Shawn Mclean Shawn Mclean - 1 month ago 19
C# Question

Algorithm for intersection of 2 lines?

I have 2 lines. Both lines containing their 2 points of X and Y. This means they both have length.

I see 2 formulas, one using determinants and one using normal algebra. Which would be the most efficient to calculate and what does the formula looks like?

I'm having a hard time using matrices in code.

This is what I have so far, can it be more efficient?

public static Vector3 Intersect(Vector3 line1V1, Vector3 line1V2, Vector3 line2V1, Vector3 line2V2)
{
//Line1
float A1 = line1V2.Y - line1V1.Y;
float B1 = line1V2.X - line1V1.X;
float C1 = A1*line1V1.X + B1*line1V1.Y;

//Line2
float A2 = line2V2.Y - line2V1.Y;
float B2 = line2V2.X - line2V1.X;
float C2 = A2 * line2V1.X + B2 * line2V1.Y;

float det = A1*B2 - A2*B1;
if (det == 0)
{
return null;//parallel lines
}
else
{
float x = (B2*C1 - B1*C2)/det;
float y = (A1 * C2 - A2 * C1) / det;
return new Vector3(x,y,0);
}
}

Answer

Assuming you have two lines of the form Ax + By = C, you can find it pretty easily:

float delta = A1*B2 - A2*B1;
if(delta == 0) 
    throw new ArgumentException("Lines are parallel");

float x = (B2*C1 - B1*C2)/delta;
float y = (A1*C2 - A2*C1)/delta;

Pulled from here