Quantization of G-code export to achieve more precise extrusionversion_2.5.0-alpha0

width control.

6 files changed, 139 insertions, 136 deletions

diff --git a/src/libslic3r/Extruder.cpp b/src/libslic3r/Extruder.cpp
index f7a5c5007..d2ff65097 100644
--- a/src/libslic3r/Extruder.cpp
+++ b/src/libslic3r/Extruder.cpp
@@ -1,4 +1,5 @@
 #include "Extruder.hpp"
+#include "GCodeWriter.hpp"
 #include "PrintConfig.hpp"
 
 namespace Slic3r {
@@ -7,24 +8,24 @@ Extruder::Extruder(unsigned int id, GCodeConfig *config) :
     m_id(id),
     m_config(config)
 {
-    reset();
-    
     // cache values that are going to be called often
     m_e_per_mm3 = this->extrusion_multiplier();
     if (! m_config->use_volumetric_e)
         m_e_per_mm3 /= this->filament_crossection();
 }
 
-double Extruder::extrude(double dE)
+std::pair<double, double> Extruder::extrude(double dE)
 {
     // in case of relative E distances we always reset to 0 before any output
     if (m_config->use_relative_e_distances)
         m_E = 0.;
+    // Quantize extruder delta to G-code resolution.
+    dE = GCodeFormatter::quantize_e(dE);
     m_E          += dE;
     m_absolute_E += dE;
     if (dE < 0.)
         m_retracted -= dE;
-    return dE;
+    return std::make_pair(dE, m_E);
 }
 
 /* This method makes sure the extruder is retracted by the specified amount
@@ -34,28 +35,33 @@ double Extruder::extrude(double dE)
    The restart_extra argument sets the extra length to be used for
    unretraction. If we're actually performing a retraction, any restart_extra
    value supplied will overwrite the previous one if any. */
-double Extruder::retract(double length, double restart_extra)
+std::pair<double, double> Extruder::retract(double retract_length, double restart_extra)
 {
     // in case of relative E distances we always reset to 0 before any output
     if (m_config->use_relative_e_distances)
         m_E = 0.;
-    double to_retract = std::max(0., length - m_retracted);
+    // Quantize extruder delta to G-code resolution.
+    double to_retract = this->retract_to_go(retract_length);
     if (to_retract > 0.) {
         m_E             -= to_retract;
         m_absolute_E    -= to_retract;
         m_retracted     += to_retract;
-        m_restart_extra = restart_extra;
+        m_restart_extra  = restart_extra;
     }
-    return to_retract;
+    return std::make_pair(to_retract, m_E);
 }
 
-double Extruder::unretract()
+double Extruder::retract_to_go(double retract_length) const
 {
-    double dE = m_retracted + m_restart_extra;
-    this->extrude(dE);
+    return std::max(0., GCodeFormatter::quantize_e(retract_length - m_retracted));
+}
+
+std::pair<double, double> Extruder::unretract()
+{
+    auto [dE, emitE] = this->extrude(m_retracted + m_restart_extra);
     m_retracted     = 0.;
     m_restart_extra = 0.;
-    return dE;
+    return std::make_pair(dE, emitE);
 }
 
 // Used filament volume in mm^3.
diff --git a/src/libslic3r/Extruder.hpp b/src/libslic3r/Extruder.hpp
index e9c6927f8..7491b1c8f 100644
--- a/src/libslic3r/Extruder.hpp
+++ b/src/libslic3r/Extruder.hpp
@@ -12,22 +12,24 @@ class Extruder
 {
 public:
     Extruder(unsigned int id, GCodeConfig *config);
-    virtual ~Extruder() {}
-
-    void   reset() {
-        m_E             = 0;
-        m_absolute_E    = 0;
-        m_retracted     = 0;
-        m_restart_extra = 0;
-    }
+    ~Extruder() = default;
 
     unsigned int id() const { return m_id; }
 
-    double extrude(double dE);
-    double retract(double length, double restart_extra);
-    double unretract();
-    double E() const { return m_E; }
-    void   reset_E() { m_E = 0.; }
+    // Following three methods emit:
+    // first  - extrusion delta
+    // second - number to emit to G-code: This may be delta for relative mode or a distance from last reset_E() for absolute mode.
+    // They also quantize the E axis to G-code resolution.
+    std::pair<double, double> extrude(double dE);
+    std::pair<double, double> retract(double retract_length, double restart_extra);
+    std::pair<double, double> unretract();
+    // How much to retract yet before retract_length is reached?
+    // The value is quantized to G-code resolution.
+    double                    retract_to_go(double retract_length) const;
+
+    // Reset the current state of the E axis (this is only needed for relative extruder addressing mode anyways).
+    // Returns true if the extruder was non-zero before reset.
+    bool   reset_E() { bool modified = m_E != 0; m_E = 0.; return modified; }
     double e_per_mm(double mm3_per_mm) const { return mm3_per_mm * m_e_per_mm3; }
     double e_per_mm3() const { return m_e_per_mm3; }
     // Used filament volume in mm^3.
@@ -57,14 +59,16 @@ private:
     GCodeConfig *m_config;
     // Print-wide global ID of this extruder.
     unsigned int m_id;
-    // Current state of the extruder axis, may be resetted if use_relative_e_distances.
-    double       m_E;
+    // Current state of the extruder axis.
+    // For absolute extruder addressing, it is the current state since the last reset (G92 E0) issued at the end of the last retraction.
+    // For relative extruder addressing, it is the E axis difference emitted into the G-code the last time.
+    double       m_E { 0 };
     // Current state of the extruder tachometer, used to output the extruded_volume() and used_filament() statistics.
-    double       m_absolute_E;
+    double       m_absolute_E { 0 };
     // Current positive amount of retraction.
-    double       m_retracted;
+    double       m_retracted { 0 };
     // When retracted, this value stores the extra amount of priming on deretraction.
-    double       m_restart_extra;
+    double       m_restart_extra { 0 };
     double       m_e_per_mm3;
 };
 
@@ -76,4 +80,4 @@ inline bool operator> (const Extruder &e1, const Extruder &e2) { return e1.id()
 
 }
 
-#endif
+#endif // slic3r_Extruder_hpp_
diff --git a/src/libslic3r/GCode.cpp b/src/libslic3r/GCode.cpp
index 13aedab1b..6a53917de 100644
--- a/src/libslic3r/GCode.cpp
+++ b/src/libslic3r/GCode.cpp
@@ -27,7 +27,6 @@
 #include <boost/foreach.hpp>
 #include <boost/filesystem.hpp>
 #include <boost/log/trivial.hpp>
-#include <boost/beast/core/detail/base64.hpp>
 
 #include <boost/nowide/iostream.hpp>
 #include <boost/nowide/cstdio.hpp>
@@ -155,63 +154,52 @@ namespace Slic3r {
 
     std::string Wipe::wipe(GCode& gcodegen, bool toolchange)
     {
-        std::string gcode;
-
-        /*  Reduce feedrate a bit; travel speed is often too high to move on existing material.
-            Too fast = ripping of existing material; too slow = short wipe path, thus more blob.  */
-        double wipe_speed = gcodegen.writer().config.travel_speed.value * 0.8;
-
-        // get the retraction length
-        double length = toolchange
-            ? gcodegen.writer().extruder()->retract_length_toolchange()
-            : gcodegen.writer().extruder()->retract_length();
-        // Shorten the retraction length by the amount already retracted before wipe.
-        length *= (1. - gcodegen.writer().extruder()->retract_before_wipe());
-
-        if (length > 0) {
-            /*  Calculate how long we need to travel in order to consume the required
-                amount of retraction. In other words, how far do we move in XY at wipe_speed
-                for the time needed to consume retract_length at retract_speed?  */
-            double wipe_dist = scale_(length / gcodegen.writer().extruder()->retract_speed() * wipe_speed);
-
-            /*  Take the stored wipe path and replace first point with the current actual position
-                (they might be different, for example, in case of loop clipping).  */
-            Polyline wipe_path;
-            wipe_path.append(gcodegen.last_pos());
-            wipe_path.append(
-                this->path.points.begin() + 1,
-                this->path.points.end()
-            );
-
-            wipe_path.clip_end(wipe_path.length() - wipe_dist);
-
-            // subdivide the retraction in segments
-            if (!wipe_path.empty()) {
-                // add tag for processor
+        std::string     gcode;
+        const Extruder &extruder = *gcodegen.writer().extruder();
+
+        // Remaining quantized retraction length.
+        if (double retract_length = extruder.retract_to_go(toolchange ? extruder.retract_length_toolchange() : extruder.retract_length()); 
+            retract_length > 0 && this->path.size() >= 2) {
+            // Reduce feedrate a bit; travel speed is often too high to move on existing material.
+            // Too fast = ripping of existing material; too slow = short wipe path, thus more blob.
+            const double wipe_speed = gcodegen.writer().config.travel_speed.value * 0.8;
+            // Reduce retraction length a bit to avoid effective retraction speed to be greater than the configured one
+            // due to rounding (TODO: test and/or better math for this).
+            const double xy_to_e    = 0.95 * extruder.retract_speed() / wipe_speed;
+            // Start with the current position, which may be different from the wipe path start in case of loop clipping.
+            Vec2d prev = gcodegen.point_to_gcode_quantized(gcodegen.last_pos());
+            auto  it   = this->path.points.begin();
+            Vec2d p    = gcodegen.point_to_gcode_quantized(*(++ it));
+            if (p != prev) {
                 gcode += ";" + GCodeProcessor::reserved_tag(GCodeProcessor::ETags::Wipe_Start) + "\n";
-                for (const Line& line : wipe_path.lines()) {
-                    double segment_length = line.length();
-                    /*  Reduce retraction length a bit to avoid effective retraction speed to be greater than the configured one
-                        due to rounding (TODO: test and/or better math for this)  */
-                    double dE = length * (segment_length / wipe_dist) * 0.95;
+                auto  end  = this->path.points.end();
+                bool  done = false;
+                for (; it != end; ++ it) {
+                    p = gcodegen.point_to_gcode_quantized(*it);
+                    double segment_length = (p - prev).norm();
+                    double dE = GCodeFormatter::quantize_e(xy_to_e * segment_length);
+                    if (dE > retract_length - EPSILON) {
+                        if (dE > retract_length + EPSILON)
+                            // Shorten the segment.
+                            p = prev + (p - prev) * (retract_length / dE);
+                        dE   = retract_length;
+                        done = true;
+                    }
                     //FIXME one shall not generate the unnecessary G1 Fxxx commands, here wipe_speed is a constant inside this cycle.
                     // Is it here for the cooling markers? Or should it be outside of the cycle?
-                    gcode += gcodegen.writer().set_speed(wipe_speed * 60, "", gcodegen.enable_cooling_markers() ? ";_WIPE" : "");
-                    gcode += gcodegen.writer().extrude_to_xy(
-                        gcodegen.point_to_gcode(line.b),
-                        -dE,
-                        "wipe and retract"
-                    );
+                    gcode += gcodegen.writer().set_speed(wipe_speed * 60, {}, gcodegen.enable_cooling_markers() ? ";_WIPE" : "");
+                    gcode += gcodegen.writer().extrude_to_xy(p, -dE, "wipe and retract");
+                    prev = p;
+                    retract_length -= dE;
                 }
                 // add tag for processor
                 gcode += ";" + GCodeProcessor::reserved_tag(GCodeProcessor::ETags::Wipe_End) + "\n";
-                gcodegen.set_last_pos(wipe_path.points.back());
+                gcodegen.set_last_pos(gcodegen.gcode_to_point(prev));
             }
-
-            // prevent wiping again on same path
-            this->reset_path();
         }
 
+        // Prevent wiping again on the same path.
+        this->reset_path();
         return gcode;
     }
 
@@ -3010,13 +2998,15 @@ std::string GCode::_extrude(const ExtrusionPath &path, std::string description,
     double path_length = 0.;
     {
         std::string comment = m_config.gcode_comments ? description : "";
-        for (const Line &line : path.polyline.lines()) {
-            const double line_length = line.length() * SCALING_FACTOR;
+        Vec2d prev = this->point_to_gcode_quantized(path.polyline.points.front());
+        auto  it   = path.polyline.points.begin();
+        auto  end  = path.polyline.points.end();
+        for (++ it; it != end; ++ it) {
+            Vec2d p = this->point_to_gcode_quantized(*it);
+            const double line_length = (p - prev).norm();
             path_length += line_length;
-            gcode += m_writer.extrude_to_xy(
-                this->point_to_gcode(line.b),
-                e_per_mm * line_length,
-                comment);
+            gcode += m_writer.extrude_to_xy(p, e_per_mm * line_length, comment);
+            prev = p;
         }
     }
     if (m_enable_cooling_markers)
@@ -3239,7 +3229,13 @@ std::string GCode::set_extruder(unsigned int extruder_id, double print_z)
 Vec2d GCode::point_to_gcode(const Point &point) const
 {
     Vec2d extruder_offset = EXTRUDER_CONFIG(extruder_offset);
-    return unscale(point) + m_origin - extruder_offset;
+    return unscaled<double>(point) + m_origin - extruder_offset;
+}
+
+Vec2d GCode::point_to_gcode_quantized(const Point &point) const
+{
+    Vec2d p = this->point_to_gcode(point);
+    return { GCodeFormatter::quantize_xyzf(p.x()), GCodeFormatter::quantize_xyzf(p.y()) };
 }
 
 // convert a model-space scaled point into G-code coordinates
diff --git a/src/libslic3r/GCode.hpp b/src/libslic3r/GCode.hpp
index f46558c35..c0e636c79 100644
--- a/src/libslic3r/GCode.hpp
+++ b/src/libslic3r/GCode.hpp
@@ -55,9 +55,9 @@ public:
     Polyline path;
     
     Wipe() : enable(false) {}
-    bool has_path() const { return !this->path.points.empty(); }
-    void reset_path() { this->path = Polyline(); }
-    std::string wipe(GCode &gcodegen, bool toolchange = false);
+    bool has_path() const { return ! this->path.empty(); }
+    void reset_path() { this->path.clear(); }
+    std::string wipe(GCode &gcodegen, bool toolchange);
 };
 
 class WipeTowerIntegration {
@@ -151,7 +151,10 @@ public:
     void            set_origin(const Vec2d &pointf);
     void            set_origin(const coordf_t x, const coordf_t y) { this->set_origin(Vec2d(x, y)); }
     const Point&    last_pos() const { return m_last_pos; }
+    // Convert coordinates of the active object to G-code coordinates, possibly adjusted for extruder offset.
     Vec2d           point_to_gcode(const Point &point) const;
+    // Convert coordinates of the active object to G-code coordinates, possibly adjusted for extruder offset and quantized to G-code resolution.
+    Vec2d           point_to_gcode_quantized(const Point &point) const;
     Point           gcode_to_point(const Vec2d &point) const;
     const FullPrintConfig &config() const { return m_config; }
     const Layer*    layer() const { return m_layer; }
diff --git a/src/libslic3r/GCodeWriter.cpp b/src/libslic3r/GCodeWriter.cpp
index 233976b19..c5279c0f5 100644
--- a/src/libslic3r/GCodeWriter.cpp
+++ b/src/libslic3r/GCodeWriter.cpp
@@ -79,7 +79,7 @@ std::string GCodeWriter::postamble() const
 std::string GCodeWriter::set_temperature(unsigned int temperature, bool wait, int tool) const
 {
     if (wait && (FLAVOR_IS(gcfMakerWare) || FLAVOR_IS(gcfSailfish)))
-        return "";
+        return {};
     
     std::string code, comment;
     if (wait && FLAVOR_IS_NOT(gcfTeacup) && FLAVOR_IS_NOT(gcfRepRapFirmware)) {
@@ -192,32 +192,18 @@ std::string GCodeWriter::set_acceleration(unsigned int acceleration)
 
 std::string GCodeWriter::reset_e(bool force)
 {
-    if (FLAVOR_IS(gcfMach3)
-        || FLAVOR_IS(gcfMakerWare)
-        || FLAVOR_IS(gcfSailfish))
-        return "";
-    
-    if (m_extruder != nullptr) {
-        if (m_extruder->E() == 0. && ! force)
-            return "";
-        m_extruder->reset_E();
-    }
-
-    if (! m_extrusion_axis.empty() && ! this->config.use_relative_e_distances) {
-        std::ostringstream gcode;
-        gcode << "G92 " << m_extrusion_axis << "0";
-        if (this->config.gcode_comments) gcode << " ; reset extrusion distance";
-        gcode << "\n";
-        return gcode.str();
-    } else {
-        return "";
-    }
+    return
+        FLAVOR_IS(gcfMach3) || FLAVOR_IS(gcfMakerWare) || FLAVOR_IS(gcfSailfish) || this->config.use_relative_e_distances ||
+        (m_extruder != nullptr && ! m_extruder->reset_E() && ! force) || 
+        m_extrusion_axis.empty() ?
+        std::string{} :
+        std::string("G92 ") + m_extrusion_axis + (this->config.gcode_comments ? "0 ; reset extrusion distance\n" : "0\n");
 }
 
 std::string GCodeWriter::update_progress(unsigned int num, unsigned int tot, bool allow_100) const
 {
     if (FLAVOR_IS_NOT(gcfMakerWare) && FLAVOR_IS_NOT(gcfSailfish))
-        return "";
+        return {};
     
     unsigned int percent = (unsigned int)floor(100.0 * num / tot + 0.5);
     if (!allow_100) percent = std::min(percent, (unsigned int)99);
@@ -269,8 +255,8 @@ std::string GCodeWriter::set_speed(double F, const std::string &comment, const s
 
 std::string GCodeWriter::travel_to_xy(const Vec2d &point, const std::string &comment)
 {
-    m_pos(0) = point(0);
-    m_pos(1) = point(1);
+    m_pos.x() = point.x();
+    m_pos.y() = point.y();
     
     GCodeG1Formatter w;
     w.emit_xy(point);
@@ -290,9 +276,9 @@ std::string GCodeWriter::travel_to_xyz(const Vec3d &point, const std::string &co
         don't perform the Z move but we only move in the XY plane and
         adjust the nominal Z by reducing the lift amount that will be 
         used for unlift. */
-    if (!this->will_move_z(point(2))) {
-        double nominal_z = m_pos(2) - m_lifted;
-        m_lifted -= (point(2) - nominal_z);
+    if (!this->will_move_z(point.z())) {
+        double nominal_z = m_pos.z() - m_lifted;
+        m_lifted -= (point.z() - nominal_z);
         // In case that retract_lift == layer_height we could end up with almost zero in_m_lifted
         // and a retract could be skipped (https://github.com/prusa3d/PrusaSlicer/issues/2154
         if (std::abs(m_lifted) < EPSILON)
@@ -318,11 +304,11 @@ std::string GCodeWriter::travel_to_z(double z, const std::string &comment)
         we don't perform the move but we only adjust the nominal Z by
         reducing the lift amount that will be used for unlift. */
     if (!this->will_move_z(z)) {
-        double nominal_z = m_pos(2) - m_lifted;
+        double nominal_z = m_pos.z() - m_lifted;
         m_lifted -= (z - nominal_z);
         if (std::abs(m_lifted) < EPSILON)
             m_lifted = 0.;
-        return "";
+        return {};
     }
     
     /*  In all the other cases, we perform an actual Z move and cancel
@@ -333,7 +319,7 @@ std::string GCodeWriter::travel_to_z(double z, const std::string &comment)
 
 std::string GCodeWriter::_travel_to_z(double z, const std::string &comment)
 {
-    m_pos(2) = z;
+    m_pos.z() = z;
 
     double speed = this->config.travel_speed_z.value;
     if (speed == 0.)
@@ -351,8 +337,8 @@ bool GCodeWriter::will_move_z(double z) const
     /* If target Z is lower than current Z but higher than nominal Z
         we don't perform an actual Z move. */
     if (m_lifted > 0) {
-        double nominal_z = m_pos(2) - m_lifted;
-        if (z >= nominal_z && z <= m_pos(2))
+        double nominal_z = m_pos.z() - m_lifted;
+        if (z >= nominal_z && z <= m_pos.z())
             return false;
     }
     return true;
@@ -360,17 +346,17 @@ bool GCodeWriter::will_move_z(double z) const
 
 std::string GCodeWriter::extrude_to_xy(const Vec2d &point, double dE, const std::string &comment)
 {
-    m_pos(0) = point(0);
-    m_pos(1) = point(1);
-    m_extruder->extrude(dE);
+    m_pos.x() = point.x();
+    m_pos.y() = point.y();
 
     GCodeG1Formatter w;
     w.emit_xy(point);
-    w.emit_e(m_extrusion_axis, m_extruder->E());
+    w.emit_e(m_extrusion_axis, m_extruder->extrude(dE).second);
     w.emit_comment(this->config.gcode_comments, comment);
     return w.string();
 }
 
+#if 0
 std::string GCodeWriter::extrude_to_xyz(const Vec3d &point, double dE, const std::string &comment)
 {
     m_pos = point;
@@ -383,6 +369,7 @@ std::string GCodeWriter::extrude_to_xyz(const Vec3d &point, double dE, const std
     w.emit_comment(this->config.gcode_comments, comment);
     return w.string();
 }
+#endif
 
 std::string GCodeWriter::retract(bool before_wipe)
 {
@@ -422,14 +409,13 @@ std::string GCodeWriter::_retract(double length, double restart_extra, const std
         restart_extra = restart_extra * area;
     }
     
-
     std::string gcode;
-    if (double dE = m_extruder->retract(length, restart_extra);  dE != 0) {
+    if (auto [dE, emitE] = m_extruder->retract(length, restart_extra);  dE != 0) {
         if (this->config.use_firmware_retraction) {
             gcode = FLAVOR_IS(gcfMachinekit) ? "G22 ; retract\n" : "G10 ; retract\n";
         } else if (! m_extrusion_axis.empty()) {
             GCodeG1Formatter w;
-            w.emit_e(m_extrusion_axis, m_extruder->E());
+            w.emit_e(m_extrusion_axis, emitE);
             w.emit_f(m_extruder->retract_speed() * 60.);
             w.emit_comment(this->config.gcode_comments, comment);
             gcode = w.string();
@@ -449,14 +435,14 @@ std::string GCodeWriter::unretract()
     if (FLAVOR_IS(gcfMakerWare))
         gcode = "M101 ; extruder on\n";
     
-    if (double dE = m_extruder->unretract(); dE != 0) {
+    if (auto [dE, emitE] = m_extruder->unretract(); dE != 0) {
         if (this->config.use_firmware_retraction) {
             gcode += FLAVOR_IS(gcfMachinekit) ? "G23 ; unretract\n" : "G11 ; unretract\n";
             gcode += this->reset_e();
         } else if (! m_extrusion_axis.empty()) {
             // use G1 instead of G0 because G0 will blend the restart with the previous travel move
             GCodeG1Formatter w;
-            w.emit_e(m_extrusion_axis, m_extruder->E());
+            w.emit_e(m_extrusion_axis, emitE);
             w.emit_f(m_extruder->deretract_speed() * 60.);
             w.emit_comment(this->config.gcode_comments, " ; unretract");
             gcode += w.string();
@@ -476,21 +462,21 @@ std::string GCodeWriter::lift()
     {
         double above = this->config.retract_lift_above.get_at(m_extruder->id());
         double below = this->config.retract_lift_below.get_at(m_extruder->id());
-        if (m_pos(2) >= above && (below == 0 || m_pos(2) <= below))
+        if (m_pos.z() >= above && (below == 0 || m_pos.z() <= below))
             target_lift = this->config.retract_lift.get_at(m_extruder->id());
     }
     if (m_lifted == 0 && target_lift > 0) {
         m_lifted = target_lift;
-        return this->_travel_to_z(m_pos(2) + target_lift, "lift Z");
+        return this->_travel_to_z(m_pos.z() + target_lift, "lift Z");
     }
-    return "";
+    return {};
 }
 
 std::string GCodeWriter::unlift()
 {
     std::string gcode;
     if (m_lifted > 0) {
-        gcode += this->_travel_to_z(m_pos(2) - m_lifted, "restore layer Z");
+        gcode += this->_travel_to_z(m_pos.z() - m_lifted, "restore layer Z");
         m_lifted = 0;
     }
     return gcode;
diff --git a/src/libslic3r/GCodeWriter.hpp b/src/libslic3r/GCodeWriter.hpp
index e8a54737e..6c36c0d3a 100644
--- a/src/libslic3r/GCodeWriter.hpp
+++ b/src/libslic3r/GCodeWriter.hpp
@@ -61,7 +61,7 @@ public:
     std::string travel_to_z(double z, const std::string &comment = std::string());
     bool        will_move_z(double z) const;
     std::string extrude_to_xy(const Vec2d &point, double dE, const std::string &comment = std::string());
-    std::string extrude_to_xyz(const Vec3d &point, double dE, const std::string &comment = std::string());
+//    std::string extrude_to_xyz(const Vec3d &point, double dE, const std::string &comment = std::string());
     std::string retract(bool before_wipe = false);
     std::string retract_for_toolchange(bool before_wipe = false);
     std::string unretract();
@@ -121,6 +121,14 @@ public:
 //    static constexpr const int E_EXPORT_DIGITS    = 9;
 #endif
 
+    static constexpr const std::array<double, 10> pow_10    {   1.,     10.,    100.,    1000.,    10000.,    100000.,    1000000.,    10000000.,    100000000.,    1000000000.};
+    static constexpr const std::array<double, 10> pow_10_inv{1./1.,  1./10., 1./100., 1./1000., 1./10000., 1./100000., 1./1000000., 1./10000000., 1./100000000., 1./1000000000.};
+
+    // Quantize doubles to a resolution of the G-code.
+    static double                                 quantize(double v, size_t ndigits) { return std::round(v * pow_10[ndigits]) * pow_10_inv[ndigits]; }
+    static double                                 quantize_xyzf(double v) { return quantize(v, XYZF_EXPORT_DIGITS); }
+    static double                                 quantize_e(double v) { return quantize(v, E_EXPORT_DIGITS); }
+
     void emit_axis(const char axis, const double v, size_t digits);
 
     void emit_xy(const Vec2d &point) {