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>
 
namespace Aleph
{
 
inline constexpr double LINE_EPSILON = 1e-10;
 
struct LineEq
{
  double y0 = 0;  
  double m = 1;   
 
  constexpr LineEq() noexcept = default;
 
  constexpr LineEq(double __y0, double __m) noexcept 
    : y0(__y0), m(__m) {}
 
  constexpr LineEq(double x1, double y1, double __m) noexcept
    : y0(y1 - __m * x1), m(__m) {}
 
  LineEq(double x1, double y1, double x2, double y2)
  {
    ah_domain_error_if(std::abs(x1 - x2) < LINE_EPSILON)
      << "Cannot create line from points with same x-coordinate (vertical line): "
      << "x1 = " << x1 << ", x2 = " << x2;
    
    m = (y2 - y1) / (x2 - x1);
    y0 = y1 - m * x1;
  }
 
  [[nodiscard]] constexpr double operator()(double x) const noexcept 
  { 
    return y0 + m * x; 
  }
 
  [[nodiscard]] constexpr double slope() const noexcept { return m; }
 
  [[nodiscard]] constexpr double y_intercept() const noexcept { return y0; }
 
  [[nodiscard]] constexpr bool is_horizontal(double epsilon = LINE_EPSILON) const noexcept
  {
    return std::abs(m) < epsilon;
  }
 
  [[nodiscard]] constexpr bool is_parallel_to(const LineEq & l, 
                                               double epsilon = LINE_EPSILON) const noexcept
  {
    return std::abs(m - l.m) < epsilon;
  }
 
  [[nodiscard]] constexpr bool is_perpendicular_to(const LineEq & l,
                                                    double epsilon = LINE_EPSILON) const noexcept
  {
    return std::abs(m * l.m + 1.0) < epsilon;
  }
 
  [[nodiscard]] double x_at(double y) const
  {
    ah_domain_error_if(is_horizontal())
      << "Cannot compute x for horizontal line (slope = 0)";
    return (y - y0) / m;
  }
 
  [[nodiscard]] std::pair<double, double> intersection(const LineEq & l,
                                                        double epsilon = LINE_EPSILON) const
  {
    ah_domain_error_if(is_parallel_to(l, epsilon))
      << "Cannot compute intersection of parallel lines: "
      << "slope1 = " << m << ", slope2 = " << l.m;
 
    double x = (y0 - l.y0) / (l.m - m);
    return {x, (*this)(x)};
  }
 
  [[nodiscard]] LineEq perpendicular_through(double px, double py) const
  {
    ah_domain_error_if(is_horizontal())
      << "Cannot compute perpendicular to horizontal line (would be vertical)";
    
    double perp_slope = -1.0 / m;
    return LineEq(px, py, perp_slope);
  }
 
  [[nodiscard]] double distance_to(double px, double py) const noexcept
  {
    double diff = py - (y0 + m * px);
    return std::abs(diff) / std::sqrt(1.0 + m * m);
  }
 
  [[nodiscard]] bool contains_point(double px, double py, 
                                    double epsilon = LINE_EPSILON) const noexcept
  {
    return std::abs(py - (*this)(px)) < epsilon;
  }
 
  [[nodiscard]] bool operator==(const LineEq & l) const noexcept
  {
    return std::abs(y0 - l.y0) < LINE_EPSILON and 
           std::abs(m - l.m) < LINE_EPSILON;
  }
 
  [[nodiscard]] bool operator!=(const LineEq & l) const noexcept
  {
    return not (*this == l);
  }
 
  [[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