fix(units): make the units selector reach what it names

The status-bar units button wrote INSUNITS, which nothing on screen reads.
INSUNITS only tells the drawing how to scale content arriving from
elsewhere, so picking a unit relabelled the drawing and changed nothing
visible — the selector looked broken because the variable it moved was
invisible.

Point the button at LUNITS instead, the setting that decides how every
coordinate and distance is written, and give the three questions the word
"units" runs together a place each:

- The button offers the five length formats, each shown beside a sample of
  itself, so Engineering and Architectural are told apart by sight.
- UNITS / DDUNITS opens a real dialog: length and angle format and
  precision, the direction angle zero points, whether positive angles run
  clockwise, and the insertion unit. Its sample comes from the same
  formatters the drawing uses, so it cannot drift from the readout.
- DWGUNITS converts. Model geometry, viewport framing, the header's length
  defaults and each dimension style's scale all move together in one undo
  step; paper space is left alone, since the sheet is still the same sheet.
  Locked layers are converted too — a half-converted drawing would be at
  two scales at once.

The coordinate readout formatted at four decimal places whatever the
drawing asked for; it now goes through the same format_length the
properties panel uses. That made the angle formats reachable in turn, so
degrees-minutes-seconds now carries the d/'/" marks that say which
convention it is, and surveyor's units are written at all.

Typed input is still plain decimal: a length the readout writes as
5'-6 1/2" cannot yet be typed back. ANGBASE and ANGDIR are stored but not
yet applied to displayed directions.

Closes #668

Co-Authored-By: Claude Opus 5 <[email protected]>

src/entities/common.rs

@@ -11,8 +11,8 @@ pub struct UnitContext {
     pub lunits: i16,
     /// LUPREC — decimal places (linear)
     pub luprec: i16,
-    /// AUNITS — 0=Decimal degrees, 1=DMS, 2=Grad, 3=Rad. Surfaced via
-    /// `format_angle`, which is read on demand by code that already
+    /// AUNITS — 0=Decimal degrees, 1=DMS, 2=Grad, 3=Rad, 4=Surveyor. Surfaced
+    /// via `format_angle`, which is read on demand by code that already
     /// formats angular values via radians.
     #[allow(dead_code)]
     pub aunits: i16,
@@ -98,26 +98,63 @@ pub fn format_angle(value_rad: f64) -> String {
     let ctx = unit_context();
     let prec = ctx.auprec.max(0) as usize;
     match ctx.aunits {
-        1 => {
-            // DMS — degrees / minutes / seconds.
-            let deg = value_rad.to_degrees();
-            let sign = if deg < 0.0 { "-" } else { "" };
-            let a = deg.abs();
-            let d = a.floor();
-            let m_full = (a - d) * 60.0;
-            let m = m_full.floor();
-            let s = (m_full - m) * 60.0;
-            format!("{}{:.0}°{:.0}'{:.*}\"", sign, d, m, prec, s)
-        }
+        1 => dms(value_rad.to_degrees(), prec),
         2 => {
             let g = value_rad.to_degrees() / 0.9;
             format!("{:.*}g", prec, g)
         }
         3 => format!("{:.*}r", prec, value_rad),
+        4 => surveyor(value_rad, prec),
         _ => format!("{:.*}°", prec, value_rad.to_degrees()),
     }
 }
 
+/// Degrees / minutes / seconds. Each part carries its own mark — `d`, `'`, `"`
+/// — so the written angle says which convention it is in.
+fn dms(degrees: f64, prec: usize) -> String {
+    let sign = if degrees < 0.0 { "-" } else { "" };
+    let a = degrees.abs();
+    let d = a.floor();
+    let m_full = (a - d) * 60.0;
+    let m = m_full.floor();
+    let s = (m_full - m) * 60.0;
+    format!("{}{:.0}d{:.0}'{:.*}\"", sign, d, m, prec, s)
+}
+
+/// Surveyor's units: a bearing away from north or south, toward east or west,
+/// so the angle is never more than a quarter turn — `N 45d0'0" E`.
+///
+/// Due north, south, east and west have no bearing to quote and are written as
+/// the single letter, which is also what keeps a 90° angle from reading as the
+/// contradictory `N 90d0'0" E`.
+fn surveyor(value_rad: f64, prec: usize) -> String {
+    let deg = value_rad.to_degrees().rem_euclid(360.0);
+    let near = |target: f64| (deg - target).abs() < 1e-9;
+    if near(0.0) {
+        return "E".into();
+    }
+    if near(90.0) {
+        return "N".into();
+    }
+    if near(180.0) {
+        return "W".into();
+    }
+    if near(270.0) {
+        return "S".into();
+    }
+    // Measured from the nearer pole, toward the side the angle falls on.
+    let (pole, bearing, side) = if deg < 90.0 {
+        ("N", 90.0 - deg, "E")
+    } else if deg < 180.0 {
+        ("N", deg - 90.0, "W")
+    } else if deg < 270.0 {
+        ("S", 270.0 - deg, "W")
+    } else {
+        ("S", deg - 270.0, "E")
+    };
+    format!("{pole} {} {side}", dms(bearing, prec))
+}
+
 /// Two interior triangles covering a quad (flat list, 6 vertices) — the
 /// click-anywhere pick surface for frame-like entities (image, OLE frame,
 /// underlay, wipeout). Corners in ring order.