cl_Bezier.hpp

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/*
 * BELFEM -- The Berkeley Lab Finite Element Framework
 * Copyright (c) 2026, The Regents of the University of California,
 * through Lawrence Berkeley National Laboratory (subject to receipt of any required
 * approvals from the U.S. Dept. of Energy).  All rights reserved.
 *
 * Developers: Christian Messe, Gregory Giard
 *
 * See the top-level LICENSE file for the complete license and disclaimer.
 */
 
#ifndef BELFEM_CL_BEZIER_HPP
#define BELFEM_CL_BEZIER_HPP
#include "typedefs.hpp"
#include "cl_Vector.hpp"
 
namespace belfem
{
//------------------------------------------------------------------------------
 
    enum class BezierType
    {
        Horizontal,
        Vertical
    };
 
//------------------------------------------------------------------------------
 
    class Bezier
    {
        // X-coordinates
        Vector< real > mX ;
 
        // Y-Coordinates
        Vector< real > mY ;
 
        // Work vector
        mutable Vector< real > mWork ;
 
 
//------------------------------------------------------------------------------
    public:
//------------------------------------------------------------------------------
 
        Bezier( const real aX0=0.0, const real aY0=0.0, const real adYdx0=0.0,
                const real aX1=1.0, const real aY1=1.0, const real adYdx1=0.0,
                const BezierType aType = BezierType::Horizontal );
 
        Bezier( const Vector< real > & aX,
                const Vector< real > & aY,
                const BezierType aType = BezierType::Horizontal );
 
//------------------------------------------------------------------------------
 
        ~Bezier() = default;
 
//------------------------------------------------------------------------------

         Vector< real > &
         basis_x();
 
         const Vector< real > &
         basis_x() const ;
 
//------------------------------------------------------------------------------

        Vector< real > &
        basis_y();
 
        const Vector< real > &
        basis_y() const ;
 
//------------------------------------------------------------------------------

        real
        x_by_xi( const real aXi ) const ;
 
//------------------------------------------------------------------------------

        real
        y_by_xi( const real aXi ) const ;
 
//------------------------------------------------------------------------------

        real
        xi_by_x( const real aX ) const ;
 
//------------------------------------------------------------------------------

        real
        xi_by_y( const real aY ) const ;
 
//------------------------------------------------------------------------------

        real
        x( const real aY ) const ;
 
//------------------------------------------------------------------------------

        real
        y( const real aX ) const ;
 
//------------------------------------------------------------------------------

        void
        point( const real aXi, real & aX, real & aY ) const ;
 
//------------------------------------------------------------------------------

        void
        dpoint( const real aXi, real & adXdXi, real & adYdXi ) const ;
 
//------------------------------------------------------------------------------

        void
        ddpoint( const real aXi, real & ad2XdXi2, real & ad2YdXi2 ) const ;
 
//------------------------------------------------------------------------------

        void
        dddpoint( real & ad3XdXi3, real & ad3YdXi3 ) const ;
 
 
//------------------------------------------------------------------------------

        real
        dydx( const real aX ) const ;
 
//------------------------------------------------------------------------------

        real
        dxdy( const real aY ) const ;
 
//------------------------------------------------------------------------------

        real
        d2ydx2( const real aX ) const ;
 
//------------------------------------------------------------------------------

        real
        d2xdy2( const real aY ) const ;
 
//------------------------------------------------------------------------------

        real
        d3ydx3( const real aX ) const ;
 
//------------------------------------------------------------------------------

        real
        d3xdy3( const real aY ) const ;
 
//------------------------------------------------------------------------------

         real
         compute_length( const uint aNumIntegrationPoints=21 ) const ;
 
//------------------------------------------------------------------------------

        real
        compute_length(
                const Vector< double > & aW,
                const Vector< double > & aXi ) const ;
 
//------------------------------------------------------------------------------
 
 
        void
        compute_basis_xwise(
                const real aX0, const real aY0,const real adYdx0,
                const real aX1, const real aY1, const real adYdx1 ) ;
 
//------------------------------------------------------------------------------
 
        void
        compute_basis_ywise(
                const real aX0, const real aY0,const real adYdx0,
                const real aX1, const real aY1, const real adYdx1 ) ;
//------------------------------------------------------------------------------
    private:
//------------------------------------------------------------------------------
 
//------------------------------------------------------------------------------
 
        // the Bezier type has a simple shape function
        void
        compute_N( const real aXi ) const ;
 
//------------------------------------------------------------------------------
 
        // first derivative of the shape function
        void
        compute_dNdXi( const real aXi ) const ;
 
//------------------------------------------------------------------------------
 
        // second derivative of the shape functionon
        void
        compute_d2NdXi2( const real aXi ) const ;
 
//------------------------------------------------------------------------------
 
    };
 
//------------------------------------------------------------------------------
 
    inline Vector< real > &
    Bezier::basis_x()
    {
        return mX ;
    }
 
    inline const Vector< real > &
    Bezier::basis_x() const
    {
        return mX ;
    }
 
 
//------------------------------------------------------------------------------
 
    inline Vector< real > &
    Bezier::basis_y()
    {
        return mY ;
    }
 
    inline const Vector< real > &
    Bezier::basis_y() const
    {
        return mY ;
    }
 
//------------------------------------------------------------------------------
}
#endif //BELFEM_CL_BEZIER_HPP