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:
-
Function
FindIntersection
: This function takes four points as input, representing the start and end points of two line segments:s1
,e1
,s2
, ande2
. -
Line Equation Parameters:
- For each line segment, it calculates the
a
,b
, andc
parameters of the line equationax + 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
isa
times the X-coordinate of the start point plusb
times the Y-coordinate of the start point.
- For each line segment, it calculates the
-
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.
-
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.
- In the
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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