Line Intersection

In Chapter 7, section 4 a line intersection algorithm was presented. Once the line sweep had identified potential intersection, it was necessary to check for an actual intersection using:

(Px,Py)=((x1y2)(x3−x4)−(x1−x2)(x3y4−y3x4)(x1−x2)(y3−y4)−(y1−y2)(x3−x4),(x1y2=y1x2)(y3−y4)−(y1−y2)(x3y4−y3x4)(x1−x2)(y3−y4)−(y1−y2)(x3−x4))(P_{x}, P_{y}) = (\dfrac{(x_1 y_2)(x_3 - x_4)-(x_1 - x_2)(x_3 y_4 - y_3 x_4)}{(x_1 - x_2)(y_3 - y_4)-(y_1 - y_2)(x_3 - x_4)}, \dfrac{(x_1 y_2 = y_1 x_2)(y_3 - y_4) - (y_1 - y_2)(x_3 y_4 - y_3 x_4)}{(x_1 - x_2)(y_3 - y_4)-(y_1 - y_2)(x_3 - x_4)})

The above is simply determinants written out! It is possible to compute the above using: