Part 2.7: Add G-code back-transform and tree support belt floor clipping

- Add BeltBackTransform class that inverts the shear/scale matrix and
  applies it in GCodeWriter::to_machine_coords() so G-code outputs in
  the machine's physical coordinate space, gated by new
  belt_gcode_back_transform config option
- Extend belt floor clipping to all three tree support pipelines
  (Prusa-style, Orca organic, TreeModelVolumes) with per-layer polygon
  clipping, anti-overhang integration, and belt raft extension layers
- Fix tree drop_nodes() belt termination, organic support global Z
  offset, collision calculation index bug, and first-layer brim/empty
  layer checks for belt printers

two-shot - first build built but didn't plumb to UI.  Woah.

add pre-slice axis remap, because Y needs to be Z

going to change tactic and move based on bbox min

switch to per axis snapping

per axis swap snap now per object

build plate tilt wasn't invalidating slicer settings

support upper bound now correct, need to get lower bound corrected

axis swapped support termination corrected

Z Shear works with and without pre-slice remap now

src/libslic3r/PrintConfig.cpp

@@ -6136,9 +6136,63 @@ void PrintConfigDef::init_fff_params()
         def->set_default_value(new ConfigOptionEnum<BeltRemapAxis>(default_axis));
     };
 
-    add_belt_remap("belt_gcode_remap_x", "X", "Which slicing axis maps to machine X in G-code output.", BeltRemapAxis::PosX);
-    add_belt_remap("belt_gcode_remap_y", "Y", "Which slicing axis maps to machine Y in G-code output.", BeltRemapAxis::PosY);
-    add_belt_remap("belt_gcode_remap_z", "Z", "Which slicing axis maps to machine Z in G-code output.", BeltRemapAxis::PosZ);
+    add_belt_remap("belt_preslice_remap_x", "X",
+        "Before slicing, which model-space axis becomes the slicer's X axis. "
+        "Use this to re-orient the coordinate system so the slicer's XY plane matches "
+        "your belt printer's physical bed plane. For a printer whose bed is in the XZ plane, "
+        "set Y to +Z and Z to +Y (or -Y) to swap the vertical and belt-travel axes. "
+        "Default +X: no change.",
+        BeltRemapAxis::PosX);
+    add_belt_remap("belt_preslice_remap_y", "Y",
+        "Before slicing, which model-space axis becomes the slicer's Y axis. "
+        "The slicer treats Y as one of the two horizontal bed axes. If your physical "
+        "belt surface runs along the Z axis, map Y to +Z here so the slicer slices "
+        "along the correct plane. Default +Y: no change.",
+        BeltRemapAxis::PosY);
+    add_belt_remap("belt_preslice_remap_z", "Z",
+        "Before slicing, which model-space axis becomes the slicer's Z axis (layer stacking direction). "
+        "The slicer builds layers upward along this axis. If your printer's layer-stacking "
+        "direction is the physical Y axis, map Z to +Y (or -Y for inverted direction). "
+        "Rev mode mirrors relative to the build volume maximum. Default +Z: no change.",
+        BeltRemapAxis::PosZ);
+
+    add_belt_remap("belt_gcode_remap_x", "X", "Which slicing axis maps to machine X in G-code output. Applied AFTER slicing, during G-code generation.", BeltRemapAxis::PosX);
+    add_belt_remap("belt_gcode_remap_y", "Y", "Which slicing axis maps to machine Y in G-code output. Applied AFTER slicing, during G-code generation.", BeltRemapAxis::PosY);
+    add_belt_remap("belt_gcode_remap_z", "Z", "Which slicing axis maps to machine Z in G-code output. Applied AFTER slicing, during G-code generation.", BeltRemapAxis::PosZ);
+
+    def = this->add("belt_gcode_back_transform", coBool);
+    def->label = L("G-code back-transform");
+    def->category = L("Printable space");
+    def->tooltip = L("Reverse the shear/scale transform applied during slicing so G-code "
+                      "coordinates are in the machine's physical coordinate space. "
+                      "Requires at least one shear axis with global mode enabled.");
+    def->mode = comAdvanced;
+    def->set_default_value(new ConfigOptionBool(false));
+
+    auto add_belt_origin_snap = [this](const char *key_snap, const char *key_offset,
+                                        const char *axis_label) {
+        auto def = this->add(key_snap, coBool);
+        def->label = L(axis_label);
+        def->category = L("Printable space");
+        std::string tip = std::string("Shift G-code output so the object's bounding box minimum on machine ")
+                          + axis_label + " equals the offset value.";
+        def->tooltip = L(tip);
+        def->mode = comAdvanced;
+        def->set_default_value(new ConfigOptionBool(false));
+
+        def = this->add(key_offset, coFloat);
+        def->label = L("Offset");
+        def->category = L("Printable space");
+        def->tooltip = L("Target coordinate for the bounding box minimum on this machine axis.");
+        def->sidetext = L("mm");
+        def->min = -10000;
+        def->max = 10000;
+        def->mode = comAdvanced;
+        def->set_default_value(new ConfigOptionFloat(0));
+    };
+    add_belt_origin_snap("belt_origin_snap_x", "belt_origin_offset_x", "X");
+    add_belt_origin_snap("belt_origin_snap_y", "belt_origin_offset_y", "Y");
+    add_belt_origin_snap("belt_origin_snap_z", "belt_origin_offset_z", "Z");
 
     // Belt support floor debug controls
     def = this->add("belt_support_floor_offset", coFloat);