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@@ -4,7 +4,8 @@
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Copyright (c) 2009-2011 Simen Svale Skogsrud
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Copyright (c) 2011 Sungeun K. Jeon
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-
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+ Copyright (c) 2020 Brad Hochgesang
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+
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Grbl is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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@@ -25,121 +26,140 @@
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// The arc is approximated by generating a huge number of tiny, linear segments. The length of each
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// segment is configured in settings.mm_per_arc_segment.
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-void mc_arc(float *position, float *target, float *offset, uint8_t axis_0, uint8_t axis_1,
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- uint8_t axis_linear, float feed_rate, float radius, bool isclockwise, uint8_t extruder)
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-{
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- // int acceleration_manager_was_enabled = plan_is_acceleration_manager_enabled();
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- // plan_set_acceleration_manager_enabled(false); // disable acceleration management for the duration of the arc
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- float center_axis0 = position[axis_0] + offset[axis_0];
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- float center_axis1 = position[axis_1] + offset[axis_1];
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- float linear_travel = target[axis_linear] - position[axis_linear];
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- float extruder_travel = target[E_AXIS] - position[E_AXIS];
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- float r_axis0 = -offset[axis_0]; // Radius vector from center to current location
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- float r_axis1 = -offset[axis_1];
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- float rt_axis0 = target[axis_0] - center_axis0;
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- float rt_axis1 = target[axis_1] - center_axis1;
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-
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- // CCW angle between position and target from circle center. Only one atan2() trig computation required.
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- float angular_travel = atan2(r_axis0*rt_axis1-r_axis1*rt_axis0, r_axis0*rt_axis0+r_axis1*rt_axis1);
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- if (angular_travel < 0) { angular_travel += 2*M_PI; }
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- if (isclockwise) { angular_travel -= 2*M_PI; }
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-
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- //20141002:full circle for G03 did not work, e.g. G03 X80 Y80 I20 J0 F2000 is giving an Angle of zero so head is not moving
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- //to compensate when start pos = target pos && angle is zero -> angle = 2Pi
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- if (position[axis_0] == target[axis_0] && position[axis_1] == target[axis_1] && angular_travel == 0)
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- {
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- angular_travel += 2*M_PI;
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- }
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- //end fix G03
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-
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- float millimeters_of_travel = hypot(angular_travel*radius, fabs(linear_travel));
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- if (millimeters_of_travel < 0.001) { return; }
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- uint16_t segments = floor(millimeters_of_travel/MM_PER_ARC_SEGMENT);
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- if(segments == 0) segments = 1;
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-
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- /*
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- // Multiply inverse feed_rate to compensate for the fact that this movement is approximated
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- // by a number of discrete segments. The inverse feed_rate should be correct for the sum of
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- // all segments.
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- if (invert_feed_rate) { feed_rate *= segments; }
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- */
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- float theta_per_segment = angular_travel/segments;
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- float linear_per_segment = linear_travel/segments;
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- float extruder_per_segment = extruder_travel/segments;
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-
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- /* Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector,
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- and phi is the angle of rotation. Based on the solution approach by Jens Geisler.
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- r_T = [cos(phi) -sin(phi);
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- sin(phi) cos(phi] * r ;
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-
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- For arc generation, the center of the circle is the axis of rotation and the radius vector is
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- defined from the circle center to the initial position. Each line segment is formed by successive
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- vector rotations. This requires only two cos() and sin() computations to form the rotation
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- matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since
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- all double numbers are single precision on the Arduino. (True double precision will not have
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- round off issues for CNC applications.) Single precision error can accumulate to be greater than
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- tool precision in some cases. Therefore, arc path correction is implemented.
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-
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- Small angle approximation may be used to reduce computation overhead further. This approximation
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- holds for everything, but very small circles and large mm_per_arc_segment values. In other words,
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- theta_per_segment would need to be greater than 0.1 rad and N_ARC_CORRECTION would need to be large
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- to cause an appreciable drift error. N_ARC_CORRECTION~=25 is more than small enough to correct for
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- numerical drift error. N_ARC_CORRECTION may be on the order a hundred(s) before error becomes an
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- issue for CNC machines with the single precision Arduino calculations.
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-
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- This approximation also allows mc_arc to immediately insert a line segment into the planner
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- without the initial overhead of computing cos() or sin(). By the time the arc needs to be applied
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- a correction, the planner should have caught up to the lag caused by the initial mc_arc overhead.
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- This is important when there are successive arc motions.
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- */
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- // Vector rotation matrix values
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- float cos_T = 1-0.5*theta_per_segment*theta_per_segment; // Small angle approximation
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- float sin_T = theta_per_segment;
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-
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- float arc_target[4];
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- float sin_Ti;
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- float cos_Ti;
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- float r_axisi;
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- uint16_t i;
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- int8_t count = 0;
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-
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- // Initialize the linear axis
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- arc_target[axis_linear] = position[axis_linear];
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-
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- // Initialize the extruder axis
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- arc_target[E_AXIS] = position[E_AXIS];
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-
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- for (i = 1; i<segments; i++) { // Increment (segments-1)
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-
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- if (count < N_ARC_CORRECTION) {
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- // Apply vector rotation matrix
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- r_axisi = r_axis0*sin_T + r_axis1*cos_T;
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- r_axis0 = r_axis0*cos_T - r_axis1*sin_T;
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- r_axis1 = r_axisi;
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- count++;
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- } else {
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- // Arc correction to radius vector. Computed only every N_ARC_CORRECTION increments.
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- // Compute exact location by applying transformation matrix from initial radius vector(=-offset).
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- cos_Ti = cos(i*theta_per_segment);
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- sin_Ti = sin(i*theta_per_segment);
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- r_axis0 = -offset[axis_0]*cos_Ti + offset[axis_1]*sin_Ti;
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- r_axis1 = -offset[axis_0]*sin_Ti - offset[axis_1]*cos_Ti;
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- count = 0;
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+void mc_arc(float* position, float* target, float* offset, float feed_rate, float radius, uint8_t isclockwise, uint8_t extruder)
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+{
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+ // Extract the position to reduce indexing at the cost of a few bytes of mem
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+ float p_x = position[X_AXIS];
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+ float p_y = position[Y_AXIS];
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+ float p_z = position[Z_AXIS];
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+ float p_e = position[E_AXIS];
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+
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+ float t_x = target[X_AXIS];
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+ float t_y = target[Y_AXIS];
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+ float t_z = target[Z_AXIS];
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+ float t_e = target[E_AXIS];
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+
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+ float r_axis_x = -offset[X_AXIS]; // Radius vector from center to current location
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+ float r_axis_y = -offset[Y_AXIS];
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+ float center_axis_x = p_x - r_axis_x;
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+ float center_axis_y = p_y - r_axis_y;
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+ float travel_z = t_z - p_z;
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+ float extruder_travel_total = t_e - p_e;
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+
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+ float rt_x = t_x - center_axis_x;
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+ float rt_y = t_y - center_axis_y;
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+ // 20200419 - Add a variable that will be used to hold the arc segment length
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+ float mm_per_arc_segment = cs.mm_per_arc_segment;
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+
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+ // CCW angle between position and target from circle center. Only one atan2() trig computation required.
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+ float angular_travel_total = atan2(r_axis_x * rt_y - r_axis_y * rt_x, r_axis_x * rt_x + r_axis_y * rt_y);
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+ if (angular_travel_total < 0) { angular_travel_total += 2 * M_PI; }
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+
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+ bool check_mm_per_arc_segment_max = false;
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+ if (cs.min_arc_segments > 0)
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+ {
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+ // 20200417 - FormerLurker - Implement MIN_ARC_SEGMENTS if it is defined - from Marlin 2.0 implementation
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+ // Do this before converting the angular travel for clockwise rotation
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+ mm_per_arc_segment = radius * ((2.0f * M_PI) / cs.min_arc_segments);
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+ check_mm_per_arc_segment_max = true;
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}
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- // Update arc_target location
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- arc_target[axis_0] = center_axis0 + r_axis0;
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- arc_target[axis_1] = center_axis1 + r_axis1;
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- arc_target[axis_linear] += linear_per_segment;
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- arc_target[E_AXIS] += extruder_per_segment;
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+ if (cs.arc_segments_per_sec > 0)
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+ {
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+ // 20200417 - FormerLurker - Implement MIN_ARC_SEGMENTS if it is defined - from Marlin 2.0 implementation
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+ float mm_per_arc_segment_sec = (feed_rate / 60.0f) * (1.0f / cs.arc_segments_per_sec);
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+ if (mm_per_arc_segment_sec < mm_per_arc_segment)
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+ mm_per_arc_segment = mm_per_arc_segment_sec;
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+ check_mm_per_arc_segment_max = true;
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+ }
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- clamp_to_software_endstops(arc_target);
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- plan_buffer_line(arc_target[X_AXIS], arc_target[Y_AXIS], arc_target[Z_AXIS], arc_target[E_AXIS], feed_rate, extruder);
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-
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- }
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- // Ensure last segment arrives at target location.
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- plan_buffer_line(target[X_AXIS], target[Y_AXIS], target[Z_AXIS], target[E_AXIS], feed_rate, extruder);
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+ if (cs.min_mm_per_arc_segment > 0)
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+ {
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+ check_mm_per_arc_segment_max = true;
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+ // 20200417 - FormerLurker - Implement MIN_MM_PER_ARC_SEGMENT if it is defined
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+ // This prevents a very high number of segments from being generated for curves of a short radius
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+ if (mm_per_arc_segment < cs.min_mm_per_arc_segment) mm_per_arc_segment = cs.min_mm_per_arc_segment;
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+ }
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+
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+ if (check_mm_per_arc_segment_max && mm_per_arc_segment > cs.mm_per_arc_segment) mm_per_arc_segment = cs.mm_per_arc_segment;
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- // plan_set_acceleration_manager_enabled(acceleration_manager_was_enabled);
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-}
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+
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+ // Adjust the angular travel if the direction is clockwise
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+ if (isclockwise) { angular_travel_total -= 2 * M_PI; }
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+
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+ //20141002:full circle for G03 did not work, e.g. G03 X80 Y80 I20 J0 F2000 is giving an Angle of zero so head is not moving
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+ //to compensate when start pos = target pos && angle is zero -> angle = 2Pi
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+ if (p_x == t_x && p_y == t_y && angular_travel_total == 0)
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+ {
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+ angular_travel_total += 2 * M_PI;
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+ }
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+ //end fix G03
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+
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+ // 20200417 - FormerLurker - rename millimeters_of_travel to millimeters_of_travel_arc to better describe what we are
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+ // calculating here
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+ float millimeters_of_travel_arc = hypot(angular_travel_total * radius, fabs(travel_z));
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+ if (millimeters_of_travel_arc < 0.001) { return; }
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+ // Calculate the total travel per segment
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+ // Calculate the number of arc segments
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+ uint16_t segments = static_cast<uint16_t>(ceil(millimeters_of_travel_arc / mm_per_arc_segment));
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+
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+
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+ // Calculate theta per segments and linear (z) travel per segment
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+ float theta_per_segment = angular_travel_total / segments;
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+ float linear_per_segment = travel_z / (segments);
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+ // Calculate the extrusion amount per segment
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+ float segment_extruder_travel = extruder_travel_total / (segments);
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+ /* Vector rotation by transformation matrix: r is the original vector, r_T is the rotated vector,
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+ and phi is the angle of rotation. Based on the solution approach by Jens Geisler.
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+ r_T = [cos(phi) -sin(phi);
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+ sin(phi) cos(phi] * r ;
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+
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+ For arc generation, the center of the circle is the axis of rotation and the radius vector is
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+ defined from the circle center to the initial position. Each line segment is formed by successive
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+ vector rotations. This requires only two cos() and sin() computations to form the rotation
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+ matrix for the duration of the entire arc. Error may accumulate from numerical round-off, since
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+ all double numbers are single precision on the Arduino. (True double precision will not have
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+ round off issues for CNC applications.) Single precision error can accumulate to be greater than
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+ tool precision in some cases. Therefore, arc path correction is implemented.
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+
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+ The small angle approximation was removed because of excessive errors for small circles (perhaps unique to
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+ 3d printing applications, causing significant path deviation and extrusion issues).
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+ Now there will be no corrections applied, but an accurate initial sin and cos will be calculated.
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+ This seems to work with a very high degree of accuracy and results in much simpler code.
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+
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+ Finding a faster way to approximate sin, knowing that there can be substantial deviations from the true
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+ arc when using the previous approximation, would be beneficial.
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+ */
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+
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+ // Don't bother calculating cot_T or sin_T if there is only 1 segment.
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+ if (segments > 1)
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+ {
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+ // Initialize the extruder axis
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+
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+ float cos_T = cos(theta_per_segment);
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+ float sin_T = sin(theta_per_segment);
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+ float r_axisi;
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+ uint16_t i;
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+
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+ for (i = 1; i < segments; i++) { // Increment (segments-1)
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+ r_axisi = r_axis_x * sin_T + r_axis_y * cos_T;
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+ r_axis_x = r_axis_x * cos_T - r_axis_y * sin_T;
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+ r_axis_y = r_axisi;
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+
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+ // Update arc_target location
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+ p_x = center_axis_x + r_axis_x;
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+ p_y = center_axis_y + r_axis_y;
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+ p_z += linear_per_segment;
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+ p_e += segment_extruder_travel;
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+ // We can't clamp to the target because we are interpolating! We would need to update a position, clamp to it
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+ // after updating from calculated values.
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+ //clamp_to_software_endstops(position);
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+ plan_buffer_line(p_x, p_y, p_z, p_e, feed_rate, extruder);
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+ }
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+ }
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+ // Ensure last segment arrives at target location.
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+ // Here we could clamp, but why bother. We would need to update our current position, clamp to it
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+ //clamp_to_software_endstops(target);
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+ plan_buffer_line(t_x, t_y, t_z, t_e, feed_rate, extruder);
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+}
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