Homogeneous coordinates
- replace 2d points with 3d points, last coordinate 1
- for a 3d point (x,y,w) the corresponding 2d point is (x/w,y/w) if w is not zero
- each 2d point (x,y) corresponds to a line in 3d; all points on this line can be written as [kx,ky,k] for some k.
- (x,y,0) does not correspond to a 2d point, corresponds to a direction (will discuss later)
- Geometric construction: 3d points are mapped to 2d points by projection to the plane z =1 from the origin