Calculating vanishing points with Linear Algebra.

I'm trying to calculate the vanishing lines of a picture of a box.

I get that you represent the x,y positions of the vertices as [x, y, 1].

But what does it mean that you obtain a supporting line [a, b, c] with the cross-product of two vertices? What do a, b, and c represent, and what does the cross-multiplying represent?

And how does cross-multiplying two supporting lines return the vanishing point in 3D?

I'm trying to implement this paper on images of a box, with [x, y, 1] being pixels, and I'm doing the above steps to obtain the vanishing lines of each face of the box.

Arithmomaniac

[Disclaimer: cross-posted on another forum].