### Sample Code or DRAW Tcl Script

#include <BOPAlgo_CellsBuilder.hxx>
#include <BOPAlgo_PaveFiller.hxx>
#include <BRepBndLib.hxx>
#include <BRepTools.hxx>
#include <BRep_Builder.hxx>
#include <Bnd_Box.hxx>

#include <GeomAPI_ProjectPointOnCurve.hxx>
#include <IntTools_Context.hxx>
#include <NCollection_IncAllocator.hxx>
#include <ShapeUpgrade_UnifySameDomain.hxx>

#include <TopExp_Explorer.hxx>

namespace {

std::pair<TopoDS_Shape, TopoDS_Shape> cut(const TopoDS_Shape &lhs, const TopoDS_Shape &rhs)
{
  BOPAlgo_PaveFiller pave_filler;

  TopTools_ListOfShape arguments;
  arguments.Append(lhs);
  arguments.Append(rhs);
  pave_filler.SetArguments(arguments);

  std::cout << "start pave filler perform" << std::endl;
  pave_filler.Perform();
  std::cout << "end pave filler perform" << std::endl;

  if (pave_filler.HasErrors())
  {
    std::ostringstream oss;
    pave_filler.DumpErrors(oss);
  }

  if (pave_filler.HasWarnings())
  {
    std::cerr << std::endl;
    pave_filler.DumpWarnings(std::cerr);
    std::cerr << std::endl;
  }

  BOPAlgo_CellsBuilder cells_builder;
  cells_builder.SetToFillHistory(Standard_False);
  cells_builder.SetCheckInverted(Standard_False);
  cells_builder.AddArgument(lhs);
  cells_builder.AddArgument(rhs);
  cells_builder.PerformWithFiller(pave_filler);

  TopoDS_Shape cut_shape;
  {
    TopTools_ListOfShape take, avoid;
    cells_builder.RemoveAllFromResult();
    take.Append(lhs);
    avoid.Append(rhs);
    cells_builder.AddToResult(take, avoid, 0, Standard_False);
    cut_shape = cells_builder.Shape();
  }

  TopoDS_Shape common_shape;
  {
    TopTools_ListOfShape take, avoid;
    cells_builder.RemoveAllFromResult();
    take.Append(lhs);
    take.Append(rhs);
    cells_builder.AddToResult(take, avoid, 0, Standard_False);
    common_shape = cells_builder.Shape();
  }

  return std::make_pair(cut_shape, common_shape);
}
} // namespace

int main()
{
  TopoDS_Shape lhs;
  BRep_Builder builder;
  const char *lhs_filename = "/path/to/lhs.brep";

  if (!BRepTools::Read(lhs, lhs_filename, builder))
  {
    std::cerr << "Failed to read " << lhs_filename << std::endl;
  }

  TopoDS_Shape rhs;
  const char *rhs_filename = "/path/to/rhs.brep";
  if (!BRepTools::Read(rhs, rhs_filename, builder))
  {
    std::cerr << "Failed to read " << rhs_filename << std::endl;
  }

  const auto [cut_shape, common_shape] = cut(lhs, rhs);

  return 0;
}