How to resolve the algorithm Find the intersection of two lines step by step in the C# programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Find the intersection of two lines step by step in the C# programming language

Table of Contents

Problem Statement

Find the point of intersection of two lines in 2D.

The 1st line passes though   (4,0)   and   (6,10) . The 2nd line passes though   (0,3)   and   (10,7) .

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Find the intersection of two lines step by step in the C# programming language

Explanation of the C# Code:

Purpose:

This C# code defines a function to find the intersection point between two line segments. It uses the line equation and solves for the intersection coordinates.

Code Walkthrough:

  1. Function FindIntersection: This function takes four points as input, representing the start and end points of two line segments: s1, e1, s2, and e2.

  2. Line Equation Parameters:

    • For each line segment, it calculates the a, b, and c parameters of the line equation ax + by + c = 0:
      • a is the difference between the Y-coordinates of the start and end points.
      • b is the difference between the X-coordinates of the start and end points, with a negative sign.
      • c is a times the X-coordinate of the start point plus b times the Y-coordinate of the start point.
  3. Solving for Intersection:

    • The intersection point is found by solving the linear equation system formed by the line equations of the two segments.
    • It uses Cramer's rule to compute the coordinates (x, y) of the intersection point.
    • If the lines are parallel or colinear, delta (the determinant of the linear equation system) will be 0, and (float.NaN, float.NaN) is returned, indicating that there is no intersection.
  4. Main Method:

    • In the Main method, two anonymous functions are used to create PointF objects for the line segment points.
    • It calls FindIntersection with two sets of line segments and prints the intersection points.

Example Outputs:

  • For the line segments defined by (4, 0), (6, 10) and (0, 3), (10, 7), the intersection point is (2.4, 3.642857142857143).
  • For the line segments defined by (0, 0), (1, 1) and (1, 2), (4, 5), the lines are parallel, so the intersection is (float.NaN, float.NaN).

Source code in the csharp programming language

using System;
using System.Drawing;
public class Program
{
    static PointF FindIntersection(PointF s1, PointF e1, PointF s2, PointF e2) {
        float a1 = e1.Y - s1.Y;
        float b1 = s1.X - e1.X;
        float c1 = a1 * s1.X + b1 * s1.Y;

        float a2 = e2.Y - s2.Y;
        float b2 = s2.X - e2.X;
        float c2 = a2 * s2.X + b2 * s2.Y;

        float delta = a1 * b2 - a2 * b1;
        //If lines are parallel, the result will be (NaN, NaN).
        return delta == 0 ? new PointF(float.NaN, float.NaN)
            : new PointF((b2 * c1 - b1 * c2) / delta, (a1 * c2 - a2 * c1) / delta);
    }

    static void Main() {
        Func<float, float, PointF> p = (x, y) => new PointF(x, y);
        Console.WriteLine(FindIntersection(p(4f, 0f), p(6f, 10f), p(0f, 3f), p(10f, 7f)));
        Console.WriteLine(FindIntersection(p(0f, 0f), p(1f, 1f), p(1f, 2f), p(4f, 5f)));
    }
}


  

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