Decouple Slicing From Machine Frame Logic (#21)

* minor logic swap

* first attempt, has a race condition

* fixed the offset issue

* found a solution, I think things work now (at least once I quash this race condition)

* still chasing down race conditions

* add manual shear / scale order strategy swap

* tweak manual shear, fix ui uninitialization crash

* fix z height / g-code desync issue

* fix shear then scale cutoff planes

* getting closer

* fix support termination planes

* fix incorrect offsets in shear-then-scale mode

* test - fix overextrusion due to model/layer scale

src/libslic3r/GCode/MachineFrameTransform.hpp

@@ -0,0 +1,43 @@
+#ifndef slic3r_MachineFrameTransform_hpp_
+#define slic3r_MachineFrameTransform_hpp_
+
+#include "../libslic3r.h"
+#include "../Point.hpp"
+#include "../PrintConfig.hpp"
+
+namespace Slic3r {
+
+// Post-stage machine-frame transform for belt printers.
+//
+// Applied in BeltGCodeWriter::to_machine_coords AFTER the back-transform
+// and the existing gcode_remap_* axis remap, and BEFORE per-axis origin snap.
+// Maps Cartesian (axis-permuted) G-code coordinates into the printer's
+// physical machine frame using a parallel set of options:
+//   gcode_shear_x/y/z + _angle + _from
+//   gcode_scale_x/y/z + _angle
+//   post_gcode_remap_x/y/z
+//
+// Composition matches the mesh-side pipeline: shear * scale * post_remap.
+class MachineFrameTransform
+{
+public:
+    MachineFrameTransform() = default;
+
+    // Initialize from belt printer config.  Returns true if a non-identity
+    // transform was computed.  Inactive when belt_printer is disabled or
+    // all three sub-stages are identity.
+    bool init_from_config(const PrintConfig &config);
+
+    // Apply the transform to a point.  Returns pos unchanged if not active.
+    Vec3d apply(const Vec3d &pos) const;
+
+    bool is_active() const { return m_active; }
+
+private:
+    bool        m_active    = false;
+    Transform3d m_transform = Transform3d::Identity();
+};
+
+} // namespace Slic3r
+
+#endif // slic3r_MachineFrameTransform_hpp_