Search for suitable rotation when arranging items larger than the bed

src/libnest2d/include/libnest2d/utils/rotcalipers.hpp

@@ -90,12 +90,29 @@ inline R rectarea(const Pt& w, const std::array<It, 4>& rect)
     return rectarea<Pt, Unit, R>(w, *rect[0], *rect[1], *rect[2], *rect[3]);
 }
 
+template<class Pt, class Unit = TCompute<Pt>, class R = TCompute<Pt>>
+inline R rectarea(const Pt& w, // the axis
+                  const Unit& a,
+                  const Unit& b)
+{
+    R m = R(a) / pl::magnsq<Pt, Unit>(w);
+    m = m * b;
+    return m;
+};
+
+template<class R, class Pt, class Unit>
+inline R rectarea(const RotatedBox<Pt, Unit> &rb)
+{
+    return rectarea<Pt, Unit, R>(rb.axis(), rb.bottom_extent(), rb.right_extent());
+};
+
 // This function is only applicable to counter-clockwise oriented convex
 // polygons where only two points can be collinear witch each other.
 template <class RawShape,
           class Unit = TCompute<RawShape>,
-          class Ratio = TCompute<RawShape>> 
+          class Ratio = TCompute<RawShape>,
-RotatedBox<TPoint<RawShape>, Unit> minAreaBoundingBox(const RawShape& sh) 
+          class VisitFn>
+void rotcalipers(const RawShape& sh, VisitFn &&visitfn)
 {
     using Point = TPoint<RawShape>;
     using Iterator = typename TContour<RawShape>::const_iterator;
@@ -106,9 +123,9 @@ RotatedBox<TPoint<RawShape>, Unit> minAreaBoundingBox(const RawShape& sh)
     auto last = std::prev(sl::cend(sh));
 
     // Check conditions and return undefined box if input is not sane.
-    if(last == first) return {};
+    if(last == first) return;
     if(getX(*first) == getX(*last) && getY(*first) == getY(*last)) --last;
-    if(last - first < 2) return {};
+    if(last - first < 2) return;
 
     RawShape shcpy; // empty at this point
     {
@@ -219,12 +236,14 @@ RotatedBox<TPoint<RawShape>, Unit> minAreaBoundingBox(const RawShape& sh)
     };
 
     Point w(1, 0);
-    Point w_min = w;
-    Ratio minarea((Unit(getX(*maxX)) - getX(*minX)) * 
-                  (Unit(getY(*maxY)) - getY(*minY)));
-    
     std::array<Iterator, 4> rect = {minY, maxX, maxY, minX};
-    std::array<Iterator, 4> minrect = rect;
+
+    {
+        Unit a = dot<Point, Unit>(w, *rect[1] - *rect[3]);
+        Unit b = dot<Point, Unit>(-perp(w), *rect[2] - *rect[0]);
+        if (!visitfn(RotatedBox<Point, Unit>{w, a, b}))
+            return;
+    }
 
     // An edge might be examined twice in which case the algorithm terminates.
     size_t c = 0, count = last - first + 1;
@@ -243,18 +262,35 @@ RotatedBox<TPoint<RawShape>, Unit> minAreaBoundingBox(const RawShape& sh)
         // get the unnormalized direction vector
         w = *rect[0] - *prev(rect[0]);
 
-        // get the area of the rotated rectangle
+        Unit a = dot<Point, Unit>(w, *rect[1] - *rect[3]);
-        Ratio rarea = rectarea<Point, Unit, Ratio>(w, rect);
+        Unit b = dot<Point, Unit>(-perp(w), *rect[2] - *rect[0]);
+        if (!visitfn(RotatedBox<Point, Unit>{w, a, b}))
+            break;
+    }
+}
 
-        // Update min area and the direction of the min bounding box;
+// This function is only applicable to counter-clockwise oriented convex
-        if(rarea <= minarea) { w_min = w; minarea = rarea; minrect = rect; }
+// polygons where only two points can be collinear witch each other.
+template <class S,
+          class Unit = TCompute<S>,
+          class Ratio = TCompute<S>>
+RotatedBox<TPoint<S>, Unit> minAreaBoundingBox(const S& sh)
+{
+    RotatedBox<TPoint<S>, Unit> minbox;
+    Ratio minarea = std::numeric_limits<Unit>::max();
+    auto minfn = [&minarea, &minbox](const RotatedBox<TPoint<S>, Unit> &rbox){
+        Ratio area = rectarea<Ratio>(rbox);
+        if (area <= minarea)  {
+            minarea = area;
+            minbox = rbox;
         }
 
-    Unit a = dot<Point, Unit>(w_min, *minrect[1] - *minrect[3]);
+        return true; // continue search
-    Unit b = dot<Point, Unit>(-perp(w_min), *minrect[2] - *minrect[0]);
+    };
-    RotatedBox<Point, Unit> bb(w_min, a, b);
 
-    return bb;
+    rotcalipers<S, Unit, Ratio>(sh, minfn);
+
+    return minbox;
 }
 
 template <class RawShape> Radians minAreaBoundingBoxRotation(const RawShape& sh)
@@ -262,7 +298,75 @@ template <class RawShape> Radians minAreaBoundingBoxRotation(const RawShape& sh)
     return minAreaBoundingBox(sh).angleToX();
 }
 
+// Function to find a rotation for a shape that makes it fit into a box.
+//
+// The method is based on finding a pair of rotations from the rotating calipers
+// algorithm such that the aspect ratio is changing from being smaller than
+// that of the target to being bigger or vice versa. So that the correct
+// AR is somewhere between the obtained pair of angles. Then bisecting that
+// interval is sufficient to find the correct angle.
+//
+// The argument eps is the absolute error limit for the searched angle interval.
+template<class S, class Unit = TCompute<S>, class Ratio = TCompute<S>>
+Radians fitIntoBoxRotation(const S &shape, const _Box<TPoint<S>> &box, Radians eps = 1e-4)
+{
+    constexpr auto get_aspect_r = [](const auto &b) -> double {
+        return double(b.width()) / b.height();
+    };
 
+    auto aspect_r = get_aspect_r(box);
+
+    RotatedBox<TPoint<S>, Unit> prev_rbox;
+    Radians a_from = 0., a_to = 0.;
+    auto visitfn = [&](const RotatedBox<TPoint<S>, Unit> &rbox) {
+        bool lower_prev    = get_aspect_r(prev_rbox) < aspect_r;
+        bool lower_current = get_aspect_r(rbox) < aspect_r;
+
+        if (lower_prev != lower_current) {
+            a_from = prev_rbox.angleToX();
+            a_to   = rbox.angleToX();
+            return false;
+        }
+
+        return true;
+    };
+
+    rotcalipers<S, Unit, Ratio>(shape, visitfn);
+
+    auto rot_shape_bb = [&shape](Radians r) {
+        auto s = shape;
+        sl::rotate(s, r);
+        return sl::boundingBox(s);
+    };
+
+    auto rot_aspect_r = [&rot_shape_bb, &get_aspect_r](Radians r) {
+        return get_aspect_r(rot_shape_bb(r));
+    };
+
+    // Lets bisect the retrieved interval where the correct aspect ratio is.
+    double ar_from = rot_aspect_r(a_from);
+    auto would_fit = [&box](const _Box<TPoint<S>> &b) {
+        return b.width() < box.width() && b.height() < box.height();
+    };
+
+    Radians middle = (a_from + a_to) / 2.;
+    _Box<TPoint<S>> box_middle = rot_shape_bb(middle);
+    while (!would_fit(box_middle) && std::abs(a_to - a_from) > eps)
+    {
+        double ar_middle = get_aspect_r(box_middle);
+        if ((ar_from < aspect_r) != (ar_middle < aspect_r))
+            a_to = middle;
+        else
+            a_from = middle;
+
+        ar_from = rot_aspect_r(a_from);
+        middle = (a_from + a_to) / 2.;
+        box_middle = rot_shape_bb(middle);
+    }
+
+    return middle;
 }
 
+} // namespace libnest2d
+
 #endif // ROTCALIPERS_HPP

src/libslic3r/Arrange.cpp

@@ -472,6 +472,12 @@ template<class S> Radians min_area_boundingbox_rotation(const S &sh)
         .angleToX();
 }
 
+template<class S>
+Radians fit_into_box_rotation(const S &sh, const _Box<TPoint<S>> &box)
+{
+    return fitIntoBoxRotation<S, TCompute<S>, boost::rational<LargeInt>>(sh, box);
+}
+
 template<class BinT> // Arrange for arbitrary bin type
 void _arrange(
         std::vector<Item> &           shapes,
@@ -509,10 +515,19 @@ void _arrange(
     // Use the minimum bounding box rotation as a starting point.
     // TODO: This only works for convex hull. If we ever switch to concave
     // polygon nesting, a convex hull needs to be calculated.
-    if (params.allow_rotations)
+    if (params.allow_rotations) {
-        for (auto &itm : shapes)
+        for (auto &itm : shapes) {
             itm.rotation(min_area_boundingbox_rotation(itm.rawShape()));
 
+            // If the item is too big, try to find a rotation that makes it fit
+            if constexpr (std::is_same_v<BinT, Box>) {
+                auto bb = itm.boundingBox();
+                if (bb.width() >= bin.width() || bb.height() >= bin.height())
+                    itm.rotate(fit_into_box_rotation(itm.transformedShape(), bin));
+            }
+        }
+    }
+
     arranger(inp.begin(), inp.end());
     for (Item &itm : inp) itm.inflate(-infl);
 }