fix non 45 degree slicing methods after regression created while cleaning up UI

src/CMakeLists.txt

@@ -90,6 +90,12 @@ if (SLIC3R_GUI)
 #    list(REMOVE_ITEM wxWidgets_LIBRARIES oleacc)
 
     find_package(wxInspector REQUIRED)
+    # wxInspector 1.0.0 installs its headers but accidentally declares the
+    # INSTALL_INTERFACE include directory PRIVATE, so its imported target does
+    # not expose them to consumers. Restore the package prefix include path until
+    # the upstream export is fixed.
+    get_filename_component(WXINSPECTOR_PREFIX "${wxInspector_DIR}/../../.." ABSOLUTE)
+    target_include_directories(wxInspector::wxInspector INTERFACE "${WXINSPECTOR_PREFIX}/include")
     list(APPEND wxWidgets_LIBRARIES "wxInspector::wxInspector")
 
     message(STATUS "wx libs: ${wxWidgets_LIBRARIES}")
@@ -175,7 +181,7 @@ endif ()
 # Add the Slic3r GUI library, libcurl, OpenGL and GLU libraries.
 if (SLIC3R_GUI)
 #    target_link_libraries(OrcaSlicer ws2_32 uxtheme setupapi libslic3r_gui ${wxWidgets_LIBRARIES})
-target_link_libraries(OrcaSlicer libslic3r_gui)
+target_link_libraries(OrcaSlicer libslic3r_gui wxInspector::wxInspector)
     if (MSVC)
         # Generate debug symbols even in release mode.
         target_link_options(OrcaSlicer PUBLIC "$<$<CONFIG:RELEASE>:/DEBUG>")

src/libslic3r/GCode/MachineFrameTransform.cpp

@@ -29,31 +29,34 @@ bool MachineFrameTransform::init_from_config(const PrintConfig &config)
         return false;
 
     const double angle_rad = Geometry::deg2rad(angle_deg);
-    const double cos_a      = std::cos(angle_rad);
-    if (std::abs(cos_a) <= EPSILON)
+    const double sin_a      = std::sin(angle_rad);
+    if (std::abs(sin_a) <= EPSILON)
         return false;
-    const double tan_a   = std::sin(angle_rad) / cos_a;
-    const double inv_cos = 1.0 / cos_a;
+    const double cot_a   = std::cos(angle_rad) / sin_a;
+    const double inv_sin = 1.0 / std::abs(sin_a);
 
-    // Couple the height axis (Z) to the belt-feed axis and stretch the belt-feed
-    // axis by 1/cos so a unit slicing move maps to the correct belt travel.  The
-    // shear sign matches the belt-floor slope derived from the same rotation in
-    // BeltTransformPipeline::compute_belt_height_and_floor:
-    //   tilt about X: feed axis Y, Z += +tan·Y, scale Y *= 1/cos
-    //   tilt about Y: feed axis X, Z += -tan·X, scale X *= 1/cos
+    // This stage runs after the conventional belt axis swap. For an X-axis
+    // slicing rotation, remapped Y is model height and remapped Z is travel
+    // along the belt. Convert those Cartesian coordinates to machine axes with
+    // the established belt-printer convention:
+    //   machine gantry = model height / sin(a)
+    //   machine belt   = model belt + model height * cot(a)
+    // The Y-rotation case is the same mapping on X/Z, with the rotation sign.
+    // At 45 degrees tan/cot and sin/cos are equal, which previously hid the
+    // incorrect complementary-angle formulas used by this unified transform.
     Matrix3d shear = Matrix3d::Identity();
     Matrix3d scale = Matrix3d::Identity();
     if (axis == BeltRotationAxis::X) {
-        shear(2, 1) =  tan_a;   // Z from Y
-        scale(1, 1) =  inv_cos; // Y
+        shear(2, 1) =  cot_a;   // Z from Y
+        scale(1, 1) =  inv_sin; // Y
     } else { // BeltRotationAxis::Y
-        shear(2, 0) = -tan_a;   // Z from X
-        scale(0, 0) =  inv_cos; // X
+        shear(2, 0) = -cot_a;   // Z from X
+        scale(0, 0) =  inv_sin; // X
     }
 
     // Apply shear first, then scale (the historical default ShearThenScale order:
     // result = scale * shear * p).  For the canonical 45°/X belt this maps
-    // (x,y,z) -> (x, y/cos, y + z), matching the previous per-axis config.
+    // (x,y,z) -> (x, y/sin, y + z), matching the previous per-axis config.
     Transform3d combined = Transform3d::Identity();
     combined.linear() = scale * shear;
 

src/libslic3r/GCode/MachineFrameTransform.hpp

@@ -15,7 +15,7 @@ namespace Slic3r {
 //
 // Derived entirely from the single belt tilt (belt_slice_rotation axis +
 // belt_slice_rotation_angle): a shear coupling the height axis to the belt-feed
-// axis (factor tan a) plus a 1/cos a scale on the belt-feed axis.  The expert
+// axis (factor cot a) plus a 1/sin a scale on the gantry-height axis.  The expert
 // belt_frame_tilt_decouple flag lets the machine-frame angle differ from the
 // pre-slice rotation angle via belt_frame_tilt_angle.
 class MachineFrameTransform

src/libslic3r/PrintConfig.cpp

@@ -7216,9 +7216,9 @@ void PrintConfigDef::init_fff_params()
     def = this->add("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->tooltip = L("Undo the pre-slice mesh transform before applying the G-code axis remap "
+                      "and machine-frame shear/scale. Required for the standard belt-printer "
+                      "rotation pipeline.");
     def->mode = comExpert;
     def->set_default_value(new ConfigOptionBool(true));