Find ideal point of homogenous line

Question

Given the line $G=(2,1,-3)$ in homogenous coordinates, how can I find the ideal point of this line?

Answer 1

To get the ideal point on a given line you intersect that line with the line at infinity. Intersection is typically calculated as cross product and the line at infinity had coordinates $(0,0,1)$ in the conventional embedding of the plane at $z=1$.