BSNS102 Study Guide - Final Guide: Rotation Matrix, Infor, Linear Map
28 Jan 2021
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Document Summary
As was mentioned in section 4. 1. 3, 4d vectors have four components, with the first three compo- nents being the standard x, y, and z components. The fourth component in a 4d vector is w (because they ran out of letters in the alphabet!) and is sometimes referred to as the homogenous coordinate. To understand how the standard physical 3d space is extended into 4d, let"s first examine homogenous coordinates in 2d, which are of the form (x, y, w). Imagine the standard 2d plane existing in 3d at the plane w = 1. So the physical 2d point (x, y) is represented in homogenous space (x, y, 1). Figure 9. 2: projecting homogenous coordinates onto the plane w = 1 in 2d. Thus, for any given physical 2d point (x, y), there are an infinite number of corresponding points in homogenous space. All of them are of the form (kx, ky, k), provided that k 0.
