ENH: auto-arrange uses inner NFP to simplify fixed_overfit

1. Add inner nfp algo.The final nfp result is inner nfp subtract outer nfp.
2. Leave 5(scaled) room in inflation to allow numeric float eps.

Change-Id: I6be0b205c9811af24a238352b256bf1399ee3716
(cherry picked from commit dbab96efc7bfa16afd9db9607b862886606b0aa0)

src/libnest2d/include/libnest2d/backends/libslic3r/geometries.hpp

@@ -261,6 +261,8 @@ inline TMultiShape<PolygonImpl> merge(const TMultiShape<PolygonImpl>& shapes)
     return Slic3r::union_ex(shapes);
 }
 
+inline TMultiShape<PolygonImpl> subtract(const TMultiShape<PolygonImpl> &outerBinNfp, const TMultiShape<PolygonImpl> &shapes) { return Slic3r::diff_ex(outerBinNfp, shapes); }
+
 } // namespace nfp
 } // namespace libnest2d
 

src/libnest2d/include/libnest2d/geometry_traits_nfp.hpp

@@ -179,6 +179,42 @@ inline TPoint<RawShape> referenceVertex(const RawShape& sh)
     return rightmostUpVertex(sh);
 }
 
+template<class RawBox, class RawShape, class Ratio = double> inline NfpResult<RawShape> nfpInnerRectBed(const RawBox &bed, const RawShape &other)
+{
+    using Vertex = TPoint<RawShape>;
+    using Edge   = _Segment<Vertex>;
+    namespace sl = shapelike;
+
+    auto    sbox         = sl::boundingBox(other);
+    auto sheight      = sbox.height();
+    auto swidth       = sbox.width();
+    Vertex  slidingTop   = rightmostUpVertex(other);
+    auto leftOffset   = slidingTop.x() - sbox.minCorner().x();
+    auto rightOffset  = slidingTop.x() - sbox.maxCorner().x();
+    auto topOffset    = 0;
+    auto bottomOffset = sheight;
+
+
+    auto boxWidth  = bed.width();
+    auto boxHeight = bed.height();
+
+    auto bedMinx = bed.minCorner().x();
+    auto bedMiny = bed.minCorner().y();
+    auto bedMaxx = bed.maxCorner().x();
+    auto bedMaxy = bed.maxCorner().y();
+
+    RawShape innerNfp{{bedMinx + leftOffset, bedMaxy + topOffset},
+                      {bedMaxx + rightOffset, bedMaxy + topOffset},
+                      {bedMaxx + rightOffset, bedMiny + bottomOffset},
+                      {bedMinx + leftOffset, bedMiny + bottomOffset},
+                      {bedMinx + leftOffset, bedMaxy + topOffset}};
+    if (sheight > boxHeight || swidth > boxWidth) {
+        return {{}, {0, 0}};
+    } else {
+        return {innerNfp, {0, 0}};
+    }
+}
+
 /**
  * The "trivial" Cuninghame-Green implementation of NFP for convex polygons.
  *

src/libnest2d/include/libnest2d/placers/nfpplacer.hpp

@@ -565,7 +565,7 @@ private:
 
     using Shapes = TMultiShape<RawShape>;
 
-    Shapes calcnfp(const Item &trsh, Lvl<nfp::NfpLevel::CONVEX_ONLY>)
+    Shapes calcnfp(const Item &trsh, const Box& bed ,Lvl<nfp::NfpLevel::CONVEX_ONLY>)
     {
         using namespace nfp;
 
@@ -598,7 +598,8 @@ private:
             nfps[n] = subnfp_r.first;
         });
 
-        return nfp::merge(nfps);
+        RawShape innerNfp = nfpInnerRectBed(bed, trsh.transformedShape()).first;
+        return nfp::subtract({innerNfp}, nfps);
     }
 
 
@@ -738,7 +739,7 @@ private:
                 // it is disjunct from the current merged pile
                 placeOutsideOfBin(item);
 
-                nfps = calcnfp(item, Lvl<MaxNfpLevel::value>());
+                nfps = calcnfp(item, binbb, Lvl<MaxNfpLevel::value>());
 
 
                 auto iv = item.referenceVertex();