/* Copyright (c) 1997-2020
   Ewgenij Gawrilow, Michael Joswig, and the polymake team
   Technische Universität Berlin, Germany
   https://polymake.org

   This program is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by the
   Free Software Foundation; either version 2, or (at your option) any
   later version: http://www.gnu.org/licenses/gpl.txt.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
--------------------------------------------------------------------------------
*/

#include "polymake/client.h"
#include "polymake/vector"
#include "polymake/Rational.h"
#include "polymake/Matrix.h"
#include "polymake/Vector.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/common/labels.h"

namespace polymake { namespace polytope {

template<typename Scalar>
BigObject bipyramid(BigObject p_in, const Scalar& z, const Scalar& z_prime, OptionSet options)
{
   if (z*z_prime >= 0) 
      throw std::runtime_error("bipyramid: z and z' must have opposite signs and be non-zero");

   BigObject p_out("Polytope", mlist<Scalar>());
   p_out.set_description() << "Bipyramid over " << p_in.name() << endl;

   const bool noc = options["no_coordinates"],
          relabel = !options["no_labels"];

   Int n_vertices = 0;
   if (noc || p_in.exists("VERTICES_IN_FACETS")) {
      const IncidenceMatrix<> VIF=p_in.give("VERTICES_IN_FACETS");
      n_vertices = VIF.cols();
      const Int n_facets = VIF.rows();
      const IncidenceMatrix<> VIF_out = (VIF / VIF) | sequence(0,n_facets) | sequence(n_facets,n_facets);

      p_out.take("N_VERTICES") << n_vertices+2;
      p_out.take("VERTICES_IN_FACETS") << VIF_out;
   }
   if (noc) {
      if (p_in.exists("COMBINATORIAL_DIM")) {
         const Int dim = p_in.give("COMBINATORIAL_DIM");
         p_out.take("COMBINATORIAL_DIM") << dim+1;
      }
   } else {
      const bool pointed=p_in.give("POINTED");
      if (!pointed)
         throw std::runtime_error("bipyramid: input polyhedron not pointed");

      const Matrix<Scalar> V=p_in.give("VERTICES");
      const Vector<Scalar> z0=p_in.give("REL_INT_POINT");
      n_vertices=V.rows();
      const Matrix<Scalar> V_out=(V | zero_vector<Scalar>()) /
                                   (z0 | z) /
                                   (z0 | z_prime);
      p_out.take("VERTICES") << V_out;
   }
   if (relabel) {
      std::vector<std::string> labels = common::read_labels(p_in, "VERTEX_LABELS", n_vertices);
      labels.emplace_back("Apex");
      labels.emplace_back("Apex'");
      p_out.take("VERTEX_LABELS") << labels;
   }
   return p_out;
}

UserFunctionTemplate4perl("# @category Producing a polytope from polytopes"
                          "# Make a bipyramid over a pointed polyhedron."
                          "# The bipyramid is the convex hull of the input polyhedron //P//"
                          "# and two points (//v//, //z//), (//v//, //z_prime//)"
                          "# on both sides of the affine span of //P//. For bounded polyhedra, the apex projections"
                          "# //v// to the affine span of //P// coincide with the vertex barycenter of //P//."
                          "# @param Polytope P"
                          "# @param Scalar z distance between the vertex barycenter and the first apex,"
                          "#  default value is 1."
                          "# @param Scalar z_prime distance between the vertex barycenter and the second apex,"
                          "#  default value is -//z//."
                          "# @option Bool no_coordinates : don't compute the coordinates, purely combinatorial description is produced."
                          "# @option Bool no_labels Do not copy [[VERTEX_LABELS]] from the original polytope. default: 0"
                          "#  label the new vertices with \"Apex\" and \"Apex'\"."
                          "# @return Polytope"
                          "# @example Here's a way to construct the 3-dimensional cross polytope:"
                          "# > $p = bipyramid(bipyramid(cube(1)));"
                          "# > print equal_polyhedra($p,cross(3));"
                          "# | true",
                          "bipyramid<Scalar>(Polytope<type_upgrade<Scalar>>; type_upgrade<Scalar>=1, type_upgrade<Scalar>=(-$_[1]), {no_coordinates => undef, no_labels => 0})");
} }

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