line.H File Reference

2D infinite line representation using slope-intercept form. More...

#include <cmath>
#include <utility>
#include <string>
#include <sstream>
#include <ah-errors.H>

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Classes
struct	Aleph::LineEq
	2D infinite line in slope-intercept form. More...

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.

Variables
constexpr double	Aleph::LINE_EPSILON = 1e-10
	Default epsilon for floating-point comparisons.

Detailed Description

2D infinite line representation using slope-intercept form.

This file provides the LineEq class for representing infinite lines in 2D space using the slope-intercept form: y = y0 + m*x

Line Equation Form

The line is stored as:

• y0: y-intercept (where line crosses y-axis)
• m: slope (rise over run)

This gives the equation: y = y0 + m*x

Features

• Construction from slope and intercept
• Construction from a point and slope
• Construction from two points
• Line evaluation at any x-coordinate
• Intersection computation between lines
• Parallel line detection
• Comparison operations with epsilon tolerance

Usage Example

#include <line.H>
 
// Line through origin with slope 2
LineEq line1(0.0, 2.0);  // y = 2x
 
// Line through two points
LineEq line2(Point(0, 0), Point(1, 1));  // y = x
 
// Evaluate line at x = 5
double y = line1(5.0);  // y = 10
 
// Find intersection
auto [x, y] = line1.intersection(line2);
 
// Check if parallel
if (line1.is_parallel_to(line2))
  std::cout << "Lines are parallel\n";

Limitations

This representation cannot handle vertical lines (infinite slope). For vertical lines, consider using parametric or implicit form.

See also

segment.H Finite line segments

point.H Point representation

Author

Leandro Rabindranath León

Definition in file line.H.