BaseQuad.h

#pragma once
 
#include <Caribou/config.h>
#include <Caribou/constants.h>
#include <Caribou/Geometry/Element.h>
#include <Eigen/Core>
 
namespace caribou::geometry {
 
template<typename Derived>
struct BaseQuad : public Element<Derived> {
    // Types
    using Base = Element<Derived>;
 
    using LocalCoordinates = typename Base::LocalCoordinates;
    using WorldCoordinates = typename Base::WorldCoordinates;
 
    using GaussNode = typename Base::GaussNode;
 
    template <UNSIGNED_INTEGER_TYPE Dim>
    using Vector = typename Base::template Vector<Dim>;
 
    template <UNSIGNED_INTEGER_TYPE Rows, UNSIGNED_INTEGER_TYPE Cols>
    using Matrix = typename Base::template Matrix<Rows, Cols>;
 
    // Constants
    static constexpr auto CanonicalDimension = Base::CanonicalDimension;
    static constexpr auto Dimension = Base::Dimension;
    static constexpr auto NumberOfNodesAtCompileTime = Base::NumberOfNodesAtCompileTime;
    static constexpr auto NumberOfGaussNodesAtCompileTime = Base::NumberOfGaussNodesAtCompileTime;
 
    static_assert(Dimension == 2 or Dimension == 3, "Quads can only be of dimension 2 or 3.");
 
    BaseQuad() = default;
 
    template<typename EigenType, REQUIRES(EigenType::RowsAtCompileTime == NumberOfNodesAtCompileTime)>
    explicit BaseQuad(Eigen::EigenBase<EigenType> & nodes) :p_nodes(nodes.derived().template cast<typename Base::Scalar>()) {}
 
    template<typename EigenType, REQUIRES(EigenType::RowsAtCompileTime == NumberOfNodesAtCompileTime)>
    explicit BaseQuad(const Eigen::EigenBase<EigenType> & nodes) :p_nodes(nodes.derived().template cast<typename Base::Scalar>()) {}
 
    template <
        typename ...Nodes,
        REQUIRES(NumberOfNodesAtCompileTime == sizeof...(Nodes)+1)
    >
    explicit BaseQuad(const WorldCoordinates & first_node, Nodes&&...remaining_nodes)
    {
        construct_from_nodes<0>(first_node, std::forward<Nodes>(remaining_nodes)...);
    }
 
    // Public methods common to all quad types
 
    inline auto edges() const {
        return self().get_boundary_elements_nodes();
    }
 
    inline auto frame() const -> Matrix<Dimension, Dimension>
    {
        return frame(LocalCoordinates::Zero());
    }
 
    inline
    auto
    frame(const LocalCoordinates & local_point) const -> Matrix<Dimension, Dimension>
    {
        // Position of the point inside the quad where the frame should be computed
        const auto p = this->world_coordinates( local_point );
 
        // Project of the point on the edge facing the u axis
        const auto projected_on_u = this->world_coordinates({1,local_point[1]});
 
        // Project of the point on the edge facing the v axis
        const auto projected_on_v = this->world_coordinates({local_point[0], 1});
 
        // Vector from the point to its projection on the edge facing the u axis
        const auto point_to_u = projected_on_u - p;
 
        // Vector from the point to its projection on the edge facing the v axis
        const auto point_to_v = projected_on_v - p;
 
        // The u-axis of the computed frame
        const auto u = point_to_u.normalized();
 
        // The v-axis of the computed frame
        auto v = point_to_v.normalized();
 
        Matrix<Dimension, Dimension> m {};
        if constexpr (Dimension == 3) {
            // The w-axis of the computed frame
            const WorldCoordinates w = u.cross(v).normalized();
            m << u, v, w;
        } else {
            m << u, v;
        }
 
        return m;
    }
 
private:
    // Implementations
    friend struct Element<Derived>;
    [[nodiscard]]
    inline auto get_number_of_nodes() const {return NumberOfNodesAtCompileTime;}
    inline auto get_number_of_gauss_nodes() const {return NumberOfGaussNodesAtCompileTime;}
    inline auto get_node(const UNSIGNED_INTEGER_TYPE & index) const {return WorldCoordinates(p_nodes.row(index));};
    inline auto get_nodes() const -> const auto & {return p_nodes;};
    inline auto get_center() const {return Base::world_coordinates(LocalCoordinates({0, 0}));};
    inline auto get_number_of_boundary_elements() const -> UNSIGNED_INTEGER_TYPE {return 4;};
    inline auto get_contains_local(const LocalCoordinates & xi, const FLOATING_POINT_TYPE & eps) const -> bool {
        const auto & u = xi[0];
        const auto & v = xi[1];
        return IN_CLOSED_INTERVAL(-1-eps, u, 1+eps) and
               IN_CLOSED_INTERVAL(-1-eps, v, 1+eps);
    }
 
    auto self() -> Derived& { return *static_cast<Derived*>(this); }
    auto self() const -> const Derived& { return *static_cast<const Derived*>(this); }
 
    template <size_t index, typename ...Nodes, REQUIRES(sizeof...(Nodes) >= 1)>
    inline
    void construct_from_nodes(const WorldCoordinates & first_node, Nodes&&...remaining_nodes) {
        p_nodes.row(index) = first_node;
        construct_from_nodes<index+1>(std::forward<Nodes>(remaining_nodes)...);
    }
 
    template <size_t index>
    inline
    void construct_from_nodes(const WorldCoordinates & last_node) {
        p_nodes.row(index) = last_node;
    }
protected:
    Matrix<NumberOfNodesAtCompileTime, Dimension> p_nodes;
};
 
}