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MarlinFirmware/Marlin/ubl_motion.cpp
Scott Lahteine 6b6630e11b Clean up trailing whitespace and tabs
2017-05-16 16:06:18 -05:00

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/**
* 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>
extern float destination[XYZE];
extern void set_current_to_destination();
extern float delta_segments_per_second;
static void debug_echo_axis(const AxisEnum axis) {
if (current_position[axis] == destination[axis])
SERIAL_ECHOPGM("-------------");
else
SERIAL_ECHO_F(destination[X_AXIS], 6);
}
void debug_current_and_destination(const char *title) {
// if the title message starts with a '!' it is so important, we are going to
// ignore the status of the g26_debug_flag
if (*title != '!' && !ubl.g26_debug_flag) return;
const float de = destination[E_AXIS] - current_position[E_AXIS];
if (de == 0.0) return;
const float dx = current_position[X_AXIS] - destination[X_AXIS],
dy = current_position[Y_AXIS] - destination[Y_AXIS],
xy_dist = HYPOT(dx, dy);
if (xy_dist == 0.0)
return;
else {
SERIAL_ECHOPGM(" fpmm=");
const float fpmm = de / xy_dist;
SERIAL_ECHO_F(fpmm, 6);
}
SERIAL_ECHOPGM(" current=( ");
SERIAL_ECHO_F(current_position[X_AXIS], 6);
SERIAL_ECHOPGM(", ");
SERIAL_ECHO_F(current_position[Y_AXIS], 6);
SERIAL_ECHOPGM(", ");
SERIAL_ECHO_F(current_position[Z_AXIS], 6);
SERIAL_ECHOPGM(", ");
SERIAL_ECHO_F(current_position[E_AXIS], 6);
SERIAL_ECHOPGM(" ) destination=( ");
debug_echo_axis(X_AXIS);
SERIAL_ECHOPGM(", ");
debug_echo_axis(Y_AXIS);
SERIAL_ECHOPGM(", ");
debug_echo_axis(Z_AXIS);
SERIAL_ECHOPGM(", ");
debug_echo_axis(E_AXIS);
SERIAL_ECHOPGM(" ) ");
SERIAL_ECHO(title);
SERIAL_EOL;
}
void ubl_line_to_destination_cartesian(const float &feed_rate, 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
*/
const 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]
};
const int cell_start_xi = ubl.get_cell_index_x(RAW_X_POSITION(start[X_AXIS])),
cell_start_yi = ubl.get_cell_index_y(RAW_Y_POSITION(start[Y_AXIS])),
cell_dest_xi = ubl.get_cell_index_x(RAW_X_POSITION(end[X_AXIS])),
cell_dest_yi = ubl.get_cell_index_y(RAW_Y_POSITION(end[Y_AXIS]));
if (ubl.g26_debug_flag) {
SERIAL_ECHOPAIR(" ubl_line_to_destination(xe=", end[X_AXIS]);
SERIAL_ECHOPAIR(", ye=", end[Y_AXIS]);
SERIAL_ECHOPAIR(", ze=", end[Z_AXIS]);
SERIAL_ECHOPAIR(", ee=", end[E_AXIS]);
SERIAL_CHAR(')');
SERIAL_EOL;
debug_current_and_destination(PSTR("Start of ubl_line_to_destination()"));
}
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_line(end[X_AXIS], end[Y_AXIS], end[Z_AXIS] + ubl.state.z_offset, end[E_AXIS], feed_rate, extruder);
set_current_to_destination();
if (ubl.g26_debug_flag)
debug_current_and_destination(PSTR("out of bounds in ubl_line_to_destination()"));
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 = (RAW_X_POSITION(end[X_AXIS]) - pgm_read_float(&ubl.mesh_index_to_xpos[cell_dest_xi])) * (1.0 / (MESH_X_DIST)),
z1 = ubl.z_values[cell_dest_xi ][cell_dest_yi ] + xratio *
(ubl.z_values[cell_dest_xi + 1][cell_dest_yi ] - ubl.z_values[cell_dest_xi][cell_dest_yi ]),
z2 = ubl.z_values[cell_dest_xi ][cell_dest_yi + 1] + xratio *
(ubl.z_values[cell_dest_xi + 1][cell_dest_yi + 1] - ubl.z_values[cell_dest_xi][cell_dest_yi + 1]);
// 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 = (RAW_Y_POSITION(end[Y_AXIS]) - pgm_read_float(&ubl.mesh_index_to_ypos[cell_dest_yi])) * (1.0 / (MESH_Y_DIST));
float z0 = z1 + (z2 - z1) * yratio;
z0 *= ubl.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;
planner._buffer_line(end[X_AXIS], end[Y_AXIS], end[Z_AXIS] + z0 + ubl.state.z_offset, end[E_AXIS], feed_rate, extruder);
if (ubl.g26_debug_flag)
debug_current_and_destination(PSTR("FINAL_MOVE in ubl_line_to_destination()"));
set_current_to_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 = LOGICAL_Y_POSITION(pgm_read_float(&ubl.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 x = inf_m_flag ? start[X_AXIS] : (next_mesh_line_y - c) / m;
float z0 = ubl.z_correction_for_x_on_horizontal_mesh_line(x, current_xi, current_yi);
z0 *= ubl.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 y = LOGICAL_Y_POSITION(pgm_read_float(&ubl.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_line() routine will filter it if that happens.
*/
if (y != start[Y_AXIS]) {
if (!inf_normalized_flag) {
on_axis_distance = use_x_dist ? x - start[X_AXIS] : 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_line(x, y, z_position + z0 + ubl.state.z_offset, e_position, feed_rate, extruder);
} //else printf("FIRST MOVE PRUNED ");
}
if (ubl.g26_debug_flag)
debug_current_and_destination(PSTR("vertical move done in ubl_line_to_destination()"));
//
// 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_to_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 = LOGICAL_X_POSITION(pgm_read_float(&ubl.mesh_index_to_xpos[current_xi])),
y = m * next_mesh_line_x + c; // Calculate Y at the next X mesh line
float z0 = ubl.z_correction_for_y_on_vertical_mesh_line(y, current_xi, current_yi);
z0 *= ubl.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 x = LOGICAL_X_POSITION(pgm_read_float(&ubl.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_line() routine will filter it if that happens.
*/
if (x != start[X_AXIS]) {
if (!inf_normalized_flag) {
on_axis_distance = use_x_dist ? x - start[X_AXIS] : y - 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_line(x, y, z_position + z0 + ubl.state.z_offset, e_position, feed_rate, extruder);
} //else printf("FIRST MOVE PRUNED ");
}
if (ubl.g26_debug_flag)
debug_current_and_destination(PSTR("horizontal move done in ubl_line_to_destination()"));
if (current_position[X_AXIS] != end[X_AXIS] || current_position[Y_AXIS] != end[Y_AXIS])
goto FINAL_MOVE;
set_current_to_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 = LOGICAL_X_POSITION(pgm_read_float(&ubl.mesh_index_to_xpos[current_xi + dxi])),
next_mesh_line_y = LOGICAL_Y_POSITION(pgm_read_float(&ubl.mesh_index_to_ypos[current_yi + dyi])),
y = m * next_mesh_line_x + c, // Calculate Y at the next X mesh line
x = (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 == (x > next_mesh_line_x)) { // Check if we hit the Y line first
// Yes! Crossing a Y Mesh Line next
float z0 = ubl.z_correction_for_x_on_horizontal_mesh_line(x, current_xi - left_flag, current_yi + dyi);
z0 *= ubl.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 ? x - 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_line(x, next_mesh_line_y, z_position + z0 + ubl.state.z_offset, e_position, feed_rate, extruder);
current_yi += dyi;
yi_cnt--;
}
else {
// Yes! Crossing a X Mesh Line next
float z0 = ubl.z_correction_for_y_on_vertical_mesh_line(y, current_xi + dxi, current_yi - down_flag);
z0 *= ubl.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] : 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_line(next_mesh_line_x, y, z_position + z0 + ubl.state.z_offset, 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 (ubl.g26_debug_flag)
debug_current_and_destination(PSTR("generic move done in ubl_line_to_destination()"));
if (current_position[X_AXIS] != end[X_AXIS] || current_position[Y_AXIS] != end[Y_AXIS])
goto FINAL_MOVE;
set_current_to_destination();
}
#if UBL_DELTA
// macro to inline copy exactly 4 floats, don't rely on sizeof operator
#define COPY_XYZE( target, source ) { \
target[X_AXIS] = source[X_AXIS]; \
target[Y_AXIS] = source[Y_AXIS]; \
target[Z_AXIS] = source[Z_AXIS]; \
target[E_AXIS] = source[E_AXIS]; \
}
#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_line directly here. Per-segmented leveling performed first.
static inline void ubl_buffer_line_segment(const float ltarget[XYZE], const float &fr_mm_s, const uint8_t extruder) {
#if IS_KINEMATIC
inverse_kinematics(ltarget); // this writes delta[ABC] from ltarget[XYZ] but does not modify ltarget
float feedrate = fr_mm_s;
#if IS_SCARA // scale the feed rate from mm/s to degrees/s
float adiff = abs(delta[A_AXIS] - scara_oldA),
bdiff = abs(delta[B_AXIS] - scara_oldB);
scara_oldA = delta[A_AXIS];
scara_oldB = delta[B_AXIS];
feedrate = max(adiff, bdiff) * scara_feed_factor;
#endif
planner._buffer_line(delta[A_AXIS], delta[B_AXIS], delta[C_AXIS], ltarget[E_AXIS], feedrate, extruder);
#else // cartesian
planner._buffer_line(ltarget[X_AXIS], ltarget[Y_AXIS], ltarget[Z_AXIS], ltarget[E_AXIS], fr_mm_s, extruder);
#endif
}
/**
* Prepare a linear move for DELTA/SCARA/CARTESIAN with UBL and FADE semantics.
* This calls planner._buffer_line multiple times for small incremental moves.
* Returns true if the caller did NOT update current_position, otherwise false.
*/
static bool ubl_prepare_linear_move_to(const float ltarget[XYZE], const float &feedrate) {
if (!position_is_reachable_xy(ltarget[X_AXIS], ltarget[Y_AXIS])) // fail if moving outside reachable boundary
return true; // did not move, so current_position still accurate
const float difference[XYZE] = { // cartesian distances moved in XYZE
ltarget[X_AXIS] - current_position[X_AXIS],
ltarget[Y_AXIS] - current_position[Y_AXIS],
ltarget[Z_AXIS] - current_position[Z_AXIS],
ltarget[E_AXIS] - current_position[E_AXIS]
};
const float cartesian_xy_mm = HYPOT(difference[X_AXIS], difference[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 segment_distance[XYZE] = { // length for each segment
difference[X_AXIS] * inv_segments,
difference[Y_AXIS] * inv_segments,
difference[Z_AXIS] * inv_segments,
difference[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.
const bool above_fade_height = (
#if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
planner.z_fade_height != 0 && planner.z_fade_height < RAW_Z_POSITION(ltarget[Z_AXIS])
#else
false
#endif
);
// Only compute leveling per segment if ubl active and target below z_fade_height.
if (!ubl.state.active || above_fade_height) { // no mesh leveling
const float z_offset = ubl.state.active ? ubl.state.z_offset : 0.0;
float seg_dest[XYZE]; // per-segment destination,
COPY_XYZE(seg_dest, current_position); // starting from current position
while (--segments) {
LOOP_XYZE(i) seg_dest[i] += segment_distance[i];
float ztemp = seg_dest[Z_AXIS];
seg_dest[Z_AXIS] += z_offset;
ubl_buffer_line_segment(seg_dest, feedrate, active_extruder);
seg_dest[Z_AXIS] = ztemp;
}
// Since repeated adding segment_distance accumulates small errors, final move to exact destination.
COPY_XYZE(seg_dest, ltarget);
seg_dest[Z_AXIS] += z_offset;
ubl_buffer_line_segment(seg_dest, feedrate, active_extruder);
return false; // moved but did not set_current_to_destination();
}
// Otherwise perform per-segment leveling
#if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
const float fade_scaling_factor = ubl.fade_scaling_factor_for_z(ltarget[Z_AXIS]);
#endif
float seg_dest[XYZE]; // per-segment destination, initialize to first segment
LOOP_XYZE(i) seg_dest[i] = current_position[i] + segment_distance[i];
const float& dx_seg = segment_distance[X_AXIS]; // alias for clarity
const float& dy_seg = segment_distance[Y_AXIS];
float rx = RAW_X_POSITION(seg_dest[X_AXIS]), // assume raw vs logical coordinates shifted but not scaled.
ry = RAW_Y_POSITION(seg_dest[Y_AXIS]);
do { // 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 = (rx - (UBL_MESH_MIN_X)) * (1.0 / (MESH_X_DIST)),
cell_yi = (ry - (UBL_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 = pgm_read_float(&(ubl.mesh_index_to_xpos[cell_xi ])), // 64 byte table lookup avoids mul+add
y0 = pgm_read_float(&(ubl.mesh_index_to_ypos[cell_yi ])), // 64 byte table lookup avoids mul+add
x1 = pgm_read_float(&(ubl.mesh_index_to_xpos[cell_xi+1])), // 64 byte table lookup avoids mul+add
y1 = pgm_read_float(&(ubl.mesh_index_to_ypos[cell_yi+1])); // 64 byte table lookup avoids mul+add
float cx = rx - x0, // cell-relative x
cy = ry - y0, // cell-relative y
z_x0y0 = ubl.z_values[cell_xi ][cell_yi ], // z at lower left corner
z_x1y0 = ubl.z_values[cell_xi+1][cell_yi ], // z at upper left corner
z_x0y1 = ubl.z_values[cell_xi ][cell_yi+1], // z at lower right corner
z_x1y1 = ubl.z_values[cell_xi+1][cell_yi+1]; // z at upper right corner
if (isnan(z_x0y0)) z_x0y0 = 0; // ideally activating ubl.state.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
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
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
// 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 * dx_seg, // per-segment adjustment to z_cxy0
z_sxym = (z_xmy1 - z_xmy0) * (1.0 / (MESH_Y_DIST)) * dx_seg; // per-segment adjustment to z_cxym
do { // for all segments within this mesh cell
float z_cxcy = z_cxy0 + z_cxym * cy; // interpolated mesh z height along cx at cy
#if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
z_cxcy *= fade_scaling_factor; // apply fade factor to interpolated mesh height
#endif
z_cxcy += ubl.state.z_offset; // add fixed mesh offset from G29 Z
if (--segments == 0) { // if this is last segment, use ltarget for exact
COPY_XYZE(seg_dest, ltarget);
seg_dest[Z_AXIS] += z_cxcy;
ubl_buffer_line_segment(seg_dest, feedrate, active_extruder);
return false; // did not set_current_to_destination()
}
const float z_orig = seg_dest[Z_AXIS]; // remember the pre-leveled segment z value
seg_dest[Z_AXIS] = z_orig + z_cxcy; // adjust segment z height per mesh leveling
ubl_buffer_line_segment(seg_dest, feedrate, active_extruder);
seg_dest[Z_AXIS] = z_orig; // restore pre-leveled z before incrementing
LOOP_XYZE(i) seg_dest[i] += segment_distance[i]; // adjust seg_dest for next segment
cx += dx_seg;
cy += dy_seg;
if (!WITHIN(cx, 0, MESH_X_DIST) || !WITHIN(cy, 0, MESH_Y_DIST)) { // done within this cell, break to next
rx = RAW_X_POSITION(seg_dest[X_AXIS]);
ry = RAW_Y_POSITION(seg_dest[Y_AXIS]);
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
} while (true); // per-segment loop exits by break after last segment within cell, or by return on final segment
} while (true); // per-cell loop
} // end of function
#endif // UBL_DELTA
#endif // AUTO_BED_LEVELING_UBL
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