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Question: What does "represent 2D points in 3D coordinate space" mean?


This is my understanding... Although our point itself can be represented in 2 dimensions (which we call x, and y), we change our representation of our point and represent it in a specific way with 3 dimensions such that the class of affine transformations becomes linear. We refer to this 3 dimensional space as homogeneous coordinate space, and the representation is as follows:

The 3D homogeneous coordinate [xh, yh, w] represents the 2D coordinate [xh/w, yh/w]. As such, every 2D point has infinite homogeneous coordinate representations. A 2D point in normal 2D space is essentially represented by a line in 3D homogeneous coordinate space.


@paluri. Good job. I'm liking it. And what are some advantages of this representation?


I am currently relying on pretty much all of the concepts in these lecture slides right now when implementing a 3D viewer for Assignment 2. Homogeneous coordinates are important and are not just for show.