diff --git a/src/app/update/command.rs b/src/app/update/command.rs
index a01824f79..15ea1e6bd 100644
--- a/src/app/update/command.rs
+++ b/src/app/update/command.rs
@@ -1723,15 +1723,13 @@ pub(super) fn on_tab_close(&mut self, idx: usize) -> Task<Message> {
                         .get_entity(popup.handle)
                         .is_some_and(|entity| match (item.action, entity) {
                             (GripMenuAction::ShowFit, acadrust::EntityType::Spline(spline)) => {
-                                !spline.cv_frame_visible
-                                    && crate::entities::spline::uses_fit_method(spline)
+                                crate::entities::spline::shows_fit_points(spline)
                             }
                             (
                                 GripMenuAction::ShowControlVertices,
                                 acadrust::EntityType::Spline(spline),
                             ) => {
-                                spline.cv_frame_visible
-                                    || !crate::entities::spline::uses_fit_method(spline)
+                                crate::entities::spline::shows_control_vertices(spline)
                             }
                             _ => false,
                         });
diff --git a/src/app/view/mod.rs b/src/app/view/mod.rs
index d1ecc1648..b77f6bdd9 100644
--- a/src/app/view/mod.rs
+++ b/src/app/view/mod.rs
@@ -591,7 +591,8 @@ bg={bg_ms:.1}ms n={view_count}"
             };
             let control_polygon = tab.selected_handle.and_then(|handle| {
                 let spline = match tab.scene.document.get_entity(handle) {
-                    Some(acadrust::EntityType::Spline(spline)) if spline.cv_frame_visible => spline,
+                    Some(acadrust::EntityType::Spline(spline))
+                        if crate::entities::spline::shows_control_vertices(spline) => spline,
                     _ => return None,
                 };
                 if tab
diff --git a/src/entities/spline.rs b/src/entities/spline.rs
index 5a8813561..481d57543 100644
--- a/src/entities/spline.rs
+++ b/src/entities/spline.rs
@@ -18,7 +18,13 @@ pub(crate) fn uses_fit_method(spline: &Spline) -> bool {
 }
 
 pub(crate) fn shows_fit_points(spline: &Spline) -> bool {
-    uses_fit_method(spline) && (!spline.cv_frame_visible || spline.flags.periodic)
+    !spline.fit_points.is_empty() && (!spline.cv_frame_visible || spline.flags.periodic)
+}
+
+pub(crate) fn shows_control_vertices(spline: &Spline) -> bool {
+    !shows_fit_points(spline)
+        && !(uses_fit_method(spline) && spline.flags.periodic)
+        && control_vertices(spline).len() >= 2
 }
 
 pub(crate) fn fit_nurbs3(spline: &Spline) -> Option<NurbsCurve3> {
@@ -105,14 +111,24 @@ pub(crate) fn spline_knot_points(spline: &Spline) -> Vec<glam::DVec3> {
 }
 
 pub(crate) fn replace_with_nurbs(spline: &mut Spline, curve: &NurbsCurve3) {
+    let mut fit_points = spline.fit_points.clone();
     spline.degree = curve.degree() as i32;
     spline.knots = curve.knots().to_vec();
     spline.control_points = curve.control_points().iter()
         .map(|point| acadrust::types::Vector3::new(point[0], point[1], point[2])).collect();
     spline.weights = curve.weights().to_vec();
-    spline.fit_points.clear();
+    if !fit_points.is_empty() {
+        if let (Some(first), Some(point)) = (fit_points.first_mut(), spline.control_points.first()) {
+            *first = *point;
+        }
+        if let (Some(last), Some(point)) = (fit_points.last_mut(), spline.control_points.last()) {
+            *last = *point;
+        }
+    }
+    spline.fit_points = fit_points;
     spline.begin_tangent = acadrust::types::Vector3::ZERO;
     spline.end_tangent = acadrust::types::Vector3::ZERO;
+    spline.cv_frame_visible = true;
     spline.flags.rational = spline.weights.windows(2)
         .any(|pair| (pair[0] - pair[1]).abs() > 1e-12);
     spline.flags.closed = false;
@@ -615,7 +631,15 @@ fn index_prop(label: &str, field: &'static str, index: usize, count: usize) -> P
 
 fn convert_to_control_method(spline: &mut Spline) -> bool {
     if !uses_fit_method(spline) {
-        return true;
+        let valid = spline.control_points.len() >= 2;
+        if valid {
+            spline.fit_points.clear();
+            spline.begin_tangent = acadrust::types::Vector3::ZERO;
+            spline.end_tangent = acadrust::types::Vector3::ZERO;
+            spline.dwg_flags1 &= !1;
+            spline.dxf_flags &= !(32 | 1024);
+        }
+        return valid;
     }
     let Some(planar) = crate::entities::curve::spline_curve(spline) else {
         return false;
@@ -647,18 +671,74 @@ fn convert_to_control_method(spline: &mut Spline) -> bool {
 }
 
 fn convert_to_fit_method(spline: &mut Spline) -> bool {
-    uses_fit_method(spline)
+    if uses_fit_method(spline) {
+        return true;
+    }
+    if spline.fit_points.len() < 2 {
+        return false;
+    }
+    spline.control_points.clear();
+    spline.knots.clear();
+    spline.weights.clear();
+    spline.flags.rational = false;
+    spline.dwg_flags1 |= 1;
+    spline.dxf_flags |= 32 | 1024;
+    true
+}
+
+fn derived_fit_points(spline: &Spline) -> Vec<acadrust::types::Vector3> {
+    if spline.flags.closed || spline.flags.periodic {
+        return Vec::new();
+    }
+    let Some(curve) = nurbs3(spline) else {
+        return Vec::new();
+    };
+    let (start, end) = curve.domain();
+    if !(start.is_finite() && end.is_finite() && end > start) {
+        return Vec::new();
+    }
+    let tolerance = (end - start).abs().max(1.0) * 1.0e-12;
+    let mut parameters = vec![start];
+    for knot in curve.knots().iter().copied() {
+        if knot > start + tolerance
+            && knot < end - tolerance
+            && parameters
+                .last()
+                .is_none_or(|previous| (knot - *previous).abs() > tolerance)
+        {
+            parameters.push(knot);
+        }
+    }
+    parameters.push(end);
+    parameters
+        .into_iter()
+        .map(|parameter| {
+            let point = curve.point_at_knot(parameter);
+            acadrust::types::Vector3::new(point[0], point[1], point[2])
+        })
+        .collect()
+}
+
+fn can_show_fit_points(spline: &Spline) -> bool {
+    spline.fit_points.len() >= 2 || derived_fit_points(spline).len() >= 2
+}
+
+fn prepare_fit_point_view(spline: &mut Spline) -> bool {
+    if spline.fit_points.len() < 2 {
+        spline.fit_points = derived_fit_points(spline);
+    }
+    spline.fit_points.len() >= 2
 }
 
 fn grips(spline: &Spline) -> Vec<GripDef> {
-    let fit_method = uses_fit_method(spline);
     let derived_control = control_vertices(spline);
-    let show_control_vertices = (spline.cv_frame_visible || !fit_method)
-        && !(fit_method && spline.flags.periodic)
+    let show_fit = shows_fit_points(spline);
+    let show_control_vertices = !show_fit
+        && !(uses_fit_method(spline) && spline.flags.periodic)
         && derived_control.len() >= 2;
     let source = if show_control_vertices {
         derived_control
-    } else if fit_method {
+    } else if show_fit {
         spline.fit_points.clone()
     } else {
         spline.control_points.clone()
@@ -885,7 +965,7 @@ fn apply_geom_prop(spline: &mut Spline, field: &str, value: &str) {
     match field {
         "spline_method" => {
             if value == "Fit" {
-                if convert_to_fit_method(spline) {
+                if prepare_fit_point_view(spline) {
                     spline.cv_frame_visible = false;
                 }
             } else if value == "Control Vertices" {
@@ -896,6 +976,12 @@ fn apply_geom_prop(spline: &mut Spline, field: &str, value: &str) {
             return;
         }
         "knot_param" => {
+            if shows_fit_points(spline)
+                && !uses_fit_method(spline)
+                && !convert_to_fit_method(spline)
+            {
+                return;
+            }
             spline.knot_parameterization = match value {
                 "Chord" => 0,
                 "Square Root" => 1,
@@ -930,9 +1016,30 @@ fn apply_geom_prop(spline: &mut Spline, field: &str, value: &str) {
     {
         return;
     }
-    if matches!(field, "ctrl_pt_x" | "ctrl_pt_y" | "ctrl_pt_z" | "weight")
-        && uses_fit_method(spline)
-        && !convert_to_control_method(spline)
+    if matches!(field, "ctrl_pt_x" | "ctrl_pt_y" | "ctrl_pt_z" | "weight") {
+        if !shows_fit_points(spline) && !spline.fit_points.is_empty() {
+            if !convert_to_control_method(spline) {
+                return;
+            }
+        } else if uses_fit_method(spline) && !convert_to_control_method(spline) {
+            return;
+        }
+    }
+    if shows_fit_points(spline)
+        && !uses_fit_method(spline)
+        && matches!(
+            field,
+            "fit_pt_x"
+                | "fit_pt_y"
+                | "fit_pt_z"
+                | "start_tan_x"
+                | "start_tan_y"
+                | "start_tan_z"
+                | "end_tan_x"
+                | "end_tan_y"
+                | "end_tan_z"
+        )
+        && !convert_to_fit_method(spline)
     {
         return;
     }
@@ -1015,16 +1122,23 @@ fn apply_grip(spline: &mut Spline, grip_id: usize, apply: GripApply) {
         return;
     }
     // First CV edit makes the displayed kernel controls authoritative.
-    let fit_method = uses_fit_method(spline);
-    if spline.cv_frame_visible && fit_method && !spline.flags.periodic {
+    let editing_fit = shows_fit_points(spline);
+    if editing_fit && !uses_fit_method(spline) {
+        if !convert_to_fit_method(spline) {
+            return;
+        }
+    } else if !editing_fit
+        && (uses_fit_method(spline) || !spline.fit_points.is_empty())
+        && !spline.flags.periodic
+    {
         if !convert_to_control_method(spline) {
             return;
         }
     }
-    let target = if (spline.cv_frame_visible && !spline.flags.periodic) || !fit_method {
-        spline.control_points.get_mut(grip_id)
-    } else {
+    let target = if editing_fit {
         spline.fit_points.get_mut(grip_id)
+    } else {
+        spline.control_points.get_mut(grip_id)
     };
     if let Some(cp) = target {
         match apply {
@@ -1088,9 +1202,10 @@ impl crate::entities::traits::Grippable for Spline {
             let fit_method = uses_fit_method(self);
             let can_show_control = control_vertices(self).len() >= 2
                 && !(fit_method && self.flags.periodic);
+            let can_show_fit = can_show_fit_points(self);
             return if !shows_fit_points(self) {
                 vec![
-                    (can_show_control && fit_method).then_some(GripMenuItem {
+                    can_show_fit.then_some(GripMenuItem {
                         label: "Fit",
                         action: GripMenuAction::ShowFit,
                     }),
@@ -1131,7 +1246,7 @@ impl crate::entities::traits::Grippable for Spline {
         use crate::scene::model::object::GripMenuAction as A;
         match action {
             A::ShowFit => {
-                if convert_to_fit_method(self) {
+                if prepare_fit_point_view(self) {
                     self.cv_frame_visible = false;
                     return;
                 }
diff --git a/src/scene/parametric_solve.rs b/src/scene/parametric_solve.rs
index 642b26925..fef63b70e 100644
--- a/src/scene/parametric_solve.rs
+++ b/src/scene/parametric_solve.rs
@@ -2961,8 +2961,8 @@ fn solve_scope(
                 }
             }
             (EntityType::Spline(spline), EntityGeom::Spline { curve, control_z }) => {
-                let mut changed =
-                    spline.fit_points.len() > 0 || spline.control_points.len() != curve.poles.len();
+                let mut changed = crate::entities::spline::uses_fit_method(spline)
+                    || spline.control_points.len() != curve.poles.len();
                 let control_points: Vec<_> = curve
                     .poles
                     .iter()
@@ -2983,7 +2983,18 @@ fn solve_scope(
                     updated.knots = curve.knots.clone();
                     updated.control_points = control_points;
                     updated.weights = curve.weights.iter().map(|id| store.get(*id)).collect();
-                    updated.fit_points.clear();
+                    if !updated.fit_points.is_empty() {
+                        if let (Some(first), Some(point)) =
+                            (updated.fit_points.first_mut(), updated.control_points.first())
+                        {
+                            *first = *point;
+                        }
+                        if let (Some(last), Some(point)) =
+                            (updated.fit_points.last_mut(), updated.control_points.last())
+                        {
+                            *last = *point;
+                        }
+                    }
                     updated.begin_tangent = Vector3::ZERO;
                     updated.end_tangent = Vector3::ZERO;
                     updated.flags.rational = updated