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- /**
- * Marlin 3D Printer Firmware
- * Copyright (c) 2020 MarlinFirmware [https://github.com/MarlinFirmware/Marlin]
- *
- * Based on Sprinter and grbl.
- * Copyright (c) 2011 Camiel Gubbels / Erik van der Zalm
- *
- * This program is free software: you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation, either version 3 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program. If not, see <http://www.gnu.org/licenses/>.
- *
- */
-
- #include "../../inc/MarlinConfig.h"
-
- #if ENABLED(ARC_SUPPORT)
-
- #include "../gcode.h"
- #include "../../module/motion.h"
- #include "../../module/planner.h"
- #include "../../module/temperature.h"
-
- #if ENABLED(DELTA)
- #include "../../module/delta.h"
- #elif ENABLED(SCARA)
- #include "../../module/scara.h"
- #endif
-
- #if N_ARC_CORRECTION < 1
- #undef N_ARC_CORRECTION
- #define N_ARC_CORRECTION 1
- #endif
-
- /**
- * Plan an arc in 2 dimensions
- *
- * The arc is approximated by generating many small linear segments.
- * The length of each segment is configured in MM_PER_ARC_SEGMENT (Default 1mm)
- * Arcs should only be made relatively large (over 5mm), as larger arcs with
- * larger segments will tend to be more efficient. Your slicer should have
- * options for G2/G3 arc generation. In future these options may be GCode tunable.
- */
- void plan_arc(
- const xyze_pos_t &cart, // Destination position
- const ab_float_t &offset, // Center of rotation relative to current_position
- const uint8_t clockwise // Clockwise?
- ) {
- #if ENABLED(CNC_WORKSPACE_PLANES)
- AxisEnum p_axis, q_axis, l_axis;
- switch (gcode.workspace_plane) {
- default:
- case GcodeSuite::PLANE_XY: p_axis = X_AXIS; q_axis = Y_AXIS; l_axis = Z_AXIS; break;
- case GcodeSuite::PLANE_YZ: p_axis = Y_AXIS; q_axis = Z_AXIS; l_axis = X_AXIS; break;
- case GcodeSuite::PLANE_ZX: p_axis = Z_AXIS; q_axis = X_AXIS; l_axis = Y_AXIS; break;
- }
- #else
- constexpr AxisEnum p_axis = X_AXIS, q_axis = Y_AXIS, l_axis = Z_AXIS;
- #endif
-
- // Radius vector from center to current location
- ab_float_t rvec = -offset;
-
- const float radius = HYPOT(rvec.a, rvec.b),
- #if ENABLED(AUTO_BED_LEVELING_UBL)
- start_L = current_position[l_axis],
- #endif
- center_P = current_position[p_axis] - rvec.a,
- center_Q = current_position[q_axis] - rvec.b,
- rt_X = cart[p_axis] - center_P,
- rt_Y = cart[q_axis] - center_Q,
- linear_travel = cart[l_axis] - current_position[l_axis],
- extruder_travel = cart.e - current_position.e;
-
- // CCW angle of rotation between position and target from the circle center. Only one atan2() trig computation required.
- float angular_travel = ATAN2(rvec.a * rt_Y - rvec.b * rt_X, rvec.a * rt_X + rvec.b * rt_Y);
- if (angular_travel < 0) angular_travel += RADIANS(360);
- #ifdef MIN_ARC_SEGMENTS
- uint16_t min_segments = CEIL((MIN_ARC_SEGMENTS) * (angular_travel / RADIANS(360)));
- NOLESS(min_segments, 1U);
- #else
- constexpr uint16_t min_segments = 1;
- #endif
- if (clockwise) angular_travel -= RADIANS(360);
-
- // Make a circle if the angular rotation is 0 and the target is current position
- if (angular_travel == 0 && current_position[p_axis] == cart[p_axis] && current_position[q_axis] == cart[q_axis]) {
- angular_travel = RADIANS(360);
- #ifdef MIN_ARC_SEGMENTS
- min_segments = MIN_ARC_SEGMENTS;
- #endif
- }
-
- const float flat_mm = radius * angular_travel,
- mm_of_travel = linear_travel ? HYPOT(flat_mm, linear_travel) : ABS(flat_mm);
- if (mm_of_travel < 0.001f) return;
-
- const feedRate_t scaled_fr_mm_s = MMS_SCALED(feedrate_mm_s);
-
- #ifdef ARC_SEGMENTS_PER_R
- float seg_length = MM_PER_ARC_SEGMENT * radius;
- LIMIT(seg_length, MM_PER_ARC_SEGMENT, ARC_SEGMENTS_PER_R);
- #elif ARC_SEGMENTS_PER_SEC
- float seg_length = scaled_fr_mm_s * RECIPROCAL(ARC_SEGMENTS_PER_SEC);
- NOLESS(seg_length, MM_PER_ARC_SEGMENT);
- #else
- constexpr float seg_length = MM_PER_ARC_SEGMENT;
- #endif
- uint16_t segments = FLOOR(mm_of_travel / seg_length);
- NOLESS(segments, min_segments);
-
- /**
- * Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector,
- * and phi is the angle of rotation. Based on the solution approach by Jens Geisler.
- * r_T = [cos(phi) -sin(phi);
- * sin(phi) cos(phi)] * r ;
- *
- * For arc generation, the center of the circle is the axis of rotation and the radius vector is
- * defined from the circle center to the initial position. Each line segment is formed by successive
- * vector rotations. This requires only two cos() and sin() computations to form the rotation
- * matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since
- * all double numbers are single precision on the Arduino. (True double precision will not have
- * round off issues for CNC applications.) Single precision error can accumulate to be greater than
- * tool precision in some cases. Therefore, arc path correction is implemented.
- *
- * Small angle approximation may be used to reduce computation overhead further. This approximation
- * holds for everything, but very small circles and large MM_PER_ARC_SEGMENT values. In other words,
- * theta_per_segment would need to be greater than 0.1 rad and N_ARC_CORRECTION would need to be large
- * to cause an appreciable drift error. N_ARC_CORRECTION~=25 is more than small enough to correct for
- * numerical drift error. N_ARC_CORRECTION may be on the order a hundred(s) before error becomes an
- * issue for CNC machines with the single precision Arduino calculations.
- *
- * This approximation also allows plan_arc to immediately insert a line segment into the planner
- * without the initial overhead of computing cos() or sin(). By the time the arc needs to be applied
- * a correction, the planner should have caught up to the lag caused by the initial plan_arc overhead.
- * This is important when there are successive arc motions.
- */
- // Vector rotation matrix values
- xyze_pos_t raw;
- const float theta_per_segment = angular_travel / segments,
- linear_per_segment = linear_travel / segments,
- extruder_per_segment = extruder_travel / segments,
- sin_T = theta_per_segment,
- cos_T = 1 - 0.5f * sq(theta_per_segment); // Small angle approximation
-
- // Initialize the linear axis
- raw[l_axis] = current_position[l_axis];
-
- // Initialize the extruder axis
- raw.e = current_position.e;
-
-
- #if ENABLED(SCARA_FEEDRATE_SCALING)
- const float inv_duration = scaled_fr_mm_s / seg_length;
- #endif
-
- millis_t next_idle_ms = millis() + 200UL;
-
- #if N_ARC_CORRECTION > 1
- int8_t arc_recalc_count = N_ARC_CORRECTION;
- #endif
-
- for (uint16_t i = 1; i < segments; i++) { // Iterate (segments-1) times
-
- thermalManager.manage_heater();
- if (ELAPSED(millis(), next_idle_ms)) {
- next_idle_ms = millis() + 200UL;
- idle();
- }
-
- #if N_ARC_CORRECTION > 1
- if (--arc_recalc_count) {
- // Apply vector rotation matrix to previous rvec.a / 1
- const float r_new_Y = rvec.a * sin_T + rvec.b * cos_T;
- rvec.a = rvec.a * cos_T - rvec.b * sin_T;
- rvec.b = r_new_Y;
- }
- else
- #endif
- {
- #if N_ARC_CORRECTION > 1
- arc_recalc_count = N_ARC_CORRECTION;
- #endif
-
- // Arc correction to radius vector. Computed only every N_ARC_CORRECTION increments.
- // Compute exact location by applying transformation matrix from initial radius vector(=-offset).
- // To reduce stuttering, the sin and cos could be computed at different times.
- // For now, compute both at the same time.
- const float cos_Ti = cos(i * theta_per_segment), sin_Ti = sin(i * theta_per_segment);
- rvec.a = -offset[0] * cos_Ti + offset[1] * sin_Ti;
- rvec.b = -offset[0] * sin_Ti - offset[1] * cos_Ti;
- }
-
- // Update raw location
- raw[p_axis] = center_P + rvec.a;
- raw[q_axis] = center_Q + rvec.b;
- #if ENABLED(AUTO_BED_LEVELING_UBL)
- raw[l_axis] = start_L;
- UNUSED(linear_per_segment);
- #else
- raw[l_axis] += linear_per_segment;
- #endif
- raw.e += extruder_per_segment;
-
- apply_motion_limits(raw);
-
- #if HAS_LEVELING && !PLANNER_LEVELING
- planner.apply_leveling(raw);
- #endif
-
- if (!planner.buffer_line(raw, scaled_fr_mm_s, active_extruder, seg_length
- #if ENABLED(SCARA_FEEDRATE_SCALING)
- , inv_duration
- #endif
- ))
- break;
- }
-
- // Ensure last segment arrives at target location.
- raw = cart;
- #if ENABLED(AUTO_BED_LEVELING_UBL)
- raw[l_axis] = start_L;
- #endif
-
- apply_motion_limits(raw);
-
- #if HAS_LEVELING && !PLANNER_LEVELING
- planner.apply_leveling(raw);
- #endif
-
- planner.buffer_line(raw, scaled_fr_mm_s, active_extruder, seg_length
- #if ENABLED(SCARA_FEEDRATE_SCALING)
- , inv_duration
- #endif
- );
-
- #if ENABLED(AUTO_BED_LEVELING_UBL)
- raw[l_axis] = start_L;
- #endif
- current_position = raw;
- } // plan_arc
-
- /**
- * G2: Clockwise Arc
- * G3: Counterclockwise Arc
- *
- * This command has two forms: IJ-form (JK, KI) and R-form.
- *
- * - Depending on the current Workspace Plane orientation,
- * use parameters IJ/JK/KI to specify the XY/YZ/ZX offsets.
- * At least one of the IJ/JK/KI parameters is required.
- * XY/YZ/ZX can be omitted to do a complete circle.
- * The given XY/YZ/ZX is not error-checked. The arc ends
- * based on the angle of the destination.
- * Mixing IJ/JK/KI with R will throw an error.
- *
- * - R specifies the radius. X or Y (Y or Z / Z or X) is required.
- * Omitting both XY/YZ/ZX will throw an error.
- * XY/YZ/ZX must differ from the current XY/YZ/ZX.
- * Mixing R with IJ/JK/KI will throw an error.
- *
- * - P specifies the number of full circles to do
- * before the specified arc move.
- *
- * Examples:
- *
- * G2 I10 ; CW circle centered at X+10
- * G3 X20 Y12 R14 ; CCW circle with r=14 ending at X20 Y12
- */
- void GcodeSuite::G2_G3(const bool clockwise) {
- if (MOTION_CONDITIONS) {
-
- #if ENABLED(SF_ARC_FIX)
- const bool relative_mode_backup = relative_mode;
- relative_mode = true;
- #endif
-
- get_destination_from_command();
-
- #if ENABLED(SF_ARC_FIX)
- relative_mode = relative_mode_backup;
- #endif
-
- ab_float_t arc_offset = { 0, 0 };
- if (parser.seenval('R')) {
- const float r = parser.value_linear_units();
- if (r) {
- const xy_pos_t p1 = current_position, p2 = destination;
- if (p1 != p2) {
- const xy_pos_t d2 = (p2 - p1) * 0.5f; // XY vector to midpoint of move from current
- const float e = clockwise ^ (r < 0) ? -1 : 1, // clockwise -1/1, counterclockwise 1/-1
- len = d2.magnitude(), // Distance to mid-point of move from current
- h2 = (r - len) * (r + len), // factored to reduce rounding error
- h = (h2 >= 0) ? SQRT(h2) : 0.0f; // Distance to the arc pivot-point from midpoint
- const xy_pos_t s = { -d2.y, d2.x }; // Perpendicular bisector. (Divide by len for unit vector.)
- arc_offset = d2 + s / len * e * h; // The calculated offset (mid-point if |r| <= len)
- }
- }
- }
- else {
- #if ENABLED(CNC_WORKSPACE_PLANES)
- char achar, bchar;
- switch (gcode.workspace_plane) {
- default:
- case GcodeSuite::PLANE_XY: achar = 'I'; bchar = 'J'; break;
- case GcodeSuite::PLANE_YZ: achar = 'J'; bchar = 'K'; break;
- case GcodeSuite::PLANE_ZX: achar = 'K'; bchar = 'I'; break;
- }
- #else
- constexpr char achar = 'I', bchar = 'J';
- #endif
- if (parser.seenval(achar)) arc_offset.a = parser.value_linear_units();
- if (parser.seenval(bchar)) arc_offset.b = parser.value_linear_units();
- }
-
- if (arc_offset) {
-
- #if ENABLED(ARC_P_CIRCLES)
- // P indicates number of circles to do
- int8_t circles_to_do = parser.byteval('P');
- if (!WITHIN(circles_to_do, 0, 100))
- SERIAL_ERROR_MSG(MSG_ERR_ARC_ARGS);
-
- while (circles_to_do--)
- plan_arc(current_position, arc_offset, clockwise);
- #endif
-
- // Send the arc to the planner
- plan_arc(destination, arc_offset, clockwise);
- reset_stepper_timeout();
- }
- else
- SERIAL_ERROR_MSG(MSG_ERR_ARC_ARGS);
- }
- }
-
- #endif // ARC_SUPPORT
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