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monster
2020-06-15 11:41:57 +03:00
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Marlin/src/module/planner_bezier.cpp
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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/>.
*
*/
/**
* planner_bezier.cpp
*
* Compute and buffer movement commands for bezier curves
*
*/
#include "../inc/MarlinConfig.h"
#if ENABLED(BEZIER_CURVE_SUPPORT)
#include "planner.h"
#include "motion.h"
#include "temperature.h"
#include "../MarlinCore.h"
#include "../core/language.h"
#include "../gcode/queue.h"
// See the meaning in the documentation of cubic_b_spline().
#define MIN_STEP 0.002f
#define MAX_STEP 0.1f
#define SIGMA 0.1f
// Compute the linear interpolation between two real numbers.
static inline float interp(const float &a, const float &b, const float &t) { return (1 - t) * a + t * b; }
/**
* Compute a Bézier curve using the De Casteljau's algorithm (see
* https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm), which is
* easy to code and has good numerical stability (very important,
* since Arudino works with limited precision real numbers).
*/
static inline float eval_bezier(const float &a, const float &b, const float &c, const float &d, const float &t) {
const float iab = interp(a, b, t),
ibc = interp(b, c, t),
icd = interp(c, d, t),
iabc = interp(iab, ibc, t),
ibcd = interp(ibc, icd, t);
return interp(iabc, ibcd, t);
}
/**
* We approximate Euclidean distance with the sum of the coordinates
* offset (so-called "norm 1"), which is quicker to compute.
*/
static inline float dist1(const float &x1, const float &y1, const float &x2, const float &y2) { return ABS(x1 - x2) + ABS(y1 - y2); }
/**
* The algorithm for computing the step is loosely based on the one in Kig
* (See https://sources.debian.net/src/kig/4:15.08.3-1/misc/kigpainter.cpp/#L759)
* However, we do not use the stack.
*
* The algorithm goes as it follows: the parameters t runs from 0.0 to
* 1.0 describing the curve, which is evaluated by eval_bezier(). At
* each iteration we have to choose a step, i.e., the increment of the
* t variable. By default the step of the previous iteration is taken,
* and then it is enlarged or reduced depending on how straight the
* curve locally is. The step is always clamped between MIN_STEP/2 and
* 2*MAX_STEP. MAX_STEP is taken at the first iteration.
*
* For some t, the step value is considered acceptable if the curve in
* the interval [t, t+step] is sufficiently straight, i.e.,
* sufficiently close to linear interpolation. In practice the
* following test is performed: the distance between eval_bezier(...,
* t+step/2) is evaluated and compared with 0.5*(eval_bezier(...,
* t)+eval_bezier(..., t+step)). If it is smaller than SIGMA, then the
* step value is considered acceptable, otherwise it is not. The code
* seeks to find the larger step value which is considered acceptable.
*
* At every iteration the recorded step value is considered and then
* iteratively halved until it becomes acceptable. If it was already
* acceptable in the beginning (i.e., no halving were done), then
* maybe it was necessary to enlarge it; then it is iteratively
* doubled while it remains acceptable. The last acceptable value
* found is taken, provided that it is between MIN_STEP and MAX_STEP
* and does not bring t over 1.0.
*
* Caveat: this algorithm is not perfect, since it can happen that a
* step is considered acceptable even when the curve is not linear at
* all in the interval [t, t+step] (but its mid point coincides "by
* chance" with the midpoint according to the parametrization). This
* kind of glitches can be eliminated with proper first derivative
* estimates; however, given the improbability of such configurations,
* the mitigation offered by MIN_STEP and the small computational
* power available on Arduino, I think it is not wise to implement it.
*/
void cubic_b_spline(
const xyze_pos_t &position, // current position
const xyze_pos_t &target, // target position
const xy_pos_t (&offsets)[2], // a pair of offsets
const feedRate_t &scaled_fr_mm_s, // mm/s scaled by feedrate %
const uint8_t extruder
) {
// Absolute first and second control points are recovered.
const xy_pos_t first = position + offsets[0], second = target + offsets[1];
xyze_pos_t bez_target;
bez_target.set(position.x, position.y);
float step = MAX_STEP;
millis_t next_idle_ms = millis() + 200UL;
for (float t = 0; t < 1;) {
thermalManager.manage_heater();
millis_t now = millis();
if (ELAPSED(now, next_idle_ms)) {
next_idle_ms = now + 200UL;
idle();
}
// First try to reduce the step in order to make it sufficiently
// close to a linear interpolation.
bool did_reduce = false;
float new_t = t + step;
NOMORE(new_t, 1);
float new_pos0 = eval_bezier(position.x, first.x, second.x, target.x, new_t),
new_pos1 = eval_bezier(position.y, first.y, second.y, target.y, new_t);
for (;;) {
if (new_t - t < (MIN_STEP)) break;
const float candidate_t = 0.5f * (t + new_t),
candidate_pos0 = eval_bezier(position.x, first.x, second.x, target.x, candidate_t),
candidate_pos1 = eval_bezier(position.y, first.y, second.y, target.y, candidate_t),
interp_pos0 = 0.5f * (bez_target.x + new_pos0),
interp_pos1 = 0.5f * (bez_target.y + new_pos1);
if (dist1(candidate_pos0, candidate_pos1, interp_pos0, interp_pos1) <= (SIGMA)) break;
new_t = candidate_t;
new_pos0 = candidate_pos0;
new_pos1 = candidate_pos1;
did_reduce = true;
}
// If we did not reduce the step, maybe we should enlarge it.
if (!did_reduce) for (;;) {
if (new_t - t > MAX_STEP) break;
const float candidate_t = t + 2 * (new_t - t);
if (candidate_t >= 1) break;
const float candidate_pos0 = eval_bezier(position.x, first.x, second.x, target.x, candidate_t),
candidate_pos1 = eval_bezier(position.y, first.y, second.y, target.y, candidate_t),
interp_pos0 = 0.5f * (bez_target.x + candidate_pos0),
interp_pos1 = 0.5f * (bez_target.y + candidate_pos1);
if (dist1(new_pos0, new_pos1, interp_pos0, interp_pos1) > (SIGMA)) break;
new_t = candidate_t;
new_pos0 = candidate_pos0;
new_pos1 = candidate_pos1;
}
// Check some postcondition; they are disabled in the actual
// Marlin build, but if you test the same code on a computer you
// may want to check they are respect.
/*
assert(new_t <= 1.0);
if (new_t < 1.0) {
assert(new_t - t >= (MIN_STEP) / 2.0);
assert(new_t - t <= (MAX_STEP) * 2.0);
}
*/
step = new_t - t;
t = new_t;
// Compute and send new position
xyze_pos_t new_bez = {
new_pos0, new_pos1,
interp(position.z, target.z, t), // FIXME. These two are wrong, since the parameter t is
interp(position.e, target.e, t) // not linear in the distance.
};
apply_motion_limits(new_bez);
bez_target = new_bez;
#if HAS_LEVELING && !PLANNER_LEVELING
xyze_pos_t pos = bez_target;
planner.apply_leveling(pos);
#else
const xyze_pos_t &pos = bez_target;
#endif
if (!planner.buffer_line(pos, scaled_fr_mm_s, active_extruder, step))
break;
}
}
#endif // BEZIER_CURVE_SUPPORT