ParametricCurve.h

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/* This file is part of MoDELib, the Mechanics Of Defects Evolution Library.
 *
 *
 * MoDELib is distributed without any warranty under the 
 * GNU General Public License (GPL) v2 <http://www.gnu.org/licenses/>.
 */
 
#ifndef model_PARAMETRICCURVE_H_
#define model_PARAMETRICCURVE_H_
 
#include <Eigen/Dense>
 
#include <Quadrature.h>
 
 
namespace model {
        
 
        
        
        
        
 
        
        
        
        template <typename Derived, short unsigned int dim>
        class ParametricCurve
    {
                
                typedef Eigen::Matrix<double, dim, 1>           VectorDim;
 
        private:
                
                Derived&   derivedCurve() { return *static_cast<Derived*>(this); }
                Derived* p_derivedCurve() { return  static_cast<Derived*>(this); }
                const Derived&   derivedCurve() const { return *static_cast<const Derived*>(this); }
                const Derived* p_derivedCurve() const { return  static_cast<const Derived*>(this); }
                
        public:
                
/*************************************************************/
                double get_j(const double & u) const {
                        return p_derivedCurve()->get_ru(u).norm();
                }
                
                /*************************************************************/
                double get_jSquare(const double & u) const {
                        return p_derivedCurve()->get_ru(u).squaredNorm();
                }
 
                /*************************************************************/
                VectorDim get_rl(const double & u) const {
                        return p_derivedCurve()->get_ru(u).normalized();
                }
 
                /*************************************************************/
                double get_ju(const double & u) const {
                        return get_rl(u).dot(p_derivedCurve()->get_ruu(u));
                }
 
                
                /*************************************************************/
                VectorDim get_rll(const double & u) const {
                        const double j2(get_jSquare(u));
                        VectorDim ru (p_derivedCurve()->get_ru (u));
                        VectorDim ruu(p_derivedCurve()->get_ruu(u));
                        return (ruu - ru*ru.dot(ruu)/j2)/j2;
                }
                
                
                /*************************************************************/
                double get_kappa(const double & u) const {
                        return get_rll(u).norm();
                }
                
                
                /*************************************************************/
                template <short unsigned int qOrder, template <short unsigned int, size_t> class QuadratureRule>
                double arcLength() const {
                        double L(0.0);
                        Quadrature<1,qOrder,QuadratureRule>::integrate(this,L,&Derived::get_j);
                        return L;
                }
 
                /*************************************************************/
                template <short unsigned int qOrder, template <short unsigned int, size_t> class QuadratureRule>
                VectorDim rm() const {
                        VectorDim temp(VectorDim::Zero());
                        Quadrature<1,qOrder,QuadratureRule>::integrate(this,temp,&Derived::rm_integrand);
                        return temp/arcLength<qOrder,QuadratureRule>();
                }
                
                VectorDim rm_integrand(const double& u) const {
                        return p_derivedCurve()->get_r(u)*get_j(u);
                }
                
        };
        
} // namespace model
#endif