PolygonUtils.cpp

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#include "PolygonUtils.hpp"
#include <polyfem/utils/ClipperUtils.hpp>
#include <geogram/numerics/predicates.h>
#include <igl/barycenter.h>
 
namespace
{
 
    inline GEO::Sign point_is_in_half_plane(
        const Eigen::RowVector2d &p, const Eigen::RowVector2d &q1, const Eigen::RowVector2d &q2)
    {
        return GEO::PCK::orient_2d(q1.data(), q2.data(), p.data());
    }
 
    inline bool intersect_segments(
        const Eigen::RowVector2d &p1, const Eigen::RowVector2d &p2,
        const Eigen::RowVector2d &q1, const Eigen::RowVector2d &q2,
        Eigen::RowVector2d &result)
    {
 
        Eigen::RowVector2d Vp = p2 - p1;
        Eigen::RowVector2d Vq = q2 - q1;
        Eigen::RowVector2d pq = q1 - p1;
 
        double a = Vp(0);
        double b = -Vq(0);
        double c = Vp(1);
        double d = -Vq(1);
 
        double delta = a * d - b * c;
        if (delta == 0.0)
        {
            return false;
        }
 
        double tp = (d * pq(0) - b * pq(1)) / delta;
 
        result << (1.0 - tp) * p1(0) + tp * p2(0),
            (1.0 - tp) * p1(1) + tp * p2(1);
 
        return true;
    }
 
} // anonymous namespace
 
// -----------------------------------------------------------------------------
 
void polyfem::mesh::clip_polygon_by_half_plane(const Eigen::MatrixXd &P_in,
                                               const Eigen::RowVector2d &q1, const Eigen::RowVector2d &q2, Eigen::MatrixXd &P_out)
{
    using namespace GEO;
    assert(P_in.cols() == 2);
    std::vector<Eigen::RowVector2d> result;
 
    if (P_in.rows() == 0)
    {
        P_out.resize(0, 2);
        return;
    }
 
    if (P_in.rows() == 1)
    {
        if (point_is_in_half_plane(P_in.row(0), q1, q2))
        {
            P_out.resize(1, 2);
            P_out << P_in.row(0);
        }
        else
        {
            P_out.resize(0, 2);
        }
        return;
    }
 
    Eigen::RowVector2d prev_p = P_in.row(P_in.rows() - 1);
    Sign prev_status = point_is_in_half_plane(prev_p, q1, q2);
 
    for (unsigned int i = 0; i < P_in.rows(); ++i)
    {
        Eigen::RowVector2d p = P_in.row(i);
        Sign status = point_is_in_half_plane(p, q1, q2);
        if (status != prev_status && status != ZERO && prev_status != ZERO)
        {
            Eigen::RowVector2d intersect;
            if (intersect_segments(prev_p, p, q1, q2, intersect))
            {
                result.push_back(intersect);
            }
        }
 
        switch (status)
        {
        case NEGATIVE:
            break;
        case ZERO:
            result.push_back(p);
            break;
        case POSITIVE:
            result.push_back(p);
            break;
        default:
            break;
        }
 
        prev_p = p;
        prev_status = status;
    }
 
    P_out.resize((int)result.size(), 2);
    for (size_t i = 0; i < result.size(); ++i)
    {
        P_out.row((int)i) = result[i];
    }
}
 
 
void polyfem::mesh::compute_visibility_kernel(const Eigen::MatrixXd &IV, Eigen::MatrixXd &OV)
{
    assert(IV.cols() == 2 || IV.cols() == 3);
 
    // 1) Start from the bounding box of the input points
    Eigen::MatrixXd src, dst;
    const auto &minV = IV.colwise().minCoeff().array();
    const auto &maxV = IV.colwise().maxCoeff().array();
    src.resize(4, 2);
    src.row(0) << minV(0), minV(1);
    src.row(1) << maxV(0), minV(1);
    src.row(2) << maxV(0), maxV(1);
    src.row(3) << minV(0), maxV(1);
    // std::cout << IV << std::endl;
    // std::cout << minV << ' ' << maxV << std::endl;
 
    // 2) Clip by half planes until we are left with the kernel
    for (unsigned int i = 0; i < IV.rows(); ++i)
    {
        unsigned int j = ((i + 1) % (int)IV.rows());
        const Eigen::RowVector2d &q1 = IV.row(i).head<2>();
        const Eigen::RowVector2d &q2 = IV.row(j).head<2>();
        clip_polygon_by_half_plane(src, q1, q2, dst);
        std::swap(src, dst);
    }
    OV = src;
}
 
 
bool polyfem::mesh::is_star_shaped(const Eigen::MatrixXd &IV, Eigen::RowVector3d &bary)
{
    Eigen::MatrixXd OV;
    compute_visibility_kernel(IV, OV);
    if (OV.rows() == 0)
    {
        return false;
    }
    else
    {
        Eigen::MatrixXi F(1, OV.rows());
        for (int i = 0; i < OV.rows(); ++i)
        {
            F(0, i) = i;
        }
        Eigen::MatrixXd BC;
        igl::barycenter(OV, F, BC);
        // std::cout << BC.rows() << 'x' << BC.cols() << std::endl;
        // std::cout << BC << std::endl;
        int n = std::min(3, (int)BC.cols());
        bary.setZero();
        bary.head(n) = BC.row(0).head(n);
        return true;
    }
}
 
// -----------------------------------------------------------------------------
 
void polyfem::mesh::offset_polygon(const Eigen::MatrixXd &IV, Eigen::MatrixXd &OV, double eps)
{
#ifdef POLYFEM_WITH_CLIPPER
    using namespace ClipperLib;
    using namespace polyfem::utils;
 
    // Convert input polygon to integer grid
    ClipperOffset co;
    co.AddPath(PolygonClipping::toClipperPolygon(IV), jtSquare, etClosedPolygon);
 
    // Compute offset in the integer grid
    Paths solution;
    co.Execute(solution, cInt(eps * DOUBLE_TO_INT_SCALE_FACTOR));
    assert(solution.size() == 1);
 
    // Convert back to double
    OV = PolygonClipping::fromClipperPolygon(solution.front());
#else
    throw "Compile with clipper!";
#endif
}
 
 
namespace
{
 
    typedef Eigen::RowVector2d Vec2d;
 
    double inline det(Vec2d u, Vec2d v)
    {
        return u[0] * v[1] - u[1] * v[0];
    }
 
    // Return true iff [a,b] intersects [c,d], and store the intersection in ans
    bool intersect_segment(const Vec2d &a, const Vec2d &b, Vec2d c, Vec2d d, Vec2d &ans)
    {
        const double eps = 1e-10; // small epsilon for numerical precision
        double x = det(c - a, d - c);
        double y = det(b - a, a - c);
        double z = det(b - a, d - c);
        if (std::abs(z) < eps || x * z < 0 || x * z > z * z || y * z < 0 || y * z > z * z)
            return false;
        ans = c + (d - c) * y / z;
        return true;
    }
 
    bool is_point_inside(const Eigen::MatrixXd &poly, const Vec2d &outside, const Vec2d &query)
    {
        int n = poly.rows();
        bool tmp, ans = false;
        for (long i = 0; i < poly.rows(); ++i)
        {
            Vec2d m; // Coordinates of intersection point
            tmp = intersect_segment(query, outside, poly.row(i), poly.row((i + 1) % n), m);
            ans = (ans != tmp);
        }
        return ans;
    }
 
} // anonymous namespace
 
// -----------------------------------------------------------------------------
 
int polyfem::mesh::is_inside(const Eigen::MatrixXd &IV, const Eigen::MatrixXd &Q, std::vector<bool> &inside)
{
    assert(IV.cols() == 2);
    Eigen::RowVector2d minV = IV.colwise().minCoeff().array();
    Eigen::RowVector2d maxV = IV.colwise().maxCoeff().array();
    Eigen::RowVector2d center = 0.5 * (maxV + minV);
    Eigen::RowVector2d outside(2.0 * minV(0) - center(0), center(1));
    inside.resize(Q.rows());
    int num_inside = 0;
    for (long i = 0; i < Q.rows(); ++i)
    {
        inside[i] = is_point_inside(IV, outside, Q.row(i));
        if (inside[i])
        {
            ++num_inside;
        }
    }
    return num_inside;
}
 
 
void polyfem::mesh::sample_polygon(const Eigen::MatrixXd &poly, int num_samples, Eigen::MatrixXd &S)
{
    assert(poly.rows() >= 2);
    int n = poly.rows();
 
    auto length = [&](int i) {
        return (poly.row(i) - poly.row((i + 1) % n)).norm();
    };
 
    // Step 1: compute starting edge + total length of the polygon
    int i0 = 0;
    double max_length = 0;
    double total_length = 0;
    for (int i = 0; i < n; ++i)
    {
        double len = length(i);
        total_length += len;
        if (len > max_length)
        {
            max_length = len;
            i0 = i;
        }
    }
 
    // Step 2: place a sample at regular intervals along the polygon,
    // starting from the middle of edge i0
    S.resize(num_samples, poly.cols());
    double spacing = total_length / num_samples; // sampling distance
    double offset = length(i0) / 2.0;            // distance from first sample to vertex i0
    double distance_to_next = length(i0);
    for (int s = 0, i = i0; s < num_samples; ++s)
    {
        double distance_to_sample = s * spacing + offset; // next sample length
        while (distance_to_sample > distance_to_next)
        {
            i = (i + 1) % n;
            distance_to_next += length(i);
        }
        double t = (distance_to_next - distance_to_sample) / length(i);
        S.row(s) = t * poly.row(i) + (1.0 - t) * poly.row((i + 1) % n);
    }
}