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Filename : infinite_line_functions.hpp
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// Boost.Geometry

// Copyright (c) 2018-2019 Barend Gehrels, Amsterdam, the Netherlands.

// Use, modification and distribution is subject to the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP
#define BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP

#include <boost/geometry/core/access.hpp>
#include <boost/geometry/core/config.hpp>
#include <boost/geometry/geometries/infinite_line.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/util/select_most_precise.hpp>

namespace boost { namespace geometry
{

namespace arithmetic
{

// Calculates intersection point of two infinite lines.
// Returns true if the lines intersect.
// Returns false if lines are parallel (or collinear, possibly opposite)
template <typename Point, typename Type>
inline bool intersection_point(model::infinite_line<Type> const& p,
    model::infinite_line<Type> const& q, Point& ip)
{
    Type const denominator = p.b * q.a - p.a * q.b;

    static Type const zero = 0;
    if (math::equals(denominator, zero))
    {
        // Lines are parallel
        return false;
    }

    // Calculate the intersection coordinates
    geometry::set<0>(ip, (p.c * q.b - p.b * q.c) / denominator);
    geometry::set<1>(ip, (p.a * q.c - p.c * q.a) / denominator);

    return true;
}

//! Return a distance-side-measure for a point to a line
//! Point is located left of the line if value is positive,
//! right of the line is value is negative, and on the line if the value
//! is exactly zero
template <typename Type, typename CoordinateType>
inline
typename select_most_precise<Type, CoordinateType>::type
side_value(model::infinite_line<Type> const& line,
    CoordinateType const& x, CoordinateType const& y)
{
    // https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_an_equation
    // Distance from point to line in general form is given as:
    // (a * x + b * y + c) / sqrt(a * a + b * b);
    // In most use cases comparisons are enough, saving the sqrt
    // and often even the division.
    // Also, this gives positive values for points left to the line,
    // and negative values for points right to the line.
    return line.a * x + line.b * y + line.c;
}

template <typename Type, typename Point>
inline
typename select_most_precise
<
    Type,
    typename geometry::coordinate_type<Point>::type
>::type
side_value(model::infinite_line<Type> const& line, Point const& p)
{
    return side_value(line, geometry::get<0>(p), geometry::get<1>(p));
}

template <typename Type>
inline bool is_degenerate(const model::infinite_line<Type>& line)
{
    static Type const zero = 0;
    return math::equals(line.a, zero) && math::equals(line.b, zero);
}


} // namespace arithmetic


}} // namespace boost::geometry


#endif // BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP