Part 2: Replace belt rotation w/ per-axis shear transforms and G-code axis remap

- Replace monolithic belt rotation transform with independent per-axis
    shear controls (mode/angle/source-axis for X, Y, Z) and G-code axis
    remapping, giving full flexibility to match any belt printer's
    coordinate system
  - Remove all rotation mode logic and intermediate type+axes dropdowns,
    simplifying the pipeline to pure shear matrices while preserving the
    default behavior (Y += Z*cot(45deg) with identity remap)
  - Clean up GCodeWriter, GCodeProcessor, and GCodeViewer for the new
    shear-only model; expose 12 new settings in printer UI via
    Tab.cpp/Preset.cpp

Implement belt printer tilted slicing

Implement the core belt slicing pipeline that makes the slicer
tilt-aware:

Step 1: GCodeWriter::to_machine_coords() - R(+alpha, X) rotation
  from slicing frame to machine frame
Step 2: PrintObject - belt-rotated object height calculation
  (y*sin(a) + z*cos(a)) for correct layer count
Step 3: PrintObjectSlice - apply R(-alpha, X) rotation trafo so
  horizontal slice planes correspond to belt-parallel planes,
  with Z-shift computed from model volumes
Step 4: GCodeProcessor - machine-frame preview (no transform needed)
Step 5: 3DBed - rotate bed visualization about X by belt angle

Fix: belt surface IS the build plate, no mesh rotation

Currently still slicing perpendicular to the belt normal.  Need to figure out why.

Fix G-code Z sign: use R(-alpha, X) so Z+ is away from belt

The previous R(+alpha, X) transform produced negative Z values
(-y*sin(a) term dominated). Changed to R(-alpha, X) which gives
machine_z = y*sin(a) + z*cos(a), always positive for points
above the belt surface. Z increases with each layer as expected.

reverting and changing slice methodology

Add pink slicing direction arrow from origin

Shows the effective slicing direction (gantry normal) as a pink
arrow from the origin. Shorter and wider than the gravity arrow.
Direction: R(+alpha, X) * Z = (0, -sin(a), cos(a)), which is
the layer stacking direction in the original mesh frame.

Fix slicing arrow visibility and add raw G-code toggle

- Disable depth test for pink slicing arrow so it renders on top of
  the tilted bed geometry (was being occluded)
- Remove unnecessary 5mm Z-offset from arrow position
- Add m_belt_show_raw toggle to GCodeViewer
- Add "Show raw G-code (slicing frame)" checkbox in legend when
  belt mode is active

Implement to_machine_coords inverse rotation for belt printer G-code

The slicing pipeline rotates the mesh by R(-alpha, X) and shifts Z to
start at 0. The G-code output now undoes this transform via
to_machine_coords: R(+alpha, X) * T(0,0,+z_shift), recovering the
original machine-frame coordinates where Y is horizontal and Z is
vertical.

Changes:
- GCodeWriter: implement to_machine_coords with inverse rotation + Z-shift
- GCodeWriter: add belt_z_shift member and setter/getter
- GCode.cpp: compute Z-shift from print objects (same logic as
  PrintObjectSlice) and pass to writer; write z_shift to G-code header
- GCodeProcessor: parse belt_z_shift from G-code header
- GCodeViewer: store belt_z_shift from processor result

Wire raw G-code toggle to apply slicing-frame view transform

When "Show raw G-code (slicing frame)" is checked in the preview
legend, the view matrix is modified to apply R(-alpha, X) * T(0,0,-z_shift)
to the toolpath rendering. This shows the G-code as it was during
slicing: rotated part with horizontal layers.

Default (unchecked): machine-frame view — upright part with tilted layers.

Remove belt printer placeholder comment from GCodeProcessor

The preview now correctly displays machine-frame G-code with the
optional raw view toggle. No transform is needed in the processor.

src/slic3r/GUI/GCodeViewer.cpp

@@ -1271,6 +1271,7 @@ void GCodeViewer::load_as_gcode(const GCodeProcessorResult& gcode_result, const
 
     m_max_print_height = gcode_result.printable_height;
     m_z_offset = gcode_result.z_offset;
+    m_belt_z_shift = gcode_result.belt_z_shift;
 
     // load_toolpaths(gcode_result, build_volume, exclude_bounding_box);
     
@@ -2209,7 +2210,16 @@ void GCodeViewer::render_toolpaths()
 {
     const Camera& camera = wxGetApp().plater()->get_camera();
     Matrix4f view = camera.get_view_matrix().matrix().cast<float>();
-    // Belt view: view matrix transform placeholder (to be implemented in next cycle).
+    // Belt "raw" view: apply slicing rotation to view matrix so toolpaths appear
+    // in the slicing frame (rotated part with horizontal layers).
+    if (m_belt_show_raw && m_belt_view_enabled && m_belt_angle_deg > 0.f) {
+        double angle_rad = Geometry::deg2rad(static_cast<double>(m_belt_angle_deg));
+        // Apply R(-alpha, X) * T(0,0,-z_shift) to bring machine coords back to slicing frame.
+        Transform3d slicing_trafo = Transform3d::Identity();
+        slicing_trafo.translate(Vec3d(0., 0., -static_cast<double>(m_belt_z_shift)));
+        slicing_trafo = Eigen::AngleAxisd(-angle_rad, Vec3d::UnitX()) * slicing_trafo;
+        view = (camera.get_view_matrix() * slicing_trafo).matrix().cast<float>();
+    }
     const libvgcode::Mat4x4 converted_view_matrix = libvgcode::convert(view);
     const libvgcode::Mat4x4 converted_projetion_matrix = libvgcode::convert(static_cast<Matrix4f>(camera.get_projection_matrix().matrix().cast<float>()));
 #if VGCODE_ENABLE_COG_AND_TOOL_MARKERS
@@ -4406,6 +4416,14 @@ void GCodeViewer::render_legend(float &legend_height, int canvas_width, int canv
     if (m_nozzle_nums > 1 && (m_viewer.get_view_type() == libvgcode::EViewType::Summary || m_viewer.get_view_type() == libvgcode::EViewType::ColorPrint)) // ORCA show only on summary and filament tab
         render_legend_color_arr_recommen(window_padding);
 
+    // Belt printer: toggle for viewing raw slicing-frame G-code
+    if (m_belt_view_enabled) {
+        ImGui::Spacing();
+        ImGui::Dummy({ window_padding, 0 });
+        ImGui::SameLine();
+        ImGui::Checkbox("Show raw G-code (slicing frame)", &m_belt_show_raw);
+    }
+
     legend_height = ImGui::GetCurrentWindow()->Size.y;
     imgui.end();
     ImGui::PopStyleColor(7);