marlin/Marlin/ubl_motion.cpp

/**
 * Marlin 3D Printer Firmware
 * Copyright (C) 2016 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 "MarlinConfig.h"

#if ENABLED(AUTO_BED_LEVELING_UBL)

  #include "Marlin.h"
  #include "ubl.h"
  #include "planner.h"
  #include "stepper.h"
  #include <avr/io.h>
  #include <math.h>

  #if AVR_AT90USB1286_FAMILY  // Teensyduino & Printrboard IDE extensions have compile errors without this
    inline void set_current_from_destination() { COPY(current_position, destination); }
  #else
    extern void set_current_from_destination();
  #endif

  #if !UBL_SEGMENTED

    void unified_bed_leveling::line_to_destination_cartesian(const float &feed_rate, const uint8_t extruder) {
      /**
       * Much of the nozzle movement will be within the same cell. So we will do as little computation
       * as possible to determine if this is the case. If this move is within the same cell, we will
       * just do the required Z-Height correction, call the Planner's buffer_line() routine, and leave
       */
      #if ENABLED(SKEW_CORRECTION)
        // For skew correction just adjust the destination point and we're done
        float start[XYZE] = { current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS], current_position[E_AXIS] },
              end[XYZE] = { destination[X_AXIS], destination[Y_AXIS], destination[Z_AXIS], destination[E_AXIS] };
        planner.skew(start[X_AXIS], start[Y_AXIS], start[Z_AXIS]);
        planner.skew(end[X_AXIS], end[Y_AXIS], end[Z_AXIS]);
      #else
        const float (&start)[XYZE] = current_position,
                      (&end)[XYZE] = destination;
      #endif

      const int cell_start_xi = get_cell_index_x(start[X_AXIS]),
                cell_start_yi = get_cell_index_y(start[Y_AXIS]),
                cell_dest_xi  = get_cell_index_x(end[X_AXIS]),
                cell_dest_yi  = get_cell_index_y(end[Y_AXIS]);

      if (g26_debug_flag) {
        SERIAL_ECHOPAIR(" ubl.line_to_destination_cartesian(xe=", destination[X_AXIS]);
        SERIAL_ECHOPAIR(", ye=", destination[Y_AXIS]);
        SERIAL_ECHOPAIR(", ze=", destination[Z_AXIS]);
        SERIAL_ECHOPAIR(", ee=", destination[E_AXIS]);
        SERIAL_CHAR(')');
        SERIAL_EOL();
        debug_current_and_destination(PSTR("Start of ubl.line_to_destination_cartesian()"));
      }

      if (cell_start_xi == cell_dest_xi && cell_start_yi == cell_dest_yi) { // if the whole move is within the same cell,
        /**
         * we don't need to break up the move
         *
         * If we are moving off the print bed, we are going to allow the move at this level.
         * But we detect it and isolate it. For now, we just pass along the request.
         */

        if (!WITHIN(cell_dest_xi, 0, GRID_MAX_POINTS_X - 1) || !WITHIN(cell_dest_yi, 0, GRID_MAX_POINTS_Y - 1)) {

          // Note: There is no Z Correction in this case. We are off the grid and don't know what
          // a reasonable correction would be.

          planner.buffer_segment(end[X_AXIS], end[Y_AXIS], end[Z_AXIS], end[E_AXIS], feed_rate, extruder);
          set_current_from_destination();

          if (g26_debug_flag)
            debug_current_and_destination(PSTR("out of bounds in ubl.line_to_destination_cartesian()"));

          return;
        }

        FINAL_MOVE:

        /**
         * Optimize some floating point operations here. We could call float get_z_correction(float x0, float y0) to
         * generate the correction for us. But we can lighten the load on the CPU by doing a modified version of the function.
         * We are going to only calculate the amount we are from the first mesh line towards the second mesh line once.
         * We will use this fraction in both of the original two Z Height calculations for the bi-linear interpolation. And,
         * instead of doing a generic divide of the distance, we know the distance is MESH_X_DIST so we can use the preprocessor
         * to create a 1-over number for us. That will allow us to do a floating point multiply instead of a floating point divide.
         */

        const float xratio = (end[X_AXIS] - mesh_index_to_xpos(cell_dest_xi)) * (1.0 / (MESH_X_DIST));

        float z1 = z_values[cell_dest_xi    ][cell_dest_yi    ] + xratio *
                  (z_values[cell_dest_xi + 1][cell_dest_yi    ] - z_values[cell_dest_xi][cell_dest_yi    ]),
              z2 = z_values[cell_dest_xi    ][cell_dest_yi + 1] + xratio *
                  (z_values[cell_dest_xi + 1][cell_dest_yi + 1] - z_values[cell_dest_xi][cell_dest_yi + 1]);

        if (cell_dest_xi >= GRID_MAX_POINTS_X - 1) z1 = z2 = 0.0;

        // we are done with the fractional X distance into the cell. Now with the two Z-Heights we have calculated, we
        // are going to apply the Y-Distance into the cell to interpolate the final Z correction.

        const float yratio = (end[Y_AXIS] - mesh_index_to_ypos(cell_dest_yi)) * (1.0 / (MESH_Y_DIST));
        float z0 = cell_dest_yi < GRID_MAX_POINTS_Y - 1 ? (z1 + (z2 - z1) * yratio) * planner.fade_scaling_factor_for_z(end[Z_AXIS]) : 0.0;

        /**
         * If part of the Mesh is undefined, it will show up as NAN
         * in z_values[][] and propagate through the
         * calculations. If our correction is NAN, we throw it out
         * because part of the Mesh is undefined and we don't have the
         * information we need to complete the height correction.
         */
        if (isnan(z0)) z0 = 0.0;

        planner.buffer_segment(end[X_AXIS], end[Y_AXIS], end[Z_AXIS] + z0, end[E_AXIS], feed_rate, extruder);

        if (g26_debug_flag)
          debug_current_and_destination(PSTR("FINAL_MOVE in ubl.line_to_destination_cartesian()"));

        set_current_from_destination();
        return;
      }

      /**
       * If we get here, we are processing a move that crosses at least one Mesh Line. We will check
       * for the simple case of just crossing X or just crossing Y Mesh Lines after we get all the details
       * of the move figured out. We can process the easy case of just crossing an X or Y Mesh Line with less
       * computation and in fact most lines are of this nature. We will check for that in the following
       * blocks of code:
       */

      const float dx = end[X_AXIS] - start[X_AXIS],
                  dy = end[Y_AXIS] - start[Y_AXIS];

      const int left_flag = dx < 0.0 ? 1 : 0,
                down_flag = dy < 0.0 ? 1 : 0;

      const float adx = left_flag ? -dx : dx,
                  ady = down_flag ? -dy : dy;

      const int dxi = cell_start_xi == cell_dest_xi ? 0 : left_flag ? -1 : 1,
                dyi = cell_start_yi == cell_dest_yi ? 0 : down_flag ? -1 : 1;

      /**
       * Compute the scaling factor for the extruder for each partial move.
       * We need to watch out for zero length moves because it will cause us to
       * have an infinate scaling factor. We are stuck doing a floating point
       * divide to get our scaling factor, but after that, we just multiply by this
       * number. We also pick our scaling factor based on whether the X or Y
       * component is larger. We use the biggest of the two to preserve precision.
       */

      const bool use_x_dist = adx > ady;

      float on_axis_distance = use_x_dist ? dx : dy,
            e_position = end[E_AXIS] - start[E_AXIS],
            z_position = end[Z_AXIS] - start[Z_AXIS];

      const float e_normalized_dist = e_position / on_axis_distance,
                  z_normalized_dist = z_position / on_axis_distance;

      int current_xi = cell_start_xi,
          current_yi = cell_start_yi;

      const float m = dy / dx,
                  c = start[Y_AXIS] - m * start[X_AXIS];

      const bool inf_normalized_flag = (isinf(e_normalized_dist) != 0),
                 inf_m_flag = (isinf(m) != 0);
      /**
       * This block handles vertical lines. These are lines that stay within the same
       * X Cell column. They do not need to be perfectly vertical. They just can
       * not cross into another X Cell column.
       */
      if (dxi == 0) {       // Check for a vertical line
        current_yi += down_flag;  // Line is heading down, we just want to go to the bottom
        while (current_yi != cell_dest_yi + down_flag) {
          current_yi += dyi;
          const float next_mesh_line_y = mesh_index_to_ypos(current_yi);

          /**
           * if the slope of the line is infinite, we won't do the calculations
           * else, we know the next X is the same so we can recover and continue!
           * Calculate X at the next Y mesh line
           */
          const float rx = inf_m_flag ? start[X_AXIS] : (next_mesh_line_y - c) / m;

          float z0 = z_correction_for_x_on_horizontal_mesh_line(rx, current_xi, current_yi)
                     * planner.fade_scaling_factor_for_z(end[Z_AXIS]);

          /**
           * If part of the Mesh is undefined, it will show up as NAN
           * in z_values[][] and propagate through the
           * calculations. If our correction is NAN, we throw it out
           * because part of the Mesh is undefined and we don't have the
           * information we need to complete the height correction.
           */
          if (isnan(z0)) z0 = 0.0;

          const float ry = mesh_index_to_ypos(current_yi);

          /**
           * Without this check, it is possible for the algorithm to generate a zero length move in the case
           * where the line is heading down and it is starting right on a Mesh Line boundary. For how often that
           * happens, it might be best to remove the check and always 'schedule' the move because
           * the planner.buffer_segment() routine will filter it if that happens.
           */
          if (ry != start[Y_AXIS]) {
            if (!inf_normalized_flag) {
              on_axis_distance = use_x_dist ? rx - start[X_AXIS] : ry - start[Y_AXIS];
              e_position = start[E_AXIS] + on_axis_distance * e_normalized_dist;
              z_position = start[Z_AXIS] + on_axis_distance * z_normalized_dist;
            }
            else {
              e_position = end[E_AXIS];
              z_position = end[Z_AXIS];
            }

            planner.buffer_segment(rx, ry, z_position + z0, e_position, feed_rate, extruder);
          } //else printf("FIRST MOVE PRUNED  ");
        }

        if (g26_debug_flag)
          debug_current_and_destination(PSTR("vertical move done in ubl.line_to_destination_cartesian()"));

        //
        // Check if we are at the final destination. Usually, we won't be, but if it is on a Y Mesh Line, we are done.
        //
        if (current_position[X_AXIS] != end[X_AXIS] || current_position[Y_AXIS] != end[Y_AXIS])
          goto FINAL_MOVE;

        set_current_from_destination();
        return;
      }

      /**
       *
       * This block handles horizontal lines. These are lines that stay within the same
       * Y Cell row. They do not need to be perfectly horizontal. They just can
       * not cross into another Y Cell row.
       *
       */

      if (dyi == 0) {             // Check for a horizontal line
        current_xi += left_flag;  // Line is heading left, we just want to go to the left
                                  // edge of this cell for the first move.
        while (current_xi != cell_dest_xi + left_flag) {
          current_xi += dxi;
          const float next_mesh_line_x = mesh_index_to_xpos(current_xi),
                      ry = m * next_mesh_line_x + c;   // Calculate Y at the next X mesh line

          float z0 = z_correction_for_y_on_vertical_mesh_line(ry, current_xi, current_yi)
                     * planner.fade_scaling_factor_for_z(end[Z_AXIS]);

          /**
           * If part of the Mesh is undefined, it will show up as NAN
           * in z_values[][] and propagate through the
           * calculations. If our correction is NAN, we throw it out
           * because part of the Mesh is undefined and we don't have the
           * information we need to complete the height correction.
           */
          if (isnan(z0)) z0 = 0.0;

          const float rx = mesh_index_to_xpos(current_xi);

          /**
           * Without this check, it is possible for the algorithm to generate a zero length move in the case
           * where the line is heading left and it is starting right on a Mesh Line boundary. For how often
           * that happens, it might be best to remove the check and always 'schedule' the move because
           * the planner.buffer_segment() routine will filter it if that happens.
           */
          if (rx != start[X_AXIS]) {
            if (!inf_normalized_flag) {
              on_axis_distance = use_x_dist ? rx - start[X_AXIS] : ry - start[Y_AXIS];
              e_position = start[E_AXIS] + on_axis_distance * e_normalized_dist;  // is based on X or Y because this is a horizontal move
              z_position = start[Z_AXIS] + on_axis_distance * z_normalized_dist;
            }
            else {
              e_position = end[E_AXIS];
              z_position = end[Z_AXIS];
            }

            planner.buffer_segment(rx, ry, z_position + z0, e_position, feed_rate, extruder);
          } //else printf("FIRST MOVE PRUNED  ");
        }

        if (g26_debug_flag)
          debug_current_and_destination(PSTR("horizontal move done in ubl.line_to_destination_cartesian()"));

        if (current_position[X_AXIS] != end[X_AXIS] || current_position[Y_AXIS] != end[Y_AXIS])
          goto FINAL_MOVE;

        set_current_from_destination();
        return;
      }

      /**
       *
       * This block handles the generic case of a line crossing both X and Y Mesh lines.
       *
       */

      int xi_cnt = cell_start_xi - cell_dest_xi,
          yi_cnt = cell_start_yi - cell_dest_yi;

      if (xi_cnt < 0) xi_cnt = -xi_cnt;
      if (yi_cnt < 0) yi_cnt = -yi_cnt;

      current_xi += left_flag;
      current_yi += down_flag;

      while (xi_cnt > 0 || yi_cnt > 0) {

        const float next_mesh_line_x = mesh_index_to_xpos(current_xi + dxi),
                    next_mesh_line_y = mesh_index_to_ypos(current_yi + dyi),
                    ry = m * next_mesh_line_x + c,   // Calculate Y at the next X mesh line
                    rx = (next_mesh_line_y - c) / m; // Calculate X at the next Y mesh line
                                                     // (No need to worry about m being zero.
                                                     //  If that was the case, it was already detected
                                                     //  as a vertical line move above.)

        if (left_flag == (rx > next_mesh_line_x)) { // Check if we hit the Y line first
          // Yes!  Crossing a Y Mesh Line next
          float z0 = z_correction_for_x_on_horizontal_mesh_line(rx, current_xi - left_flag, current_yi + dyi)
                     * planner.fade_scaling_factor_for_z(end[Z_AXIS]);

          /**
           * If part of the Mesh is undefined, it will show up as NAN
           * in z_values[][] and propagate through the
           * calculations. If our correction is NAN, we throw it out
           * because part of the Mesh is undefined and we don't have the
           * information we need to complete the height correction.
           */
          if (isnan(z0)) z0 = 0.0;

          if (!inf_normalized_flag) {
            on_axis_distance = use_x_dist ? rx - start[X_AXIS] : next_mesh_line_y - start[Y_AXIS];
            e_position = start[E_AXIS] + on_axis_distance * e_normalized_dist;
            z_position = start[Z_AXIS] + on_axis_distance * z_normalized_dist;
          }
          else {
            e_position = end[E_AXIS];
            z_position = end[Z_AXIS];
          }
          planner.buffer_segment(rx, next_mesh_line_y, z_position + z0, e_position, feed_rate, extruder);
          current_yi += dyi;
          yi_cnt--;
        }
        else {
          // Yes!  Crossing a X Mesh Line next
          float z0 = z_correction_for_y_on_vertical_mesh_line(ry, current_xi + dxi, current_yi - down_flag)
                     * planner.fade_scaling_factor_for_z(end[Z_AXIS]);

          /**
           * If part of the Mesh is undefined, it will show up as NAN
           * in z_values[][] and propagate through the
           * calculations. If our correction is NAN, we throw it out
           * because part of the Mesh is undefined and we don't have the
           * information we need to complete the height correction.
           */
          if (isnan(z0)) z0 = 0.0;

          if (!inf_normalized_flag) {
            on_axis_distance = use_x_dist ? next_mesh_line_x - start[X_AXIS] : ry - start[Y_AXIS];
            e_position = start[E_AXIS] + on_axis_distance * e_normalized_dist;
            z_position = start[Z_AXIS] + on_axis_distance * z_normalized_dist;
          }
          else {
            e_position = end[E_AXIS];
            z_position = end[Z_AXIS];
          }

          planner.buffer_segment(next_mesh_line_x, ry, z_position + z0, e_position, feed_rate, extruder);
          current_xi += dxi;
          xi_cnt--;
        }

        if (xi_cnt < 0 || yi_cnt < 0) break; // we've gone too far, so exit the loop and move on to FINAL_MOVE
      }

      if (g26_debug_flag)
        debug_current_and_destination(PSTR("generic move done in ubl.line_to_destination_cartesian()"));

      if (current_position[X_AXIS] != end[X_AXIS] || current_position[Y_AXIS] != end[Y_AXIS])
        goto FINAL_MOVE;

      set_current_from_destination();
    }

  #else // UBL_SEGMENTED

    #if IS_SCARA // scale the feed rate from mm/s to degrees/s
      static float scara_feed_factor, scara_oldA, scara_oldB;
    #endif

    // We don't want additional apply_leveling() performed by regular buffer_line or buffer_line_kinematic,
    // so we call buffer_segment directly here.  Per-segmented leveling and kinematics performed first.

    inline void _O2 ubl_buffer_segment_raw(const float (&in_raw)[XYZE], const float &fr) {

      #if ENABLED(SKEW_CORRECTION)
        float raw[XYZE] = { in_raw[X_AXIS], in_raw[Y_AXIS], in_raw[Z_AXIS], in_raw[E_AXIS] };
        planner.skew(raw[X_AXIS], raw[Y_AXIS], raw[Z_AXIS]);
      #else
        const float (&raw)[XYZE] = in_raw;
      #endif

      #if ENABLED(DELTA)  // apply delta inverse_kinematics

        DELTA_RAW_IK();
        planner.buffer_segment(delta[A_AXIS], delta[B_AXIS], delta[C_AXIS], in_raw[E_AXIS], fr, active_extruder);

      #elif IS_SCARA  // apply scara inverse_kinematics (should be changed to save raw->logical->raw)

        inverse_kinematics(raw);  // this writes delta[ABC] from raw[XYZE]
                                  // should move the feedrate scaling to scara inverse_kinematics

        const float adiff = FABS(delta[A_AXIS] - scara_oldA),
                    bdiff = FABS(delta[B_AXIS] - scara_oldB);
        scara_oldA = delta[A_AXIS];
        scara_oldB = delta[B_AXIS];
        float s_feedrate = max(adiff, bdiff) * scara_feed_factor;

        planner.buffer_segment(delta[A_AXIS], delta[B_AXIS], delta[C_AXIS], in_raw[E_AXIS], s_feedrate, active_extruder);

      #else // CARTESIAN

        planner.buffer_segment(raw[X_AXIS], raw[Y_AXIS], raw[Z_AXIS], in_raw[E_AXIS], fr, active_extruder);

      #endif
    }

    #if IS_SCARA
      #define DELTA_SEGMENT_MIN_LENGTH 0.25 // SCARA minimum segment size is 0.25mm
    #elif ENABLED(DELTA)
      #define DELTA_SEGMENT_MIN_LENGTH 0.10 // mm (still subject to DELTA_SEGMENTS_PER_SECOND)
    #else // CARTESIAN
      #ifdef LEVELED_SEGMENT_LENGTH
        #define DELTA_SEGMENT_MIN_LENGTH LEVELED_SEGMENT_LENGTH
      #else
        #define DELTA_SEGMENT_MIN_LENGTH 1.00 // mm (similar to G2/G3 arc segmentation)
      #endif
    #endif

    /**
     * Prepare a segmented linear move for DELTA/SCARA/CARTESIAN with UBL and FADE semantics.
     * This calls planner.buffer_segment multiple times for small incremental moves.
     * Returns true if did NOT move, false if moved (requires current_position update).
     */

    bool _O2 unified_bed_leveling::prepare_segmented_line_to(const float (&rtarget)[XYZE], const float &feedrate) {

      if (!position_is_reachable(rtarget[X_AXIS], rtarget[Y_AXIS]))  // fail if moving outside reachable boundary
        return true; // did not move, so current_position still accurate

      const float total[XYZE] = {
        rtarget[X_AXIS] - current_position[X_AXIS],
        rtarget[Y_AXIS] - current_position[Y_AXIS],
        rtarget[Z_AXIS] - current_position[Z_AXIS],
        rtarget[E_AXIS] - current_position[E_AXIS]
      };

      const float cartesian_xy_mm = HYPOT(total[X_AXIS], total[Y_AXIS]);  // total horizontal xy distance

      #if IS_KINEMATIC
        const float seconds = cartesian_xy_mm / feedrate;                                  // seconds to move xy distance at requested rate
        uint16_t segments = lroundf(delta_segments_per_second * seconds),                  // preferred number of segments for distance @ feedrate
                 seglimit = lroundf(cartesian_xy_mm * (1.0 / (DELTA_SEGMENT_MIN_LENGTH))); // number of segments at minimum segment length
        NOMORE(segments, seglimit);                                                        // limit to minimum segment length (fewer segments)
      #else
        uint16_t segments = lroundf(cartesian_xy_mm * (1.0 / (DELTA_SEGMENT_MIN_LENGTH))); // cartesian fixed segment length
      #endif

      NOLESS(segments, 1);                        // must have at least one segment
      const float inv_segments = 1.0 / segments;  // divide once, multiply thereafter

      #if IS_SCARA // scale the feed rate from mm/s to degrees/s
        scara_feed_factor = cartesian_xy_mm * inv_segments * feedrate;
        scara_oldA = stepper.get_axis_position_degrees(A_AXIS);
        scara_oldB = stepper.get_axis_position_degrees(B_AXIS);
      #endif

      const float diff[XYZE] = {
        total[X_AXIS] * inv_segments,
        total[Y_AXIS] * inv_segments,
        total[Z_AXIS] * inv_segments,
        total[E_AXIS] * inv_segments
      };

      // Note that E segment distance could vary slightly as z mesh height
      // changes for each segment, but small enough to ignore.

      float raw[XYZE] = {
        current_position[X_AXIS],
        current_position[Y_AXIS],
        current_position[Z_AXIS],
        current_position[E_AXIS]
      };

      // Only compute leveling per segment if ubl active and target below z_fade_height.
      if (!planner.leveling_active || !planner.leveling_active_at_z(rtarget[Z_AXIS])) {   // no mesh leveling
        while (--segments) {
          LOOP_XYZE(i) raw[i] += diff[i];
          ubl_buffer_segment_raw(raw, feedrate);
        }
        ubl_buffer_segment_raw(rtarget, feedrate);
        return false; // moved but did not set_current_from_destination();
      }

      // Otherwise perform per-segment leveling

      #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
        const float fade_scaling_factor = planner.fade_scaling_factor_for_z(rtarget[Z_AXIS]);
      #endif

      // increment to first segment destination
      LOOP_XYZE(i) raw[i] += diff[i];

      for(;;) {  // for each mesh cell encountered during the move

        // Compute mesh cell invariants that remain constant for all segments within cell.
        // Note for cell index, if point is outside the mesh grid (in MESH_INSET perimeter)
        // the bilinear interpolation from the adjacent cell within the mesh will still work.
        // Inner loop will exit each time (because out of cell bounds) but will come back
        // in top of loop and again re-find same adjacent cell and use it, just less efficient
        // for mesh inset area.

        int8_t cell_xi = (raw[X_AXIS] - (MESH_MIN_X)) * (1.0 / (MESH_X_DIST)),
               cell_yi = (raw[Y_AXIS] - (MESH_MIN_Y)) * (1.0 / (MESH_X_DIST));

        cell_xi = constrain(cell_xi, 0, (GRID_MAX_POINTS_X) - 1);
        cell_yi = constrain(cell_yi, 0, (GRID_MAX_POINTS_Y) - 1);

        const float x0 = mesh_index_to_xpos(cell_xi),   // 64 byte table lookup avoids mul+add
                    y0 = mesh_index_to_ypos(cell_yi);

        float z_x0y0 = z_values[cell_xi  ][cell_yi  ],  // z at lower left corner
              z_x1y0 = z_values[cell_xi+1][cell_yi  ],  // z at upper left corner
              z_x0y1 = z_values[cell_xi  ][cell_yi+1],  // z at lower right corner
              z_x1y1 = z_values[cell_xi+1][cell_yi+1];  // z at upper right corner

        if (isnan(z_x0y0)) z_x0y0 = 0;              // ideally activating planner.leveling_active (G29 A)
        if (isnan(z_x1y0)) z_x1y0 = 0;              //   should refuse if any invalid mesh points
        if (isnan(z_x0y1)) z_x0y1 = 0;              //   in order to avoid isnan tests per cell,
        if (isnan(z_x1y1)) z_x1y1 = 0;              //   thus guessing zero for undefined points

        float cx = raw[X_AXIS] - x0,   // cell-relative x and y
              cy = raw[Y_AXIS] - y0;

        const float z_xmy0 = (z_x1y0 - z_x0y0) * (1.0 / (MESH_X_DIST)),   // z slope per x along y0 (lower left to lower right)
                    z_xmy1 = (z_x1y1 - z_x0y1) * (1.0 / (MESH_X_DIST));   // z slope per x along y1 (upper left to upper right)

              float z_cxy0 = z_x0y0 + z_xmy0 * cx;            // z height along y0 at cx (changes for each cx in cell)

        const float z_cxy1 = z_x0y1 + z_xmy1 * cx,            // z height along y1 at cx
                    z_cxyd = z_cxy1 - z_cxy0;                 // z height difference along cx from y0 to y1

              float z_cxym = z_cxyd * (1.0 / (MESH_Y_DIST));  // z slope per y along cx from y0 to y1 (changes for each cx in cell)

        //    float z_cxcy = z_cxy0 + z_cxym * cy;            // interpolated mesh z height along cx at cy (do inside the segment loop)

        // As subsequent segments step through this cell, the z_cxy0 intercept will change
        // and the z_cxym slope will change, both as a function of cx within the cell, and
        // each change by a constant for fixed segment lengths.

        const float z_sxy0 = z_xmy0 * diff[X_AXIS],                                     // per-segment adjustment to z_cxy0
                    z_sxym = (z_xmy1 - z_xmy0) * (1.0 / (MESH_Y_DIST)) * diff[X_AXIS];  // per-segment adjustment to z_cxym

        for(;;) {  // for all segments within this mesh cell

          if (--segments == 0)                      // if this is last segment, use rtarget for exact
            COPY(raw, rtarget);

          const float z_cxcy = (z_cxy0 + z_cxym * cy) // interpolated mesh z height along cx at cy
            #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
              * fade_scaling_factor                   // apply fade factor to interpolated mesh height
            #endif
          ;

          const float z = raw[Z_AXIS];
          raw[Z_AXIS] += z_cxcy;
          ubl_buffer_segment_raw(raw, feedrate);
          raw[Z_AXIS] = z;

          if (segments == 0)                        // done with last segment
            return false;                           // did not set_current_from_destination()

          LOOP_XYZE(i) raw[i] += diff[i];

          cx += diff[X_AXIS];
          cy += diff[Y_AXIS];

          if (!WITHIN(cx, 0, MESH_X_DIST) || !WITHIN(cy, 0, MESH_Y_DIST))    // done within this cell, break to next
            break;

          // Next segment still within same mesh cell, adjust the per-segment
          // slope and intercept to compute next z height.

          z_cxy0 += z_sxy0;   // adjust z_cxy0 by per-segment z_sxy0
          z_cxym += z_sxym;   // adjust z_cxym by per-segment z_sxym

        } // segment loop
      } // cell loop
    }

  #endif // UBL_SEGMENTED

#endif // AUTO_BED_LEVELING_UBL