ENH: 3D Honeycomb

Cherry-picks new 3D Honeycomb from Orca Slicer by David Eccles (gringer).
jira: 6697

Orignal commit message:
3D Honeycomb - switch direction at smallest bridge point, rather than every layer (#4425)

Co-authored-by: SoftFever <softfeverever@gmail.com>
Change-Id: Ida2e5b76a7b906be21045e053200519af1bd9489
(cherry picked from commit a9f521c37e04a0cf404184848aa738b8a6043f87)

src/libslic3r/Fill/Fill3DHoneycomb.cpp

@@ -6,6 +6,11 @@
 
 namespace Slic3r {
 
+// sign function
+template <typename T> int sgn(T val) {
+  return (T(0) < val) - (val < T(0));
+}
+  
 /*
 Creates a contiguous sequence of points at a specified height that make
 up a horizontal slice of the edges of a space filling truncated
@@ -16,50 +21,100 @@ and Y axes.
 Credits: David Eccles (gringer).
 */
 
+// triangular wave function
+// this has period (gridSize * 2), and amplitude (gridSize / 2),
+// with triWave(pos = 0) = 0
+static coordf_t triWave(coordf_t pos, coordf_t gridSize)
+{
+  float t = (pos / (gridSize * 2.)) + 0.25; // convert relative to grid size
+  t = t - (int)t; // extract fractional part
+  return((1. - abs(t * 8. - 4.)) * (gridSize / 4.) + (gridSize / 4.));
+}
+
+// truncated octagonal waveform, with period and offset
+// as per the triangular wave function. The Z position adjusts
+// the maximum offset [between -(gridSize / 4) and (gridSize / 4)], with a
+// period of (gridSize * 2) and troctWave(Zpos = 0) = 0
+static coordf_t troctWave(coordf_t pos, coordf_t gridSize, coordf_t Zpos)
+{
+  coordf_t Zcycle = triWave(Zpos, gridSize);
+  coordf_t perpOffset = Zcycle / 2;
+  coordf_t y = triWave(pos, gridSize);
+  return((abs(y) > abs(perpOffset)) ?
+	 (sgn(y) * perpOffset) :
+	 (y * sgn(perpOffset)));
+}
+
+// Identify the important points of curve change within a truncated
+// octahedron wave (as waveform fraction t):
+// 1. Start of wave (always 0.0)
+// 2. Transition to upper "horizontal" part
+// 3. Transition from upper "horizontal" part
+// 4. Transition to lower "horizontal" part
+// 5. Transition from lower "horizontal" part
+/*    o---o
+ *   /     \
+ * o/       \
+ *           \       /
+ *            \     /
+ *             o---o
+ */
+static std::vector<coordf_t> getCriticalPoints(coordf_t Zpos, coordf_t gridSize)
+{
+  std::vector<coordf_t> res = {0.};
+  coordf_t perpOffset = abs(triWave(Zpos, gridSize) / 2.);
+
+  coordf_t normalisedOffset = perpOffset / gridSize;
+  // // for debugging: just generate evenly-distributed points
+  // for(coordf_t i = 0; i < 2; i += 0.05){
+  //   res.push_back(gridSize * i);
+  // }
+  // note: 0 == straight line
+  if(normalisedOffset > 0){
+    res.push_back(gridSize * (0. + normalisedOffset));
+    res.push_back(gridSize * (1. - normalisedOffset));
+    res.push_back(gridSize * (1. + normalisedOffset));
+    res.push_back(gridSize * (2. - normalisedOffset));
+  }
+  return(res);
+}
+
 // Generate an array of points that are in the same direction as the
 // basic printing line (i.e. Y points for columns, X points for rows)
 // Note: a negative offset only causes a change in the perpendicular
 // direction
-static std::vector<coordf_t> colinearPoints(const coordf_t offset, const size_t baseLocation, size_t gridLength)
+static std::vector<coordf_t> colinearPoints(const coordf_t Zpos, coordf_t gridSize, std::vector<coordf_t> critPoints,
+					     const size_t baseLocation, size_t gridLength)
 {
-    const coordf_t offset2 = std::abs(offset / coordf_t(2.));
   std::vector<coordf_t> points;
-    points.push_back(baseLocation - offset2);
+  points.push_back(baseLocation);
-    for (size_t i = 0; i < gridLength; ++i) {
+  for (coordf_t cLoc = baseLocation; cLoc < gridLength; cLoc+= (gridSize*2)) {
-        points.push_back(baseLocation + i + offset2);
+    for(size_t pi = 0; pi < critPoints.size(); pi++){
-        points.push_back(baseLocation + i + 1 - offset2);
+      points.push_back(baseLocation + cLoc + critPoints[pi]);
     }
-    points.push_back(baseLocation + gridLength + offset2);
+  }
+  points.push_back(gridLength);
   return points;
 }
 
 // Generate an array of points for the dimension that is perpendicular to
 // the basic printing line (i.e. X points for columns, Y points for rows)
-static std::vector<coordf_t> perpendPoints(const coordf_t offset, const size_t baseLocation, size_t gridLength)
+  static std::vector<coordf_t> perpendPoints(const coordf_t Zpos, coordf_t gridSize, std::vector<coordf_t> critPoints,
+					     size_t baseLocation, size_t gridLength,
+                                             size_t offsetBase, coordf_t perpDir)
 {
-    coordf_t offset2 = offset / coordf_t(2.);
-    coord_t  side    = 2 * (baseLocation & 1) - 1;
   std::vector<coordf_t> points;
-    points.push_back(baseLocation - offset2 * side);
+  points.push_back(offsetBase);
-    for (size_t i = 0; i < gridLength; ++i) {
+  for (coordf_t cLoc = baseLocation; cLoc < gridLength; cLoc+= gridSize*2) {
-        side = 2*((i+baseLocation) & 1) - 1;
+    for(size_t pi = 0; pi < critPoints.size(); pi++){
-        points.push_back(baseLocation + offset2 * side);
+      coordf_t offset = troctWave(critPoints[pi], gridSize, Zpos);
-        points.push_back(baseLocation + offset2 * side);
+      points.push_back(offsetBase + (offset * perpDir));
     }
-    points.push_back(baseLocation - offset2 * side);
+  }
+  points.push_back(offsetBase);
   return points;
 }
 
-// Trims an array of points to specified rectangular limits. Point
-// components that are outside these limits are set to the limits.
-static inline void trim(Pointfs &pts, coordf_t minX, coordf_t minY, coordf_t maxX, coordf_t maxY)
-{
-    for (Vec2d &pt : pts) {
-        pt.x() = std::clamp(pt.x(), minX, maxX);
-        pt.y() = std::clamp(pt.y(), minY, maxY);
-    }
-}
-
 static inline Pointfs zip(const std::vector<coordf_t> &x, const std::vector<coordf_t> &y)
 {
     assert(x.size() == y.size());
@@ -71,43 +126,33 @@ static inline Pointfs zip(const std::vector<coordf_t> &x, const std::vector<coor
 }
 
 // Generate a set of curves (array of array of 2d points) that describe a
-// horizontal slice of a truncated regular octahedron with edge length 1.
+// horizontal slice of a truncated regular octahedron.
-// curveType specifies which lines to print, 1 for vertical lines
+static std::vector<Pointfs> makeActualGrid(coordf_t Zpos, coordf_t gridSize, size_t boundsX, size_t boundsY)
-// (columns), 2 for horizontal lines (rows), and 3 for both.
-static std::vector<Pointfs> makeNormalisedGrid(coordf_t z, size_t gridWidth, size_t gridHeight, size_t curveType)
 {
-    // offset required to create a regular octagram
-    coordf_t octagramGap = coordf_t(0.5);
-    
-    // sawtooth wave function for range f($z) = [-$octagramGap .. $octagramGap]
-    coordf_t a = std::sqrt(coordf_t(2.));  // period
-    coordf_t wave = fabs(fmod(z, a) - a/2.)/a*4. - 1.;
-    coordf_t offset = wave * octagramGap;
-    
   std::vector<Pointfs> points;
-    if ((curveType & 1) != 0) {
+  std::vector<coordf_t> critPoints = getCriticalPoints(Zpos, gridSize);
-        for (size_t x = 0; x <= gridWidth; ++x) {
+  coordf_t zCycle = fmod(Zpos + gridSize/2, gridSize * 2.) / (gridSize * 2.);
+  bool printVert = zCycle < 0.5;
+  if (printVert) {
+    int perpDir = -1;
+    for (coordf_t x = 0; x <= (boundsX); x+= gridSize, perpDir *= -1) {
       points.push_back(Pointfs());
       Pointfs &newPoints = points.back();
       newPoints = zip(
-                perpendPoints(offset, x, gridHeight), 
+		      perpendPoints(Zpos, gridSize, critPoints, 0, boundsY, x, perpDir),
-                colinearPoints(offset, 0, gridHeight));
+		      colinearPoints(Zpos, gridSize, critPoints, 0, boundsY));
-            // trim points to grid edges
+      if (perpDir == 1)
-            trim(newPoints, coordf_t(0.), coordf_t(0.), coordf_t(gridWidth), coordf_t(gridHeight));
-            if (x & 1)
 	std::reverse(newPoints.begin(), newPoints.end());
     }
-    }
+  } else {
-    if ((curveType & 2) != 0) {
+    int perpDir = 1;
-        for (size_t y = 0; y <= gridHeight; ++y) {
+    for (coordf_t y = gridSize; y <= (boundsY); y+= gridSize, perpDir *= -1) {
       points.push_back(Pointfs());
       Pointfs &newPoints = points.back();
       newPoints = zip(
-                colinearPoints(offset, 0, gridWidth),
+		      colinearPoints(Zpos, gridSize, critPoints, 0, boundsX),
-                perpendPoints(offset, y, gridWidth));
+		      perpendPoints(Zpos, gridSize, critPoints, 0, boundsX, y, perpDir));
-            // trim points to grid edges
+      if (perpDir == -1)
-            trim(newPoints, coordf_t(0.), coordf_t(0.), coordf_t(gridWidth), coordf_t(gridHeight));
-            if (y & 1)
 	std::reverse(newPoints.begin(), newPoints.end());
     }
   }
@@ -117,22 +162,31 @@ static std::vector<Pointfs> makeNormalisedGrid(coordf_t z, size_t gridWidth, siz
 // Generate a set of curves (array of array of 2d points) that describe a
 // horizontal slice of a truncated regular octahedron with a specified
 // grid square size.
-static Polylines makeGrid(coord_t z, coord_t gridSize, size_t gridWidth, size_t gridHeight, size_t curveType)
+// gridWidth and gridHeight define the width and height of the bounding box respectively
+static Polylines makeGrid(coordf_t z, coordf_t gridSize, coordf_t boundWidth, coordf_t boundHeight, bool fillEvenly)
 {
-    coord_t  scaleFactor = gridSize;
+  std::vector<Pointfs> polylines = makeActualGrid(z, gridSize, boundWidth, boundHeight);
-    coordf_t normalisedZ = coordf_t(z) / coordf_t(scaleFactor);
-    std::vector<Pointfs> polylines = makeNormalisedGrid(normalisedZ, gridWidth, gridHeight, curveType);
   Polylines result;
   result.reserve(polylines.size());
-    for (std::vector<Pointfs>::const_iterator it_polylines = polylines.begin(); it_polylines != polylines.end(); ++ it_polylines) {
+  for (std::vector<Pointfs>::const_iterator it_polylines = polylines.begin();
+       it_polylines != polylines.end(); ++ it_polylines) {
     result.push_back(Polyline());
     Polyline &polyline = result.back();
     for (Pointfs::const_iterator it = it_polylines->begin(); it != it_polylines->end(); ++ it)
-            polyline.points.push_back(Point(coord_t((*it)(0) * scaleFactor), coord_t((*it)(1) * scaleFactor)));
+      polyline.points.push_back(Point(coord_t((*it)(0)), coord_t((*it)(1))));
   }
   return result;
 }
 
+// FillParams has the following useful information:
+// density <0 .. 1>  [proportion of space to fill]
+// anchor_length     [???]
+// anchor_length_max [???]
+// dont_connect()    [avoid connect lines]
+// dont_adjust       [avoid filling space evenly]
+// monotonic         [fill strictly left to right]
+// complete          [complete each loop]
+  
 void Fill3DHoneycomb::_fill_surface_single(
     const FillParams                &params, 
     unsigned int                     thickness_layers,
@@ -142,27 +196,75 @@ void Fill3DHoneycomb::_fill_surface_single(
 {
     // no rotation is supported for this infill pattern
     BoundingBox bb = expolygon.contour.bounding_box();
-    coord_t     distance = coord_t(scale_(this->spacing) / params.density);
+
+    // Note: with equally-scaled X/Y/Z, the pattern will create a vertically-stretched
+    // truncated octahedron; so Z is pre-adjusted first by scaling by sqrt(2)
+    coordf_t zScale = sqrt(2);
+
+    // adjustment to account for the additional distance of octagram curves
+    // note: this only strictly applies for a rectangular area where the total
+    //       Z travel distance is a multiple of the spacing... but it should
+    //       be at least better than the prevous estimate which assumed straight
+    //       lines
+    // = 4 * integrate(func=4*x(sqrt(2) - 1) + 1, from=0, to=0.25)
+    // = (sqrt(2) + 1) / 2 [... I think]
+    // make a first guess at the preferred grid Size
+    coordf_t gridSize = (scale_(this->spacing) * ((zScale + 1.) / 2.) / params.density);
+
+    // This density calculation is incorrect for many values > 25%, possibly
+    // due to quantisation error, so this value is used as a first guess, then the
+    // Z scale is adjusted to make the layer patterns consistent / symmetric
+    // This means that the resultant infill won't be an ideal truncated octahedron,
+    // but it should look better than the equivalent quantised version
+    
+    coordf_t layerHeight = scale_(thickness_layers);
+    // ceiling to an integer value of layers per Z
+    // (with a little nudge in case it's close to perfect)
+    coordf_t layersPerModule = floor((gridSize * 2) / (zScale * layerHeight) + 0.05);
+    if(params.density > 0.42){ // exact layer pattern for >42% density
+      layersPerModule = 2;
+      // re-adjust the grid size for a partial octahedral path
+      // (scale of 1.1 guessed based on modeling)
+      gridSize = (scale_(this->spacing) * 1.1 / params.density);
+      // re-adjust zScale to make layering consistent
+      zScale = (gridSize * 2) / (layersPerModule * layerHeight);
+    } else {
+      if(layersPerModule < 2){
+	layersPerModule = 2;
+      }
+      // re-adjust zScale to make layering consistent
+      zScale = (gridSize * 2) / (layersPerModule * layerHeight);
+      // re-adjust the grid size to account for the new zScale
+      gridSize = (scale_(this->spacing) * ((zScale + 1.) / 2.) / params.density);
+      // re-calculate layersPerModule and zScale
+      layersPerModule = floor((gridSize * 2) / (zScale * layerHeight) + 0.05);
+      if(layersPerModule < 2){
+	layersPerModule = 2;
+      }
+      zScale = (gridSize * 2) / (layersPerModule * layerHeight);
+    }
 
     // align bounding box to a multiple of our honeycomb grid module
-    // (a module is 2*$distance since one $distance half-module is 
+    // (a module is 2*$gridSize since one $gridSize half-module is 
-    // growing while the other $distance half-module is shrinking)
+    // growing while the other $gridSize half-module is shrinking)
-    bb.merge(align_to_grid(bb.min, Point(2*distance, 2*distance)));
+    bb.merge(align_to_grid(bb.min, Point(gridSize*4, gridSize*4)));
     
     // generate pattern
-    Polylines   polylines = makeGrid(
+    Polylines polylines =
-        scale_(this->z),
+      makeGrid(
-        distance,
+	       scale_(this->z) * zScale,
-        ceil(bb.size()(0) / distance) + 1,
+	       gridSize,
-        ceil(bb.size()(1) / distance) + 1,
+	       bb.size()(0),
-        ((this->layer_id/thickness_layers) % 2) + 1);
+	       bb.size()(1),
+	       !params.dont_adjust);
     
     // move pattern in place
-	for (Polyline &pl : polylines)
+    for (Polyline &pl : polylines){
       pl.translate(bb.min);
+    }
 
     // clip pattern to boundaries, chain the clipped polylines
-    polylines = intersection_pl(polylines, expolygon);
+    polylines = intersection_pl(polylines, to_polygons(expolygon));
 
     // connect lines if needed
     if (params.dont_connect() || polylines.size() <= 1)

src/libslic3r/Fill/Fill3DHoneycomb.hpp

@@ -15,9 +15,6 @@ public:
     Fill* clone() const override { return new Fill3DHoneycomb(*this); };
     ~Fill3DHoneycomb() override {}
 
-	// require bridge flow since most of this pattern hangs in air
-    bool use_bridge_flow() const override { return true; }
-
 protected:
 	void _fill_surface_single(
 	    const FillParams                &params,