// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
//                    Qingnan Zhou <qnzhou@gmail.com>
// 
// This Source Code Form is subject to the terms of the Mozilla Public License 
// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
// obtain one at http://mozilla.org/MPL/2.0/.
//
#include "mesh_boolean.h"
#include <igl/cgal/assign_scalar.h>
#include <igl/cgal/propagate_winding_numbers.h>
#include <igl/cgal/remesh_self_intersections.h>
#include <igl/remove_unreferenced.h>
#include <igl/unique_simplices.h>

#include <CGAL/Exact_predicates_exact_constructions_kernel.h>

namespace igl {
    namespace boolean {
        namespace mesh_boolean_helper {
            typedef CGAL::Epeck Kernel;
            typedef Kernel::FT ExactScalar;

            template<
                typename DerivedV,
                typename DerivedF,
                typename DerivedVo,
                typename DerivedFo,
                typename DerivedJ>
            void igl_resolve(
                    const Eigen::PlainObjectBase<DerivedV>& V,
                    const Eigen::PlainObjectBase<DerivedF>& F,
                    Eigen::PlainObjectBase<DerivedVo>& Vo,
                    Eigen::PlainObjectBase<DerivedFo>& Fo,
                    Eigen::PlainObjectBase<DerivedJ>& J) {
                Eigen::VectorXi I;
                igl::cgal::RemeshSelfIntersectionsParam params;

                DerivedVo Vr;
                DerivedFo Fr;
                Eigen::MatrixXi IF;
                igl::cgal::remesh_self_intersections(V, F, params, Vr, Fr, IF, J, I);
                assert(I.size() == Vr.rows());

                // Merge coinciding vertices into non-manifold vertices.
                std::for_each(Fr.data(), Fr.data()+Fr.size(),
                        [&I](typename DerivedF::Scalar& a) { a=I[a]; });

                // Remove unreferenced vertices.
                Eigen::VectorXi UIM;
                igl::remove_unreferenced(Vr, Fr, Vo, Fo, UIM);
            }

            // Combine mesh A with mesh B and resolve all intersections.
            template<
                typename DerivedVA,
                typename DerivedVB,
                typename DerivedFA,
                typename DerivedFB,
                typename ResolveFunc,
                typename DerivedVC,
                typename DerivedFC,
                typename DerivedJ>
            void resolve_intersections(
                    const Eigen::PlainObjectBase<DerivedVA>& VA,
                    const Eigen::PlainObjectBase<DerivedFA>& FA,
                    const Eigen::PlainObjectBase<DerivedVB>& VB,
                    const Eigen::PlainObjectBase<DerivedFB>& FB,
                    const ResolveFunc& resolve_func,
                    Eigen::PlainObjectBase<DerivedVC>& VC,
                    Eigen::PlainObjectBase<DerivedFC>& FC,
                    Eigen::PlainObjectBase<DerivedJ>& J) {
                DerivedVA V(VA.rows()+VB.rows(),3);
                DerivedFA F(FA.rows()+FB.rows(),3);
                V << VA, VB;
                F << FA, FB.array() + VA.rows();
                resolve_func(V, F, VC, FC, J);
            }

            template<
                typename DerivedF1,
                typename DerivedJ1,
                typename DerivedF2,
                typename DerivedJ2 >
            void resolve_duplicated_faces(
                    const Eigen::PlainObjectBase<DerivedF1>& F1,
                    const Eigen::PlainObjectBase<DerivedJ1>& J1,
                    Eigen::PlainObjectBase<DerivedF2>& F2,
                    Eigen::PlainObjectBase<DerivedJ2>& J2) {
                typedef typename DerivedF1::Scalar Index;
                Eigen::VectorXi IA,IC;
                DerivedF1 uF;
                igl::unique_simplices(F1,uF,IA,IC);

                const size_t num_faces = F1.rows();
                const size_t num_unique_faces = uF.rows();
                assert(IA.rows() == num_unique_faces);
                // faces ontop of each unique face
                std::vector<std::vector<int> > uF2F(num_unique_faces);
                // signed counts
                Eigen::VectorXi counts = Eigen::VectorXi::Zero(num_unique_faces);
                Eigen::VectorXi ucounts = Eigen::VectorXi::Zero(num_unique_faces);
                // loop over all faces
                for (size_t i=0; i<num_faces; i++) {
                    const size_t ui = IC(i);
                    const bool consistent = 
                        (F1(i,0) == uF(ui, 0) &&
                         F1(i,1) == uF(ui, 1) &&
                         F1(i,2) == uF(ui, 2)) ||
                        (F1(i,0) == uF(ui, 1) &&
                         F1(i,1) == uF(ui, 2) &&
                         F1(i,2) == uF(ui, 0)) ||
                        (F1(i,0) == uF(ui, 2) &&
                         F1(i,1) == uF(ui, 0) &&
                         F1(i,2) == uF(ui, 1));
                    uF2F[ui].push_back(int(i+1) * (consistent?1:-1));
                    counts(ui) += consistent ? 1:-1;
                    ucounts(ui)++;
                }

                std::vector<size_t> kept_faces;
                for (size_t i=0; i<num_unique_faces; i++) {
                    if (ucounts[i] == 1) {
                        kept_faces.push_back(abs(uF2F[i][0])-1);
                        continue;
                    }
                    if (counts[i] == 1) {
                        bool found = false;
                        for (auto fid : uF2F[i]) {
                            if (fid > 0) {
                                kept_faces.push_back(abs(fid)-1);
                                found = true;
                                break;
                            }
                        }
                        assert(found);
                    } else if (counts[i] == -1) {
                        bool found = false;
                        for (auto fid : uF2F[i]) {
                            if (fid < 0) {
                                kept_faces.push_back(abs(fid)-1);
                                found = true;
                                break;
                            }
                        }
                        assert(found);
                    } else {
                        assert(counts[i] == 0);
                    }
                }

                const size_t num_kept = kept_faces.size();
                F2.resize(num_kept, 3);
                J2.resize(num_kept, 1);
                for (size_t i=0; i<num_kept; i++) {
                    F2.row(i) = F1.row(kept_faces[i]);
                    J2.row(i) = J1.row(kept_faces[i]);
                }
            }

            typedef Eigen::Matrix<int, 1, Eigen::Dynamic> WindingNumbers;
            typedef std::function<int(const WindingNumbers&)> WindingNumberOperation;

            WindingNumberOperation binary_union() {
                return [](const WindingNumbers& win_nums) -> int{
                    return win_nums[0] > 0 || win_nums[1] > 0;
                };
            }

            WindingNumberOperation binary_intersect() {
                return [](const WindingNumbers& win_nums) -> int{
                    return win_nums[0] > 0 && win_nums[1] > 0;
                };
            }

            WindingNumberOperation binary_difference() {
                return [](const WindingNumbers& win_nums) -> int{
                    return win_nums[0] > 0 && win_nums[1] <= 0;
                };
            }

            WindingNumberOperation binary_xor() {
                return [](const WindingNumbers& win_nums) -> int{
                    return (win_nums[0] > 0 && win_nums[1] <= 0) ||
                           (win_nums[0] <= 0 && win_nums[1] > 0);
                };
            }

            WindingNumberOperation binary_resolve() {
                return [](const WindingNumbers& win_nums) -> int{
                    return true;
                };
            }

            typedef std::function<short(int, int)> ToKeepFunc;
            ToKeepFunc keep_inside() {
                return [](int out_w, int in_w) -> short {
                    if (in_w > 0 && out_w <= 0) return 1;
                    else if (in_w <= 0 && out_w > 0) return -1;
                    else return 0;
                };
            }

            ToKeepFunc keep_all() {
                return [](int out_w, int in_w) -> short {
                    return true;
                };
            }
        }
    }
}

template <
typename DerivedVA,
typename DerivedFA,
typename DerivedVB,
typename DerivedFB,
typename WindingNumberOp,
typename KeepFunc,
typename ResolveFunc,
typename DerivedVC,
typename DerivedFC,
typename DerivedJ>
IGL_INLINE void igl::boolean::per_face_winding_number_binary_operation(
        const Eigen::PlainObjectBase<DerivedVA> & VA,
        const Eigen::PlainObjectBase<DerivedFA> & FA,
        const Eigen::PlainObjectBase<DerivedVB> & VB,
        const Eigen::PlainObjectBase<DerivedFB> & FB,
        const WindingNumberOp& wind_num_op,
        const KeepFunc& keep,
        const ResolveFunc& resolve_fun,
        Eigen::PlainObjectBase<DerivedVC > & VC,
        Eigen::PlainObjectBase<DerivedFC > & FC,
        Eigen::PlainObjectBase<DerivedJ > & J) {
    using namespace igl::boolean::mesh_boolean_helper;

    typedef typename DerivedVC::Scalar Scalar;
    typedef typename DerivedFC::Scalar Index;
    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,3> MatrixX3S;
    typedef Eigen::Matrix<Index,Eigen::Dynamic,Eigen::Dynamic> MatrixXI;
    typedef Eigen::Matrix<typename DerivedJ::Scalar,Eigen::Dynamic,1> VectorXJ;

    // Generate combined mesh.
    typedef Eigen::Matrix<
        ExactScalar,
        Eigen::Dynamic,
        Eigen::Dynamic,
        DerivedVC::IsRowMajor> MatrixXES;
    MatrixXES V;
    DerivedFC F;
    VectorXJ  CJ;
    resolve_intersections(VA, FA, VB, FB, resolve_fun, V, F, CJ);

    // Compute winding numbers on each side of each facet.
    const size_t num_faces = F.rows();
    Eigen::MatrixXi W;
    Eigen::VectorXi labels(num_faces);
    std::transform(CJ.data(), CJ.data()+CJ.size(), labels.data(),
            [&](int i) { return i<FA.rows() ? 0:1; });
    igl::cgal::propagate_winding_numbers_beta(V, F, labels, W);
    assert(W.rows() == num_faces);
    if (W.cols() == 2) {
        assert(FB.rows() == 0);
        Eigen::MatrixXi W_tmp(num_faces, 4);
        W_tmp << W, Eigen::MatrixXi::Zero(num_faces, 2);
        W = W_tmp;
    } else {
        assert(W.cols() == 4);
    }

    // Compute resulting winding number.
    Eigen::MatrixXi Wr(num_faces, 2);
    for (size_t i=0; i<num_faces; i++) {
        Eigen::MatrixXi w_out(1,2), w_in(1,2);
        w_out << W(i,0), W(i,2);
        w_in  << W(i,1), W(i,3);
        Wr(i,0) = wind_num_op(w_out);
        Wr(i,1) = wind_num_op(w_in);
    }

    // Extract boundary separating inside from outside.
    auto index_to_signed_index = [&](size_t i, bool ori) -> int{
        return (i+1)*(ori?1:-1);
    };
    auto signed_index_to_index = [&](int i) -> size_t {
        return abs(i) - 1;
    };
    std::vector<int> selected;
    for(size_t i=0; i<num_faces; i++) {
        auto should_keep = keep(Wr(i,0), Wr(i,1));
        if (should_keep > 0) {
            selected.push_back(index_to_signed_index(i, true));
        } else if (should_keep < 0) {
            selected.push_back(index_to_signed_index(i, false));
        }
    }

    const size_t num_selected = selected.size();
    DerivedFC kept_faces(num_selected, 3);
    DerivedJ  kept_face_indices;
    kept_face_indices.resize(num_selected, 1);
    for (size_t i=0; i<num_selected; i++) {
        size_t idx = abs(selected[i]) - 1;
        if (selected[i] > 0) {
            kept_faces.row(i) = F.row(idx);
        } else {
            kept_faces.row(i) = F.row(idx).reverse();
        }
        kept_face_indices(i, 0) = CJ[idx];
    }


    // Finally, remove duplicated faces and unreferenced vertices.
    {
        DerivedFC G;
        DerivedJ J;
        resolve_duplicated_faces(kept_faces, kept_face_indices, G, J);

        MatrixX3S Vs(V.rows(), V.cols());
        for (size_t i=0; i<V.rows(); i++) {
            for (size_t j=0; j<V.cols(); j++) {
                igl::cgal::assign_scalar(V(i,j), Vs(i,j));
            }
        }
        Eigen::VectorXi newIM;
        igl::remove_unreferenced(Vs,G,VC,FC,newIM);
    }
}

template <
typename DerivedVA,
typename DerivedFA,
typename DerivedVB,
typename DerivedFB,
typename DerivedVC,
typename DerivedFC,
typename DerivedJ>
IGL_INLINE void igl::boolean::mesh_boolean(
        const Eigen::PlainObjectBase<DerivedVA > & VA,
        const Eigen::PlainObjectBase<DerivedFA > & FA,
        const Eigen::PlainObjectBase<DerivedVB > & VB,
        const Eigen::PlainObjectBase<DerivedFB > & FB,
        const MeshBooleanType & type,
        Eigen::PlainObjectBase<DerivedVC > & VC,
        Eigen::PlainObjectBase<DerivedFC > & FC,
        Eigen::PlainObjectBase<DerivedJ > & J) {
    using namespace igl::boolean::mesh_boolean_helper;
    WindingNumberOperation op;
    ToKeepFunc keep;
    switch (type) {
        case MESH_BOOLEAN_TYPE_UNION:
            op = binary_union();
            keep = keep_inside();
            break;
        case MESH_BOOLEAN_TYPE_INTERSECT:
            op = binary_intersect();
            keep = keep_inside();
            break;
        case MESH_BOOLEAN_TYPE_MINUS:
            op = binary_difference();
            keep = keep_inside();
            break;
        case MESH_BOOLEAN_TYPE_XOR:
            op = binary_xor();
            keep = keep_inside();
            break;
        case MESH_BOOLEAN_TYPE_RESOLVE:
            op = binary_resolve();
            keep = keep_all();
            break;
        default:
            throw std::runtime_error("Unsupported boolean type.");
    }

    typedef Eigen::Matrix<
        ExactScalar,
        Eigen::Dynamic,
        Eigen::Dynamic,
        DerivedVC::IsRowMajor> MatrixXES;
    std::function<void(
            const Eigen::PlainObjectBase<DerivedVA>&,
            const Eigen::PlainObjectBase<DerivedFA>&,
            Eigen::PlainObjectBase<MatrixXES>&,
            Eigen::PlainObjectBase<DerivedFC>&,
            Eigen::PlainObjectBase<DerivedJ>&)> resolve_func =
        igl_resolve<DerivedVA, DerivedFA, MatrixXES, DerivedFC, DerivedJ>;

    igl::boolean::per_face_winding_number_binary_operation(
            VA, FA, VB, FB, op, keep, resolve_func, VC, FC, J);
}

template <
typename DerivedVA,
typename DerivedFA,
typename DerivedVB,
typename DerivedFB,
typename DerivedVC,
typename DerivedFC>
IGL_INLINE void igl::boolean::mesh_boolean(
        const Eigen::PlainObjectBase<DerivedVA > & VA,
        const Eigen::PlainObjectBase<DerivedFA > & FA,
        const Eigen::PlainObjectBase<DerivedVB > & VB,
        const Eigen::PlainObjectBase<DerivedFB > & FB,
        const MeshBooleanType & type,
        Eigen::PlainObjectBase<DerivedVC > & VC,
        Eigen::PlainObjectBase<DerivedFC > & FC) {
    Eigen::Matrix<typename DerivedFC::Index, Eigen::Dynamic,1> J;
    return igl::boolean::mesh_boolean(VA,FA,VB,FB,type,VC,FC,J);
}

#ifdef IGL_STATIC_LIBRARY
// Explicit template specialization
template void igl::boolean::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::boolean::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
#endif