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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));
- }
- // Returns true for two lines which are supposed to be (close to) collinear
- // (which is not checked) and have a similar direction
- // (in practice up to 45 degrees, TO BE VERIFIED)
- // true: -----------------> p -----------------> q
- // false: -----------------> p <----------------- q
- template <typename Type>
- inline
- bool similar_direction(const model::infinite_line<Type>& p,
- const model::infinite_line<Type>& q)
- {
- return p.a * q.a >= 0 && p.b * q.b >= 0;
- }
- 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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