MRLine.h

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#pragma once
 
#include "MRAffineXf.h"
#include <iosfwd>
 
namespace MR
{
 

template <typename V>
struct Line
{
    using T = typename V::ValueType;
 
    V p, d;
 
    constexpr Line() noexcept = default;
    constexpr Line( const V & p, const V & d ) noexcept : p( p ), d( d ) { }
    template <typename U>
    constexpr explicit Line( const Line<U> & l ) noexcept : p( l.p ), d( l.d ) { }

    [[nodiscard]] V operator()( T param ) const { return p + param * d; }

    [[nodiscard]] T distanceSq( const V & x ) const
        { return ( x - project( x ) ).lengthSq(); }

    [[nodiscard]] Line operator -() const { return Line( p, -d ); }

    [[nodiscard]] const Line & operator +() const { return *this; }

    [[nodiscard]] Line normalized() const { return { p, d.normalized() }; }

    [[nodiscard]] T projectionParam( const V & x ) const { return dot( d, x - p ) / d.lengthSq(); }

    [[nodiscard]] V project( const V & x ) const { return operator()( projectionParam( x ) ); }
 
    friend std::ostream& operator<<( std::ostream& s, const Line& l )
    {
        return s << l.p << '\n' << l.d;
    }
 
    friend std::istream& operator>>( std::istream& s, Line& l )
    {
        return s >> l.p >> l.d;
    }
};


template <typename V>
[[nodiscard]] inline Line<V> transformed( const Line<V> & l, const AffineXf<V> & xf )
{
    return Line<V>{ xf( l.p ), xf.A * l.d };
}
 
template <typename V>
[[nodiscard]] inline bool operator == ( const Line<V> & a, const Line<V> & b )
{
    return a.p == b.p && a.d == b.d;
}

 
}