// Boost.Geometry
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// Copyright (c) 2018-2019 Barend Gehrels, Amsterdam, the Netherlands.
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// Use, modification and distribution is subject to the Boost Software License,
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// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP
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#define BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP
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#include <boost/geometry/core/access.hpp>
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#include <boost/geometry/core/config.hpp>
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#include <boost/geometry/geometries/infinite_line.hpp>
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#include <boost/geometry/util/math.hpp>
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#include <boost/geometry/util/select_most_precise.hpp>
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namespace boost { namespace geometry
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{
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namespace arithmetic
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{
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// Calculates intersection point of two infinite lines.
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// Returns true if the lines intersect.
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// Returns false if lines are parallel (or collinear, possibly opposite)
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template <typename Point, typename Type>
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inline bool intersection_point(model::infinite_line<Type> const& p,
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model::infinite_line<Type> const& q, Point& ip)
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{
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Type const denominator = p.b * q.a - p.a * q.b;
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static Type const zero = 0;
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if (math::equals(denominator, zero))
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{
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// Lines are parallel
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return false;
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}
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// Calculate the intersection coordinates
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geometry::set<0>(ip, (p.c * q.b - p.b * q.c) / denominator);
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geometry::set<1>(ip, (p.a * q.c - p.c * q.a) / denominator);
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return true;
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}
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//! Return a distance-side-measure for a point to a line
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//! Point is located left of the line if value is positive,
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//! right of the line is value is negative, and on the line if the value
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//! is exactly zero
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template <typename Type, typename CoordinateType>
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inline
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typename select_most_precise<Type, CoordinateType>::type
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side_value(model::infinite_line<Type> const& line,
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CoordinateType const& x, CoordinateType const& y)
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{
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// https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_an_equation
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// Distance from point to line in general form is given as:
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// (a * x + b * y + c) / sqrt(a * a + b * b);
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// In most use cases comparisons are enough, saving the sqrt
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// and often even the division.
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// Also, this gives positive values for points left to the line,
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// and negative values for points right to the line.
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return line.a * x + line.b * y + line.c;
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}
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template <typename Type, typename Point>
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inline
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typename select_most_precise
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<
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Type,
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typename geometry::coordinate_type<Point>::type
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>::type
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side_value(model::infinite_line<Type> const& line, Point const& p)
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{
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return side_value(line, geometry::get<0>(p), geometry::get<1>(p));
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}
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template <typename Type>
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inline bool is_degenerate(const model::infinite_line<Type>& line)
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{
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static Type const zero = 0;
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return math::equals(line.a, zero) && math::equals(line.b, zero);
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}
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} // namespace arithmetic
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}} // namespace boost::geometry
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#endif // BOOST_GEOMETRY_ARITHMETIC_LINE_FUNCTIONS_HPP
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