Fundamentals of Computer Graphics, Fourth Edition

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• The principal difference is between a single rotation and two different orthogonal matrices. This difference causes another, less important, difference. Because the SVD has different singular vectors on the two sides, there is no need for negative Singular values: we can always flip the sign of a singular value, reverse the direction of one of the associated singular vectors, and end up with the same transformation again. For this reason, the SVD always produces a diagonal matrix with all positive entries. but the matrices U and V are not guaranteed to be rotations-they could include reflection as well. In geometric applications like graphics this is an inconvenience, but a minor one: it is easy to differentiate ro tations from reflections by checking the determinant, which is +1 for rota... (查看原文)

  7086 3赞 2021-09-21 09:46:30

• However, this type of transformation, in which one of the coordinates of the input vector appears in the denominator, can’t be achieved using affine transformations. We can allow for division with a simple generalization of the mechanism of homogeneous coordinates that we have been using for affine transformations. (查看原文)

  7086 1赞 2021-05-13 11:01:33

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