libigl_Martin/include/igl/cgal/order_facets_around_edge.cpp

#include "order_facets_around_edge.h"
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>

namespace igl {
    namespace cgal {
        namespace order_facets_around_edges_helper {
            template<typename T>
            std::vector<size_t> index_sort(const std::vector<T>& data) {
                const size_t len = data.size();
                std::vector<size_t> order(len);
                for (size_t i=0; i<len; i++) order[i] = i;

                auto comp = [&](size_t i, size_t j) {
                    return data[i] < data[j];
                };
                std::sort(order.begin(), order.end(), comp);
                return order;
            }
        }
    }
}

// adj_faces contains signed index starting from +- 1.
template<
    typename DerivedV,
    typename DerivedF,
    typename DerivedI >
void igl::cgal::order_facets_around_edge(
    const Eigen::PlainObjectBase<DerivedV>& V,
    const Eigen::PlainObjectBase<DerivedF>& F,
    size_t s, size_t d, 
    const std::vector<int>& adj_faces,
    Eigen::PlainObjectBase<DerivedI>& order) {

    using namespace igl::cgal::order_facets_around_edges_helper;

    // Although we only need exact predicates in the algorithm,
    // exact constructions are needed to avoid degeneracies due to
    // casting to double.
    typedef CGAL::Exact_predicates_exact_constructions_kernel K;
    typedef K::Point_3 Point_3;
    typedef K::Plane_3 Plane_3;

    auto get_face_index = [&](int adj_f)->size_t{
        return abs(adj_f) - 1;
    };

    auto get_opposite_vertex = [&](size_t fid)->size_t {
        if (F(fid, 0) != s && F(fid, 0) != d) return F(fid, 0);
        if (F(fid, 1) != s && F(fid, 1) != d) return F(fid, 1);
        if (F(fid, 2) != s && F(fid, 2) != d) return F(fid, 2);
        assert(false);
        return -1;
    };

    // Handle base cases
    if (adj_faces.size() == 0) {
        order.resize(0, 1);
        return;
    } else if (adj_faces.size() == 1) {
        order.resize(1, 1);
        order(0, 0) = 0;
        return;
    } else if (adj_faces.size() == 2) {
        const size_t o1 =
            get_opposite_vertex(get_face_index(adj_faces[0]));
        const size_t o2 =
            get_opposite_vertex(get_face_index(adj_faces[1]));
        const Point_3 ps(V(s, 0), V(s, 1), V(s, 2));
        const Point_3 pd(V(d, 0), V(d, 1), V(d, 2));
        const Point_3 p1(V(o1, 0), V(o1, 1), V(o1, 2));
        const Point_3 p2(V(o2, 0), V(o2, 1), V(o2, 2));
        order.resize(2, 1);
        switch (CGAL::orientation(ps, pd, p1, p2)) {
            case CGAL::POSITIVE:
                order(0, 0) = 1;
                order(1, 0) = 0;
                break;
            case CGAL::NEGATIVE:
                order(0, 0) = 0;
                order(1, 0) = 1;
                break;
            case CGAL::COPLANAR:
                {
                    switch (CGAL::coplanar_orientation(ps, pd, p1, p2)) {
                        case CGAL::POSITIVE:
                            // Duplicated face, use index to break tie.
                            order(0, 0) = adj_faces[0] < adj_faces[1] ? 0:1;
                            order(1, 0) = adj_faces[0] < adj_faces[1] ? 1:0;
                            break;
                        case CGAL::NEGATIVE:
                            // Coplanar faces, one on each side of the edge.
                            // It is equally valid to order them (0, 1) or (1, 0).
                            // I cannot think of any reason to prefer one to the
                            // other.  So just use (0, 1) ordering by default.
                            order(0, 0) = 0;
                            order(1, 0) = 1;
                            break;
                        case CGAL::COLLINEAR:
                            std::cerr << "Degenerated triangle detected." <<
                                std::endl;
                            assert(false);
                            break;
                        default:
                            assert(false);
                    }
                }
                break;
            default:
                assert(false);
        }
        return;
    }

    const size_t num_adj_faces = adj_faces.size();
    const size_t o = get_opposite_vertex(
            get_face_index(adj_faces[0]));
    const Point_3 p_s(V(s, 0), V(s, 1), V(s, 2));
    const Point_3 p_d(V(d, 0), V(d, 1), V(d, 2));
    const Point_3 p_o(V(o, 0), V(o, 1), V(o, 2));
    const Plane_3 separator(p_s, p_d, p_o);
    assert(!separator.is_degenerate());

    std::vector<Point_3> opposite_vertices;
    for (size_t i=0; i<num_adj_faces; i++) {
        const size_t o = get_opposite_vertex(
                get_face_index(adj_faces[i]));
        opposite_vertices.emplace_back(
                V(o, 0), V(o, 1), V(o, 2));
    }

    std::vector<int> positive_side;
    std::vector<int> negative_side;
    std::vector<int> tie_positive_oriented;
    std::vector<int> tie_negative_oriented;

    std::vector<size_t> positive_side_index;
    std::vector<size_t> negative_side_index;
    std::vector<size_t> tie_positive_oriented_index;
    std::vector<size_t> tie_negative_oriented_index;

    for (size_t i=0; i<num_adj_faces; i++) {
        const int f = adj_faces[i];
        const Point_3& p_a = opposite_vertices[i];
        auto orientation = separator.oriented_side(p_a);
        switch (orientation) {
            case CGAL::ON_POSITIVE_SIDE:
                positive_side.push_back(f);
                positive_side_index.push_back(i);
                break;
            case CGAL::ON_NEGATIVE_SIDE:
                negative_side.push_back(f);
                negative_side_index.push_back(i);
                break;
            case CGAL::ON_ORIENTED_BOUNDARY:
                {
                    auto inplane_orientation = CGAL::coplanar_orientation(
                            p_s, p_d, p_o, p_a);
                    switch (inplane_orientation) {
                        case CGAL::POSITIVE:
                            tie_positive_oriented.push_back(f);
                            tie_positive_oriented_index.push_back(i);
                            break;
                        case CGAL::NEGATIVE:
                            tie_negative_oriented.push_back(f);
                            tie_negative_oriented_index.push_back(i);
                            break;
                        case CGAL::COLLINEAR:
                        default:
                            assert(false);
                            break;
                    }
                }
                break;
            default:
                // Should not be here.
                assert(false);
        }
    }

    Eigen::PlainObjectBase<DerivedI> positive_order, negative_order;
    order_facets_around_edge(V, F, s, d, positive_side, positive_order);
    order_facets_around_edge(V, F, s, d, negative_side, negative_order);
    std::vector<size_t> tie_positive_order =
        index_sort(tie_positive_oriented);
    std::vector<size_t> tie_negative_order =
        index_sort(tie_negative_oriented);

    // Copy results into order vector.
    const size_t tie_positive_size = tie_positive_oriented.size();
    const size_t tie_negative_size = tie_negative_oriented.size();
    const size_t positive_size = positive_order.size();
    const size_t negative_size = negative_order.size();

    order.resize(tie_positive_size + positive_size +
            tie_negative_size + negative_size, 1);

    size_t count=0;
    for (size_t i=0; i<tie_positive_size; i++) {
        order(count+i, 0) =
            tie_positive_oriented_index[tie_positive_order[i]];
    }
    count += tie_positive_size;

    for (size_t i=0; i<negative_size; i++) {
        order(count+i, 0) = negative_side_index[negative_order(i, 0)];
    }
    count += negative_size;

    for (size_t i=0; i<tie_negative_size; i++) {
        order(count+i, 0) =
            tie_negative_oriented_index[tie_negative_order[i]];
    }
    count += tie_negative_size;

    for (size_t i=0; i<positive_size; i++) {
        order(count+i, 0) = positive_side_index[positive_order(i, 0)];
    }
    count += positive_size;
    assert(count == num_adj_faces);

    // Find the correct start point.
    size_t start_idx = 0;
    for (size_t i=0; i<num_adj_faces; i++) {
        const Point_3& p_a = opposite_vertices[order(i, 0)];
        const Point_3& p_b =
            opposite_vertices[order((i+1)%num_adj_faces, 0)];
        auto orientation = CGAL::orientation(p_s, p_d, p_a, p_b);
        if (orientation == CGAL::POSITIVE) {
            // Angle between triangle (p_s, p_d, p_a) and (p_s, p_d, p_b) is
            // more than 180 degrees.
            start_idx = (i+1)%num_adj_faces;
            break;
        } else if (orientation == CGAL::COPLANAR &&
                Plane_3(p_s, p_d, p_a).orthogonal_direction() !=
                Plane_3(p_s, p_d, p_b).orthogonal_direction()) {
            // All 4 points are coplanar, but p_a and p_b are on each side of
            // the edge (p_s, p_d).  This means the angle between triangle
            // (p_s, p_d, p_a) and (p_s, p_d, p_b) is exactly 180 degrees.
            start_idx = (i+1)%num_adj_faces;
            break;
        }
    }
    DerivedI circular_order = order;
    for (size_t i=0; i<num_adj_faces; i++) {
        order(i, 0) = circular_order((start_idx + i)%num_adj_faces, 0);
    }
}

template<
    typename DerivedV,
    typename DerivedF,
    typename DerivedI>
IGL_INLINE
void igl::cgal::order_facets_around_edge(
        const Eigen::PlainObjectBase<DerivedV>& V,
        const Eigen::PlainObjectBase<DerivedF>& F,
        size_t s, size_t d, 
        const std::vector<int>& adj_faces,
        const Eigen::PlainObjectBase<DerivedV>& pivot_point,
        Eigen::PlainObjectBase<DerivedI>& order) {

    assert(V.cols() == 3);
    assert(F.cols() == 3);
    auto signed_index_to_index = [&](int signed_idx) {
        return abs(signed_idx) -1;
    };
    auto get_opposite_vertex_index = [&](size_t fid) {
        if (F(fid, 0) != s && F(fid, 0) != d) return F(fid, 0);
        if (F(fid, 1) != s && F(fid, 1) != d) return F(fid, 1);
        if (F(fid, 2) != s && F(fid, 2) != d) return F(fid, 2);
        assert(false);
        // avoid warning
        return -1;
    };

    {
        // Check if s, d and pivot are collinear.
        typedef CGAL::Exact_predicates_exact_constructions_kernel K;
        K::Point_3 ps(V(s,0), V(s,1), V(s,2));
        K::Point_3 pd(V(d,0), V(d,1), V(d,2));
        K::Point_3 pp(pivot_point(0,0), pivot_point(0,1), pivot_point(0,2));
        if (CGAL::collinear(ps, pd, pp)) {
            throw "Pivot point is collinear with the outer edge!";
        }
    }

    const size_t N = adj_faces.size();
    const size_t num_faces = N + 1; // N adj faces + 1 pivot face

    // Because face indices are used for tie breaking, the original face indices
    // in the new faces array must be ascending.
    auto comp = [&](int i, int j) {
        return signed_index_to_index(i) < signed_index_to_index(j);
    };
    std::vector<int> ordered_adj_faces(adj_faces);
    std::sort(ordered_adj_faces.begin(), ordered_adj_faces.end(), comp);

    DerivedV vertices(num_faces + 2, 3);
    for (size_t i=0; i<N; i++) {
        const size_t fid = signed_index_to_index(ordered_adj_faces[i]);
        vertices.row(i) = V.row(get_opposite_vertex_index(fid));
    }
    vertices.row(N  ) = pivot_point;
    vertices.row(N+1) = V.row(s);
    vertices.row(N+2) = V.row(d);

    DerivedF faces(num_faces, 3);
    for (size_t i=0; i<N; i++) {
        if (ordered_adj_faces[i] < 0) {
            faces(i,0) = N+1; // s
            faces(i,1) = N+2; // d
            faces(i,2) = i  ;
        } else {
            faces(i,0) = N+2; // d
            faces(i,1) = N+1; // s
            faces(i,2) = i  ;
        }
    }
    // Last face is the pivot face.
    faces(N, 0) = N+1;
    faces(N, 1) = N+2;
    faces(N, 2) = N;

    std::vector<int> adj_faces_with_pivot(num_faces);
    for (size_t i=0; i<num_faces; i++) {
        if (faces(i,0) == N+1 && faces(i,1) == N+2) {
            adj_faces_with_pivot[i] = int(i+1) * -1;
        } else {
            adj_faces_with_pivot[i] = int(i+1);
        }
    }

    DerivedI order_with_pivot;
    igl::cgal::order_facets_around_edge(
            vertices, faces, N+1, N+2,
            adj_faces_with_pivot, order_with_pivot);

    assert(order_with_pivot.size() == num_faces);
    order.resize(N);
    size_t pivot_index = num_faces + 1;
    for (size_t i=0; i<num_faces; i++) {
        if (order_with_pivot[i] == N) {
            pivot_index = i;
            break;
        }
    }
    assert(pivot_index < num_faces);

    for (size_t i=0; i<N; i++) {
        order[i] = order_with_pivot[(pivot_index+i+1)%num_faces];
    }
}


#ifdef IGL_STATIC_LIBRARY
// Explicit template specialization
template void igl::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::__1::vector<int, std::__1::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
template void igl::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::__1::vector<int, std::__1::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
template void igl::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -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&, unsigned long, unsigned long, std::__1::vector<int, std::__1::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
template void igl::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::__1::vector<int, std::__1::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
template void igl::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::__1::vector<int, std::__1::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
template void igl::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -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&, unsigned long, unsigned long, std::__1::vector<int, std::__1::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
#endif