As in the one- and two-dimensional cases, all homogeneous coordinate vectors must be rescaled to make the last element equal to unity. If the vectors are viewed as two-dimensional rather than one-dimensional, this means that all real one-dimensional coordinates lie along the two-dimensional line parameterized by the equation y = 1. Rescaling of vectors to make the final element equal to unity is effectively the same as moving any point that is not on the line y = 1 along a line through the origin until it reaches the line y = 1. In this context, a one-dimensional translation corresponds to a skew along the x-dimension. Since a skew along x does not change the y coordinate, translations map points from the line y = 1 back to a modified position on that line. This is illustrated in Fig. 10. In contrast, a skew along y will shift points off of the line y = 1. When these points are rescaled to make the final coordinate unity once again, a perspective distortion is induced. This is illustrated in Fig. 10. The matrix description of a pure skew f along y is

' n * x' '


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