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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
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