Add support for G2/G3 with R parameter

Marlin/Marlin_main.cpp

@@ -2511,6 +2511,25 @@ inline void gcode_G0_G1() {
 /**
  * G2: Clockwise Arc
  * G3: Counterclockwise Arc
+ *
+ * This command has two forms: IJ-form and R-form.
+ *
+ *  - I specifies an X offset. J specifies a Y offset.
+ *    At least one of the IJ parameters is required.
+ *    X and Y can be omitted to do a complete circle.
+ *    The given XY is not error-checked. The arc ends
+ *     based on the angle of the destination.
+ *    Mixing I or J with R will throw an error.
+ *
+ *  - R specifies the radius. X or Y is required.
+ *    Omitting both X and Y will throw an error.
+ *    X or Y must differ from the current XY.
+ *    Mixing R with I or J will throw an error.
+ *
+ *  Examples:
+ *
+ *    G2 I10           ; CW circle centered at X+10
+ *    G3 X20 Y12 R14   ; CCW circle with r=14 ending at X20 Y12
  */
 #if ENABLED(ARC_SUPPORT)
   inline void gcode_G2_G3(bool clockwise) {
@@ -2527,17 +2546,39 @@ inline void gcode_G0_G1() {
         relative_mode = relative_mode_backup;
       #endif
 
-      // Center of arc as offset from current_position
-      float arc_offset[2] = {
-        code_seen('I') ? code_value_axis_units(X_AXIS) : 0,
-        code_seen('J') ? code_value_axis_units(Y_AXIS) : 0
-      };
+      float arc_offset[2] = { 0.0, 0.0 };
+      if (code_seen('R')) {
+        const float r = code_value_axis_units(X_AXIS),
+                    x1 = current_position[X_AXIS], y1 = current_position[Y_AXIS],
+                    x2 = destination[X_AXIS], y2 = destination[Y_AXIS];
+        if (r && (x2 != x1 || y2 != y1)) {
+          const float e = clockwise ? -1 : 1,                     // clockwise -1, counterclockwise 1
+                      dx = x2 - x1, dy = y2 - y1,                 // X and Y differences
+                      d = HYPOT(dx, dy),                          // Linear distance between the points
+                      h = sqrt(sq(r) - sq(d * 0.5)),              // Distance to the arc pivot-point
+                      mx = (x1 + x2) * 0.5, my = (y1 + y2) * 0.5, // Point between the two points
+                      sx = -dy / d, sy = dx / d,                  // Slope of the perpendicular bisector
+                      cx = mx + e * h * sx, cy = my + e * h * sy; // Pivot-point of the arc
+          arc_offset[X_AXIS] = cx - x1;
+          arc_offset[Y_AXIS] = cy - y1;
+        }
+      }
+      else {
+        if (code_seen('I')) arc_offset[X_AXIS] = code_value_axis_units(X_AXIS);
+        if (code_seen('J')) arc_offset[Y_AXIS] = code_value_axis_units(Y_AXIS);
+      }
 
+      if (arc_offset[0] || arc_offset[1]) {
         // Send an arc to the planner
         plan_arc(destination, arc_offset, clockwise);
-
         refresh_cmd_timeout();
       }
+      else {
+        // Bad arguments
+        SERIAL_ERROR_START;
+        SERIAL_ERRORLNPGM(MSG_ERR_ARC_ARGS);
+      }
+    }
   }
 #endif
 

Marlin/language.h

@@ -150,6 +150,7 @@
 #define MSG_ERR_MATERIAL_INDEX              "M145 S<index> out of range (0-1)"
 #define MSG_ERR_M421_PARAMETERS             "M421 requires XYZ or IJZ parameters"
 #define MSG_ERR_MESH_XY                     "Mesh XY or IJ cannot be resolved"
+#define MSG_ERR_ARC_ARGS                    "G2/G3 bad parameters"
 #define MSG_ERR_M428_TOO_FAR                "Too far from reference point"
 #define MSG_ERR_M303_DISABLED               "PIDTEMP disabled"
 #define MSG_M119_REPORT                     "Reporting endstop status"