) } else { Vec2::new(45.0, 40.0) }, None).unwrap();
+        if upright {
+            sk.add_constraint(ConstraintKind::DistanceX { p: 0, q: p, value: 40.0 }, None).unwrap();
+            sk.add_constraint(ConstraintKind::DistanceY { p: q, q: p, value: 5.0 }, None).unwrap();
+        } else {
+            sk.add_constraint(ConstraintKind::DistanceY { p: 0, q: p, value: 40.0 }, None).unwrap();
+            sk.add_constraint(ConstraintKind::DistanceX { p: q, q: p, value: 5.0 }, None).unwrap();
+        }
+        assert!(solve(&mut sk).ok());
+        for height in [20.0, 6.0, 400.0] {
+            let at = moved(&sk, &link, &end(height), true).points[p].pos;
+            let (along, across) = if upright { (at.y, at.x) } else { (at.x, at.y) };
+            assert!((along - (height - 5.0)).abs() < 1e-9 && (across - 40.0).abs() < 1e-9, "upright {upright}, {height}: {at:?}");
+        }
+        let at = moved(&sk, &link, &end(20.0), false).points[p].pos;
+        assert!(((if upright { at.y } else { at.x }) - 25.0).abs() < 1e-9, "upright {upright}: {at:?}");
+    }
+}
+
+/// A corner 50 from both ends of a linked line: below the line, or its mirror image above.
+#[test]
+fn a_corner_dimensioned_from_two_linked_points_keeps_its_turn_when_they_move_past() {
+    let mut sk = Sketch::new();
+    let link = sk.add_link(LinkKind::Project, source(), &rail(50.0)).unwrap();
+    let ends = sk.link_points(&link);
+    let p = sk.add_point(Vec2::new(40.0, 20.0), None).unwrap();
+    for end in ends {
+        sk.add_constraint(ConstraintKind::Distance { p: end, q: p, value: 50.0 }, None).unwrap();
+    }
+    assert!(solve(&mut sk).ok());
+    assert!(near(sk.points[p].pos, 40.0, 20.0));
+    for height in [10.0, -200.0, 300.0] {
+        let at = moved(&sk, &link, &rail(height), true).points[p].pos;
+        assert!(near(at, 40.0, height - 30.0), "{height}: {at:?}");
+    }
+    let at = moved(&sk, &link, &rail(10.0), false).points[p].pos;
+    assert!(near(at, 40.0, 40.0), "{at:?}");
+}
+
+#[test]
+fn stored_positions_are_matched_by_point_id() {
+    let mut stored = Sketch::new();
+    let link = stored.add_link(LinkKind::Project, source(), &rail(50.0)).unwrap();
+    let p = stored.add_point(Vec2::new(40.0, 45.0), Some("p")).unwrap();
+    assert_eq!(stored.positions_in(&stored), None, "nothing moved");
+
+    let mut sk = stored.clone();
+    sk.update_link(&link, &rail(20.0)).unwrap();
+    let was: Vec<Vec2> = stored.points.iter().map(|q| q.pos).collect();
+    assert_eq!(sk.positions_in(&stored), Some(was));
+
+    // A link of another shape is built anew: its points are new, and the points after it
+    // change places in the list.
+    let mut sk = stored.clone();
+    let bent = [LinkGeom::Line(Vec2::new(0.0, 20.0), Vec2::new(40.0, 30.0)), LinkGeom::Line(Vec2::new(40.0, 30.0), Vec2::new(80.0, 20.0))];
+    assert!(sk.update_link(&link, &bent).unwrap());
+    let now = sk.point_index("p").unwrap();
+    assert_ne!(now, p);
+    assert_eq!(sk.positions_in(&stored), None, "the new points have no stored place and `p` has not moved");
+    sk.points[now].pos = Vec2::new(60.0, 45.0);
+    let was = sk.positions_in(&stored).unwrap();
+    assert_eq!(was[now], Vec2::new(40.0, 45.0));
+    for i in sk.link_points(&link) {
+        assert_eq!(was[i], sk.points[i].pos);
+    }
+}
diff --git a/crates/sketch/src/solver.rs b/crates/sketch/src/solver.rs
index 1c43c21f..8df6972f 100644
--- a/crates/sketch/src/solver.rs
+++ b/crates/sketch/src/solver.rs
@@ -1275,8 +1275,19 @@ pub type DrivingValues = std::collections::BTreeMap<String, f64>;
 /// again by stepping its changed values from old to new (see `continue_values`). Where no
 /// value changed a solve behaves as [`solve`].
 pub fn solve_after_value_edit(sk: &mut Sketch, old: &DrivingValues) -> SolveReport {
+    solve_after_edit(sk, old, None)
+}
+
+/// [`solve_after_value_edit`] of a sketch whose linked geometry may have moved as well: once
+/// its links are refreshed ([`Sketch::update_link`]), the linked points are where their sources
+/// are now and everything else is still the stored solved state. `stored` has every point's
+/// position in that state ([`Sketch::positions_in`]; `None` when no link moved), and the sides
+/// and turns the solve keeps are read there, as [`solve_with`] reads them from the positions
+/// before an interactive move. Read where the links are now, a point dimensioned from a
+/// projected line is on the far side of it as soon as the source moves the line past the point.
+pub fn solve_after_edit(sk: &mut Sketch, old: &DrivingValues, stored: Option<&[Vec2]>) -> SolveReport {
     let old_values: Vec<Option<f64>> = sk.constraints.iter().map(|c| old.get(&c.id).copied()).collect();
-    solve_from(sk, &Hold::default(), None, Analysis::Full, Some(&old_values), &mut Budget::full())
+    solve_from(sk, &Hold::default(), stored, Analysis::Full, Some(&old_values), &mut Budget::full())
 }
 
 impl Sketch {
@@ -1736,7 +1747,11 @@ fn solve_inner(
     let mut constructed = vec![false; lay.n];
     if crate::construct::switch::seed_on() {
         let given: Vec<bool> = lay.pvar.iter().map(Option::is_none).collect();
-        let seeded = crate::construct::seed(sk, &given, reference, &on_curve, budget);
+        // A drag step solves against its reference and moves only held points. Any other solve
+        // applies edits: also the one after linked geometry moved, whose reference is the
+        // stored state.
+        let edits = reference.is_none() || old_values.is_some();
+        let seeded = crate::construct::seed(sk, &given, reference, edits, &on_curve, budget);
         for (i, (at, how)) in seeded.pos.iter().zip(&seeded.placed_by).enumerate() {
             if let (Some(at), Some(how), Some(v)) = (at, how, lay.pvar.get(i).copied().flatten())
                 && how.anchors()
diff --git a/crates/sketch/src/tests.rs b/crates/sketch/src/tests.rs
index 2a5c0a6c..564b2214 100644
--- a/crates/sketch/src/tests.rs
+++ b/crates/sketch/src/tests.rs
@@ -39,7 +39,7 @@ pub(crate) fn given(sk: &Sketch) -> Vec<bool> {
 
 /// The constructive seed of a plain solve.
 pub(crate) fn seed_of(sk: &Sketch) -> crate::construct::Seed {
-    crate::construct::seed(sk, &given(sk), None, &crate::solver::points_on_curves(sk), &mut crate::decompose::Budget::full())
+    crate::construct::seed(sk, &given(sk), None, true, &crate::solver::points_on_curves(sk), &mut crate::decompose::Budget::full())
 }
 
 /// Rough rectangle from four lines sharing corner points.