Fix Arachne duplicate extrusion caused by bead count mismatch (#14031)

* Add test for Arachne duplicate wall segment detection

Add test cases that reproduce an issue where Arachne generates
duplicate/coinciding extrusion segments at certain min_bead_width settings.

Test configuration:
- Profile: 0.28mm Extra Draft @BBL X1C (0.4mm nozzle, 0.28mm layer)
- outer_wall_line_width: 0.42mm, inner_wall_line_width: 0.45mm
- wall_loops: 2, precise_outer_wall: enabled
- Test polygon: outer rectangle (0,0)-(20,20) with inner cutout (0.5,0.5)-(19.5,19.5)
  This creates a 0.5mm wide frame around the perimeter.

Results:
- 50% min_bead_width (0.20mm): FAILS - detects 4 duplicate segments (all 4 sides)
- 60% min_bead_width (0.24mm): PASSES - no duplicates

At 50%, Arachne generates two separate closed loops that share all 4 edges
of the inner square. At 60%, Arachne generates a single closed loop.

SVG output is exported to /tmp/opencode/ for visual debugging.

* Fix Arachne duplicate extrusion caused by bead count mismatch

WideningBeadingStrategy::compute() used optimal_width (inner wall width)
to determine if a thin wall should produce a single bead. However,
getOptimalBeadCount() uses optimal_width_outer (outer wall width) via
RedistributeBeadingStrategy to decide the bead count.

This inconsistency caused situations where getOptimalBeadCount() returned
2 beads, but compute() produced only 1 bead at full thickness. The single
bead was then generated for both inner and outer contours, resulting in
duplicate extrusion paths.

Fix: Use getTransitionThickness(1) instead of optimal_width. This method
returns the exact threshold for the 1-to-2 bead transition, ensuring
consistency between bead count calculation and bead generation.

Reproduces with: 50% min_bead_width, 0.42mm outer wall, 0.45mm inner wall,
0.5mm polygon inset creating ~0.38mm wall thickness.

Fixes #13917

---------

Co-authored-by: SoftFever <softfeverever@gmail.com>

src/libslic3r/Arachne/BeadingStrategy/WideningBeadingStrategy.cpp

@@ -26,7 +26,13 @@ std::string WideningBeadingStrategy::toString() const
 
 WideningBeadingStrategy::Beading WideningBeadingStrategy::compute(coord_t thickness, coord_t bead_count) const
 {
-    if (thickness < optimal_width) {
+    // Use getTransitionThickness(1) to determine if this is a thin wall that should produce
+    // a single bead. This ensures consistency with getOptimalBeadCount() which uses the same
+    // threshold (via RedistributeBeadingStrategy) to decide between 1 and 2 beads.
+    // Previously used optimal_width which could differ from the outer wall width used in
+    // bead count calculations, causing inconsistency where bead_count=2 was requested but
+    // only 1 bead was produced.
+    if (thickness < getTransitionThickness(1)) {
         Beading ret;
         ret.total_thickness = thickness;
         if (thickness >= min_input_width) {