I notice that the comments on slide 34, 35, and 36 are all asking the same question.

Homogeneous coordinates are a space where the mapping between homogeneous space and non-homogeneous space is performed by dividing all components by the extra component (which we typically denote as the "w" coordinate), and then dropping w. Here, since this is a 2D-homogeneous space, points in that space are represented by 3-vectors.

By this definition there are *many points* in 2D homogeneous space that correspond to the same point (x,y) in the 2D Euclidean space. For example (x,y,1), (2x, 2y, 2), (3x,3y,3), etc.

As a result, given a point (x,y) in 2D, constructing its homogeneous representation is given by constructing (wx, wy, w). (for any value of w).

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How do you determine what your homogenous coordinate is? I assume it's not always 1. What difference does it make?