Scott Lahteine
9 years ago
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/**
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* Marlin 3D Printer Firmware
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* Copyright (C) 2016 MarlinFirmware [https://github.com/MarlinFirmware/Marlin]
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*
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* Based on Sprinter and grbl.
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* Copyright (C) 2011 Camiel Gubbels / Erik van der Zalm
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*
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* This program 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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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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*/
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/**
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* planner_bezier.cpp
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*
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* Compute and buffer movement commands for bezier curves
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*
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*/
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#include "Marlin.h"
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#if ENABLED(BEZIER_CURVE_SUPPORT)
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#include "planner.h"
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#include "language.h"
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// See the meaning in the documentation of cubic_b_spline().
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#define MIN_STEP 0.002
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#define MAX_STEP 0.1
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#define SIGMA 0.1
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/* Compute the linear interpolation between to real numbers.
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*/
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inline static float interp(float a, float b, float t) { return (1.0 - t) * a + t * b; }
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/**
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* Compute a Bézier curve using the De Casteljau's algorithm (see
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* https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm), which is
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* easy to code and has good numerical stability (very important,
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* since Arudino works with limited precision real numbers).
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*/
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inline static float eval_bezier(float a, float b, float c, float d, float t) {
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float iab = interp(a, b, t);
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float ibc = interp(b, c, t);
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float icd = interp(c, d, t);
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float iabc = interp(iab, ibc, t);
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float ibcd = interp(ibc, icd, t);
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float iabcd = interp(iabc, ibcd, t);
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return iabcd;
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}
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/**
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* We approximate Euclidean distance with the sum of the coordinates
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* offset (so-called "norm 1"), which is quicker to compute.
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*/
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inline static float dist1(float x1, float y1, float x2, float y2) { return fabs(x1 - x2) + fabs(y1 - y2); }
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/**
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* The algorithm for computing the step is loosely based on the one in Kig
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* (See https://sources.debian.net/src/kig/4:15.08.3-1/misc/kigpainter.cpp/#L759)
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* However, we do not use the stack.
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*
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* The algorithm goes as it follows: the parameters t runs from 0.0 to
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* 1.0 describing the curve, which is evaluated by eval_bezier(). At
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* each iteration we have to choose a step, i.e., the increment of the
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* t variable. By default the step of the previous iteration is taken,
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* and then it is enlarged or reduced depending on how straight the
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* curve locally is. The step is always clamped between MIN_STEP/2 and
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* 2*MAX_STEP. MAX_STEP is taken at the first iteration.
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*
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* For some t, the step value is considered acceptable if the curve in
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* the interval [t, t+step] is sufficiently straight, i.e.,
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* sufficiently close to linear interpolation. In practice the
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* following test is performed: the distance between eval_bezier(...,
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* t+step/2) is evaluated and compared with 0.5*(eval_bezier(...,
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* t)+eval_bezier(..., t+step)). If it is smaller than SIGMA, then the
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* step value is considered acceptable, otherwise it is not. The code
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* seeks to find the larger step value which is considered acceptable.
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*
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* At every iteration the recorded step value is considered and then
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* iteratively halved until it becomes acceptable. If it was already
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* acceptable in the beginning (i.e., no halving were done), then
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* maybe it was necessary to enlarge it; then it is iteratively
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* doubled while it remains acceptable. The last acceptable value
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* found is taken, provided that it is between MIN_STEP and MAX_STEP
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* and does not bring t over 1.0.
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*
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* Caveat: this algorithm is not perfect, since it can happen that a
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* step is considered acceptable even when the curve is not linear at
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* all in the interval [t, t+step] (but its mid point coincides "by
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* chance" with the midpoint according to the parametrization). This
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* kind of glitches can be eliminated with proper first derivative
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* estimates; however, given the improbability of such configurations,
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* the mitigation offered by MIN_STEP and the small computational
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* power available on Arduino, I think it is not wise to implement it.
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*/
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void cubic_b_spline(const float position[NUM_AXIS], const float target[NUM_AXIS], const float offset[4], float feed_rate, uint8_t extruder) {
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// Absolute first and second control points are recovered.
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float first0 = position[X_AXIS] + offset[0];
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float first1 = position[Y_AXIS] + offset[1];
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float second0 = target[X_AXIS] + offset[2];
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float second1 = target[Y_AXIS] + offset[3];
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float t = 0.0;
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float tmp[4];
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tmp[X_AXIS] = position[X_AXIS];
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tmp[Y_AXIS] = position[Y_AXIS];
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float step = MAX_STEP;
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while (t < 1.0) {
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// First try to reduce the step in order to make it sufficiently
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// close to a linear interpolation.
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bool did_reduce = false;
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float new_t = t + step;
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NOMORE(new_t, 1.0);
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float new_pos0 = eval_bezier(position[X_AXIS], first0, second0, target[X_AXIS], new_t);
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float new_pos1 = eval_bezier(position[Y_AXIS], first1, second1, target[Y_AXIS], new_t);
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for (;;) {
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if (new_t - t < (MIN_STEP)) break;
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float candidate_t = 0.5 * (t + new_t);
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float candidate_pos0 = eval_bezier(position[X_AXIS], first0, second0, target[X_AXIS], candidate_t);
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float candidate_pos1 = eval_bezier(position[Y_AXIS], first1, second1, target[Y_AXIS], candidate_t);
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float interp_pos0 = 0.5 * (tmp[X_AXIS] + new_pos0);
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float interp_pos1 = 0.5 * (tmp[Y_AXIS] + new_pos1);
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if (dist1(candidate_pos0, candidate_pos1, interp_pos0, interp_pos1) <= (SIGMA)) break;
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new_t = candidate_t;
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new_pos0 = candidate_pos0;
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new_pos1 = candidate_pos1;
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did_reduce = true;
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}
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// If we did not reduce the step, maybe we should enlarge it.
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if (!did_reduce) for (;;) {
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if (new_t - t > MAX_STEP) break;
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float candidate_t = t + 2.0 * (new_t - t);
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if (candidate_t >= 1.0) break;
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float candidate_pos0 = eval_bezier(position[X_AXIS], first0, second0, target[X_AXIS], candidate_t);
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float candidate_pos1 = eval_bezier(position[Y_AXIS], first1, second1, target[Y_AXIS], candidate_t);
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float interp_pos0 = 0.5 * (tmp[X_AXIS] + candidate_pos0);
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float interp_pos1 = 0.5 * (tmp[Y_AXIS] + candidate_pos1);
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if (dist1(new_pos0, new_pos1, interp_pos0, interp_pos1) > (SIGMA)) break;
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new_t = candidate_t;
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new_pos0 = candidate_pos0;
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new_pos1 = candidate_pos1;
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}
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// Check some postcondition; they are disabled in the actual
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// Marlin build, but if you test the same code on a computer you
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// may want to check they are respect.
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/*
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assert(new_t <= 1.0);
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if (new_t < 1.0) {
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assert(new_t - t >= (MIN_STEP) / 2.0);
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assert(new_t - t <= (MAX_STEP) * 2.0);
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}
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*/
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step = new_t - t;
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t = new_t;
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// Compute and send new position
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tmp[X_AXIS] = new_pos0;
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tmp[Y_AXIS] = new_pos1;
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// FIXME. The following two are wrong, since the parameter t is
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// not linear in the distance.
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tmp[Z_AXIS] = interp(position[Z_AXIS], target[Z_AXIS], t);
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tmp[E_AXIS] = interp(position[E_AXIS], target[E_AXIS], t);
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clamp_to_software_endstops(tmp);
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planner.buffer_line(tmp[X_AXIS], tmp[Y_AXIS], tmp[Z_AXIS], tmp[E_AXIS], feed_rate, extruder);
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}
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}
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#endif // BEZIER_CURVE_SUPPORT
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@ -0,0 +1,43 @@
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/**
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* Marlin 3D Printer Firmware
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* Copyright (C) 2016 MarlinFirmware [https://github.com/MarlinFirmware/Marlin]
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*
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* Based on Sprinter and grbl.
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* Copyright (C) 2011 Camiel Gubbels / Erik van der Zalm
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*
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* This program 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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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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*/
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/**
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* planner_bezier.h
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*
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* Compute and buffer movement commands for bezier curves
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*
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*/
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#ifndef PLANNER_BEZIER_H
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#define PLANNER_BEZIER_H
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#include "Marlin.h"
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void cubic_b_spline(
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const float position[NUM_AXIS], // current position
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const float target[NUM_AXIS], // target position
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const float offset[4], // a pair of offsets
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float feed_rate,
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uint8_t extruder
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);
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#endif // PLANNER_BEZIER_H
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