line.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef LINE_H
# define LINE_H
 
#include <cmath>
#include <utility>
#include <string>
#include <sstream>
#include <ah-errors.H>
#include <point.H>
 
namespace Aleph
{
 
inline const Geom_Number LINE_EPSILON(0);
 
struct LineEq
{
  Geom_Number y0{0};  
  Geom_Number m{1};   
 
  constexpr LineEq() noexcept = default;
 
  LineEq(const Geom_Number & __y0, const Geom_Number & __m) noexcept
    : y0(__y0), m(__m) {}
 
  LineEq(const Geom_Number & x1, const Geom_Number & y1, const Geom_Number & __m) noexcept
    : y0(y1 - __m * x1), m(__m) {}
 
  LineEq(const Geom_Number & x1, const Geom_Number & y1,
         const Geom_Number & x2, const Geom_Number & y2)
  {
    ah_domain_error_if(x1 == x2)
      << "Cannot create line from points with same x-coordinate (vertical line): "
      << "x1 = " << x1 << ", x2 = " << x2;
 
    m = (y2 - y1) / (x2 - x1);
    y0 = y1 - m * x1;
  }
 
  LineEq(const Point & p, const Geom_Number & __m) noexcept
    : LineEq(p.get_x(), p.get_y(), __m) {}
 
  LineEq(const Point & p1, const Point & p2)
    : LineEq(p1.get_x(), p1.get_y(), p2.get_x(), p2.get_y()) {}
 
  [[nodiscard]] Geom_Number operator()(const Geom_Number & x) const noexcept
  {
    return y0 + m * x;
  }
 
  [[nodiscard]] const Geom_Number & slope() const noexcept { return m; }
 
  [[nodiscard]] const Geom_Number & y_intercept() const noexcept { return y0; }
 
  [[nodiscard]] bool is_horizontal(const Geom_Number & epsilon = LINE_EPSILON) const noexcept
  {
    return abs(m) <= epsilon;
  }
 
  [[nodiscard]] bool is_parallel_to(const LineEq & l,
                                     const Geom_Number & epsilon = LINE_EPSILON) const noexcept
  {
    return abs(m - l.m) <= epsilon;
  }
 
  [[nodiscard]] bool is_perpendicular_to(const LineEq & l,
                                          const Geom_Number & epsilon = LINE_EPSILON) const noexcept
  {
    return abs(m * l.m + Geom_Number(1)) <= epsilon;
  }
 
  [[nodiscard]] Geom_Number x_at(const Geom_Number & y) const
  {
    ah_domain_error_if(is_horizontal())
      << "Cannot compute x for horizontal line (slope = 0)";
    return (y - y0) / m;
  }
 
  [[nodiscard]] std::pair<Geom_Number, Geom_Number> intersection(const LineEq & l,
                                                                  const Geom_Number & epsilon = LINE_EPSILON) const
  {
    ah_domain_error_if(is_parallel_to(l, epsilon))
      << "Cannot compute intersection of parallel lines: "
      << "slope1 = " << m << ", slope2 = " << l.m;
 
    Geom_Number x = (y0 - l.y0) / (l.m - m);
    return {x, (*this)(x)};
  }
 
  [[nodiscard]] LineEq perpendicular_through(const Geom_Number & px, const Geom_Number & py) const
  {
    ah_domain_error_if(is_horizontal())
      << "Cannot compute perpendicular to horizontal line (would be vertical)";
 
    const Geom_Number perp_slope = Geom_Number(-1) / m;
    return {px, py, perp_slope};
  }
 
  [[nodiscard]] Geom_Number distance_to(const Geom_Number & px, const Geom_Number & py) const noexcept
  {
    const Geom_Number diff = py - (y0 + m * px);
    // Use mpfr for sqrt, then convert back to rational
    const mpfr_class denominator = sqrt(mpfr_class(1) + mpfr_class(m) * mpfr_class(m));
    return abs(diff) / Geom_Number(denominator);
  }
 
  [[nodiscard]] bool contains_point(const Geom_Number & px, const Geom_Number & py,
                                     const Geom_Number & epsilon = LINE_EPSILON) const noexcept
  {
    return abs(py - (*this)(px)) <= epsilon;
  }
 
  [[nodiscard]] Geom_Number distance_to(const Point & p) const noexcept
  {
    return distance_to(p.get_x(), p.get_y());
  }
 
  [[nodiscard]] LineEq perpendicular_through(const Point & p) const
  {
    return perpendicular_through(p.get_x(), p.get_y());
  }
 
  [[nodiscard]] bool contains_point(const Point & p,
                                     const Geom_Number & epsilon = LINE_EPSILON) const noexcept
  {
    return contains_point(p.get_x(), p.get_y(), epsilon);
  }
 
  [[nodiscard]] Point intersection_point(const LineEq & l,
                                          const Geom_Number & epsilon = LINE_EPSILON) const
  {
    auto [x, y] = intersection(l, epsilon);
    return {x, y};
  }
 
  [[nodiscard]] bool operator==(const LineEq & l) const noexcept
  {
    return y0 == l.y0 and m == l.m;
  }
 
  [[nodiscard]] bool operator!=(const LineEq & l) const noexcept
  {
    return not (*this == l);
  }
 
  [[nodiscard]] bool approx_equal(const LineEq & l, const Geom_Number & epsilon) const noexcept
  {
    return abs(y0 - l.y0) <= epsilon and abs(m - l.m) <= epsilon;
  }
 
  [[nodiscard]] std::string to_string() const
  {
    std::ostringstream s;
    s << "y = " << y0 << " + " << m << " * x";
    return s.str();
  }
 
  friend std::ostream & operator<<(std::ostream & out, const LineEq & l)
  {
    return out << l.to_string();
  }
};
 
} // namespace Aleph
 
// Global namespace compatibility
using Aleph::LineEq;
using Aleph::LINE_EPSILON;
 
# endif // LINE_H