继续按 align-linuxcnc 约束：补极坐标源码覆盖，测试通过

test-linuxcnc-source-link.sh

@@ -547,6 +547,35 @@ CNC_SIM_RS274_VAR="$var_file" \
 CNC_SIM_RS274_VAR="$var_file" \
     "$build_dir/linuxcnc_rs274_source_dump" tests/gcode/linuxcnc_arc_distance_modes.ngc \
     >"$output_dir/cnc_sim_linuxcnc_source_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_source_dump" tests/gcode/linuxcnc_polar_coordinates.ngc \
+    >"$output_dir/cnc_sim_linuxcnc_source_polar_coordinates.json"
+polar_coordinate_error_cases=(
+    "linuxcnc_polar_g18_error|Cannot use polar coordinate except in G17 plane"
+    "linuxcnc_polar_with_x_error|Cannot specify both polar coordinate and X word"
+    "linuxcnc_polar_with_y_error|Cannot specify both polar coordinate and Y word"
+    "linuxcnc_polar_g92_error|Polar coordinates can only be used for motion"
+    "linuxcnc_polar_g53_error|Cannot use polar coordinates with G53"
+    "linuxcnc_polar_radius_origin_error|Must specify angle in polar coordinate if at the origin"
+    "linuxcnc_polar_incremental_radius_origin_error|Incremental motion with polar coordinates is indeterminate when at the origin"
+    "linuxcnc_polar_incremental_theta_origin_error|G91 motion with polar coordinates is indeterminate when at the origin"
+)
+for case in "${polar_coordinate_error_cases[@]}"; do
+    fixture=${case%%|*}
+    expected=${case#*|}
+    if CNC_SIM_RS274_VAR="$var_file" \
+        "$build_dir/linuxcnc_rs274_source_dump" "tests/gcode/$fixture.ngc" \
+        >"$output_dir/cnc_sim_linuxcnc_source_$fixture.json" 2>"$output_dir/cnc_sim_linuxcnc_source_$fixture.err"; then
+        echo "expected $fixture.ngc to fail" >&2
+        exit 1
+    fi
+    grep -Fq "$expected" "$output_dir/cnc_sim_linuxcnc_source_$fixture.err"
+done
 CNC_SIM_RS274_VAR="$var_file" \
     "$build_dir/linuxcnc_rs274_source_dump" tests/gcode/linuxcnc_predefined_positions.ngc \
     >"$output_dir/cnc_sim_linuxcnc_source_predefined_positions.json"
@@ -2051,6 +2080,25 @@ expected_arc_centers = [(5, 5, 0), (7, 15, 0), (9, 25, 0)]
 if arc_centers != expected_arc_centers:
     raise SystemExit(f"unexpected source-linked G90.1/G91.1 arc centers: {arc_centers!r}")
 
+polar_coordinates = json.loads((OUTPUT_DIR / "cnc_sim_linuxcnc_source_polar_coordinates.json").read_text())
+polar_linear_events = [
+    event
+    for event in polar_coordinates
+    if event["type"] == "linear-feed"
+]
+expected_polar_linear_ends = [(3, 10, 0), (4, 0, 10)]
+if len(polar_linear_events) != len(expected_polar_linear_ends) or any(
+    event["line"] != line or
+    abs(event["end"]["x"] - x) > 1e-9 or
+    abs(event["end"]["y"] - y) > 1e-9
+    for event, (line, x, y) in zip(polar_linear_events, expected_polar_linear_ends)
+):
+    polar_linear_ends = [
+        (event["line"], event["end"]["x"], event["end"]["y"])
+        for event in polar_linear_events
+    ]
+    raise SystemExit(f"unexpected source-linked polar-coordinate endpoints: {polar_linear_ends!r}")
+
 predefined = json.loads((OUTPUT_DIR / "cnc_sim_linuxcnc_source_predefined_positions.json").read_text())
 predefined_rapids = [
     (

test-native.sh

@@ -145,6 +145,8 @@ grep -F 'convert_lathe_diameter_mode() scales G7/G8 X words and G76 I/J/K words'
 grep -F 'tests/gcode/linuxcnc_lathe_diameter_mode.ngc' docs/linuxcnc-porting.md >/dev/null
 grep -F 'tests/gcode/linuxcnc_lathe_diameter_g76.ngc' docs/linuxcnc-porting.md >/dev/null
 grep -F 'missing source-linked G7 diameter-mode G76 final threading pass' test-linuxcnc-source-link.sh >/dev/null
+grep -F 'read_atsign()' test-linuxcnc-source-link.sh >/dev/null
+grep -F 'tests/gcode/linuxcnc_polar_coordinates.ngc' test-linuxcnc-source-link.sh >/dev/null
 grep -F 'lookup_named_param()' test-linuxcnc-rs274-native.sh >/dev/null
 grep -F 'tests/gcode/linuxcnc_readonly_named_parameters.ngc' docs/linuxcnc-porting.md >/dev/null
 grep -F 'rs274ngc_pre.cc ini_load() consumes INI_FILE_NAME' test-web-wasm-node-smoke.cjs >/dev/null

tests/gcode/linuxcnc_polar_coordinates.ngc

@@ -0,0 +1,5 @@
+G21 G90 G17
+G0 X0 Y0 Z0
+G1 @10 ^0 F100
+G1 @10 ^90
+M30

tests/gcode/linuxcnc_polar_g18_error.ngc

@@ -0,0 +1,3 @@
+G21 G90 G18
+G1 @10 ^45 F100
+M30

tests/gcode/linuxcnc_polar_g53_error.ngc

@@ -0,0 +1,3 @@
+G21 G90 G17
+G53 G1 @10 ^45 F100
+M30

tests/gcode/linuxcnc_polar_g92_error.ngc

@@ -0,0 +1,3 @@
+G21 G90 G17
+G92 @10 ^45
+M30

tests/gcode/linuxcnc_polar_incremental_radius_origin_error.ngc

@@ -0,0 +1,3 @@
+G21 G91 G17
+G1 @10 F100
+M30

tests/gcode/linuxcnc_polar_incremental_theta_origin_error.ngc

@@ -0,0 +1,3 @@
+G21 G91 G17
+G1 ^45 F100
+M30

tests/gcode/linuxcnc_polar_radius_origin_error.ngc

@@ -0,0 +1,3 @@
+G21 G90 G17
+G1 @10 F100
+M30

tests/gcode/linuxcnc_polar_with_x_error.ngc

@@ -0,0 +1,3 @@
+G21 G90 G17
+G1 X1 @10 ^45 F100
+M30

tests/gcode/linuxcnc_polar_with_y_error.ngc

@@ -0,0 +1,3 @@
+G21 G90 G17
+G1 Y1 @10 ^45 F100
+M30