继续按 align-linuxcnc 约束：补极坐标 native 覆盖，测试通过

结论：补齐 LinuxCNC interp_read.cc、interp_internal.cc、interp_find.cc 极坐标路径，以及 interp_convert.cc 扩展平面 arc/NURBS 错误 fixture 的 native 校验；./test-native.sh 与 ./test-linuxcnc-source-link.sh 均通过，未扩展 smoke。

docs/linuxcnc-porting.md

@@ -191,6 +191,7 @@ This matrix tracks LinuxCNC feature coverage for the web/WASM simulator. A featu
 | Area | Status | Regression |
 | --- | --- | --- |
 | Basic modal motion `G0/G1/G2/G3` | covered, including `G91` incremental linear motion, R-format arcs, `G18`/`G19` arc plane mapping, and `G90.1`/`G91.1` IJK modes | `tests/gcode/linuxcnc_basic_motion.ngc`, `tests/gcode/basic_mill.ngc`, `tests/gcode/incremental_and_r_arc.ngc`, `tests/gcode/linuxcnc_arc_planes.ngc`, `tests/gcode/linuxcnc_arc_distance_modes.ngc` |
+| Polar coordinates and extended-plane motion restrictions | covered through LinuxCNC native/source `@`/`^` polar parsing, G17-only polar motion validation, absolute/incremental polar endpoint mapping, G53/origin rejection, and extended-plane arc/NURBS rejection | `tests/gcode/linuxcnc_polar_coordinates.ngc`, `tests/gcode/linuxcnc_polar_coordinate_variants.ngc`, `tests/gcode/linuxcnc_polar_g18_error.ngc`, `tests/gcode/linuxcnc_polar_with_x_error.ngc`, `tests/gcode/linuxcnc_polar_with_y_error.ngc`, `tests/gcode/linuxcnc_polar_g92_error.ngc`, `tests/gcode/linuxcnc_polar_g53_error.ngc`, `tests/gcode/linuxcnc_polar_radius_origin_error.ngc`, `tests/gcode/linuxcnc_polar_incremental_radius_origin_error.ngc`, `tests/gcode/linuxcnc_polar_incremental_theta_origin_error.ngc`, `tests/gcode/linuxcnc_extended_plane_arc_error.ngc`, `tests/gcode/linuxcnc_g62_extended_plane_error.ngc` |
 | Block-level axis/motion validation | covered through LinuxCNC native/source `enhance_block()` checks for invalid `G80` axes, missing `G52/G92` or motion axes, bare axes without active motion, and modal-0 axis consumers on motion blocks | `tests/gcode/linuxcnc_g80_axis_error.ngc`, `tests/gcode/linuxcnc_g52_missing_axis_error.ngc`, `tests/gcode/linuxcnc_g92_missing_axis_error.ngc`, `tests/gcode/linuxcnc_motion_missing_axis_error.ngc`, `tests/gcode/linuxcnc_axis_without_motion_error.ngc`, `tests/gcode/linuxcnc_motion_with_g92_axis_error.ngc` |
 | Predefined position moves `G28/G28.1`, `G30/G30.1` | covered for stored position, waypoint, selected-axis return, and all-axis return | `tests/gcode/linuxcnc_predefined_positions.ngc` |
 | Machine-coordinate move `G53` | covered for explicit/modal `G0`, `G1`, arc rejection, and incremental-mode rejection through LinuxCNC native/source backends | `tests/gcode/linuxcnc_machine_coordinates.ngc`, `tests/gcode/linuxcnc_g53_arc_error.ngc`, `tests/gcode/linuxcnc_g53_incremental_error.ngc` |

test-linuxcnc-rs274-native.sh

@@ -478,6 +478,52 @@ CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linux
 CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_canned_cycle_planes.ngc >"$output_dir/cnc_sim_linuxcnc_canned_cycle_planes.json"
 CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_arc_planes.ngc >"$output_dir/cnc_sim_linuxcnc_arc_planes.json"
 CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_arc_distance_modes.ngc >"$output_dir/cnc_sim_linuxcnc_arc_distance_modes.json"
+# Source basis: LinuxCNC src/emc/rs274ngc/interp_read.cc read_atsign()
+# and read_carat() parse @/^ polar words; src/emc/rs274ngc/interp_internal.cc
+# enhance_block() restricts polar coordinates to G17 motion without X/Y words;
+# src/emc/rs274ngc/interp_find.cc find_ends() maps absolute polar radius/angle
+# to XY endpoints and rejects G53 or origin-indeterminate polar motions.
+CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_polar_coordinates.ngc >"$output_dir/cnc_sim_linuxcnc_polar_coordinates.json"
+CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_polar_coordinate_variants.ngc >"$output_dir/cnc_sim_linuxcnc_polar_coordinate_variants.json"
+polar_coordinate_error_cases=(
+    "linuxcnc_polar_g18_error|Cannot use polar coordinate except in G17 plane"
+    "linuxcnc_polar_with_x_error|Cannot specify both polar coordinate and X word"
+    "linuxcnc_polar_with_y_error|Cannot specify both polar coordinate and Y word"
+    "linuxcnc_polar_g92_error|Polar coordinates can only be used for motion"
+    "linuxcnc_polar_g53_error|Cannot use polar coordinates with G53"
+    "linuxcnc_polar_radius_origin_error|Must specify angle in polar coordinate if at the origin"
+    "linuxcnc_polar_incremental_radius_origin_error|Incremental motion with polar coordinates is indeterminate when at the origin"
+    "linuxcnc_polar_incremental_theta_origin_error|G91 motion with polar coordinates is indeterminate when at the origin"
+)
+for case in "${polar_coordinate_error_cases[@]}"; do
+    fixture=${case%%|*}
+    expected=${case#*|}
+    if CNC_SIM_RS274_VAR="$var_file" \
+        "$build_dir/linuxcnc_rs274_dump" "tests/gcode/$fixture.ngc" \
+        >"$output_dir/cnc_sim_linuxcnc_$fixture.json" 2>"$output_dir/cnc_sim_linuxcnc_$fixture.err"; then
+        echo "expected $fixture.ngc to fail" >&2
+        exit 1
+    fi
+    grep -Fq "$expected" "$output_dir/cnc_sim_linuxcnc_$fixture.err"
+done
+# Source basis: LinuxCNC src/emc/rs274ngc/interp_convert.cc convert_arc()
+# rejects arcs in extended planes, and convert_nurbs() requires canonical
+# XY/YZ/ZX planes before NURBS setup.
+extended_plane_error_cases=(
+    "linuxcnc_extended_plane_arc_error|Cannot do an arc in planes G17.1, G18.1, or G19.1"
+    "linuxcnc_g62_extended_plane_error|one plane must be selected for nurbs: XY, YZ, ZX"
+)
+for case in "${extended_plane_error_cases[@]}"; do
+    fixture=${case%%|*}
+    expected=${case#*|}
+    if CNC_SIM_RS274_VAR="$var_file" \
+        "$build_dir/linuxcnc_rs274_dump" "tests/gcode/$fixture.ngc" \
+        >"$output_dir/cnc_sim_linuxcnc_$fixture.json" 2>"$output_dir/cnc_sim_linuxcnc_$fixture.err"; then
+        echo "expected $fixture.ngc to fail" >&2
+        exit 1
+    fi
+    grep -Fq "$expected" "$output_dir/cnc_sim_linuxcnc_$fixture.err"
+done
 CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_predefined_positions.ngc >"$output_dir/cnc_sim_linuxcnc_predefined_positions.json"
 CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_machine_coordinates.ngc >"$output_dir/cnc_sim_linuxcnc_machine_coordinates.json"
 CNC_SIM_RS274_VAR="$var_file" "$build_dir/linuxcnc_rs274_dump" tests/gcode/linuxcnc_cutter_comp.ngc >"$output_dir/cnc_sim_linuxcnc_cutter_comp.json"