circlepoints.hh

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#ifndef DUMUX_MULTIDOMAIN_EMBEDDED_CIRCLEPOINTS_HH
#define DUMUX_MULTIDOMAIN_EMBEDDED_CIRCLEPOINTS_HH
 
#include <vector>
#include <cmath>
 
#include <dune/common/exceptions.hh>
 
namespace Dumux {
namespace EmbeddedCoupling {

template<class GlobalPosition>
std::vector<GlobalPosition> circlePoints(const GlobalPosition& center,
                                         const GlobalPosition& normal,
                                         const typename GlobalPosition::value_type radius,
                                         const std::size_t numPoints = 20)
{
    using std::abs; using std::sin; using std::cos;
    using ctype = typename GlobalPosition::value_type;
 
    constexpr ctype eps = 1.5e-7;
    static_assert(GlobalPosition::dimension == 3, "Only implemented for world dimension 3");
 
    std::vector<GlobalPosition> points(numPoints);
 
    // make sure n is a unit vector
    auto n = normal;
    n /= n.two_norm();
 
    // caculate a vector u perpendicular to n
    GlobalPosition u;
    if (abs(n[0]) < eps && abs(n[1]) < eps)
        if (abs(n[2]) < eps)
            DUNE_THROW(Dune::MathError, "The normal vector has to be non-zero!");
        else
            u = {0, 1, 0};
    else
        u = {-n[1], n[0], 0};
 
    u *= radius/u.two_norm();
 
    // the circle parameterization is p(t) = r*cos(t)*u + r*sin(t)*(n x u) + c
    auto tangent = crossProduct(u, n);
    tangent *= radius/tangent.two_norm();
 
    // the parameter with an offset
    ctype t = 0 + 0.1;
    // insert the vertices
    for (std::size_t i = 0; i < numPoints; ++i)
    {
        points[i] = GlobalPosition({u[0]*cos(t) + tangent[0]*sin(t) + center[0],
                                    u[1]*cos(t) + tangent[1]*sin(t) + center[1],
                                    u[2]*cos(t) + tangent[2]*sin(t) + center[2]});
 
        t += 2*M_PI/numPoints;
 
        // periodic t
        if(t > 2*M_PI)
            t -= 2*M_PI;
    }
 
    return points;
}
 
} // end namespace EmbeddedCoupling
} // end namespace Dumux
 
#endif