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Unformatted text preview: hod. Following this approach, a hybrid model has been developed that combines the warping variation covariance found from the orthogonal polynomial model with the waviness and roughness variation covariance found from the frequency spectrum model to obtain the full surface variation covariance. Given a vector a that defines the variation of a surface, a linear combination of a vectors representing the normalized warping variation, aw, and the normalized waviness and roughness variation, awr, can be obtained such that a = c w a w + c wr a wr (7) where cw and cwr scale the normalized vectors. Assuming any dependence between aw and awr is negligible, the covariance of a is found from the covariances of aw and awr, 2 2 Σ a = c w Σ w + c wr Σ wr (8) where Σw is found from Eq. (6) and Σwr is found using the frequency spectrum method. The hybrid covariance model uses three variation descriptors to accurately model the geometric covariance for a general surface. The descriptors are the coefficie...
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- Spring '10
- The Land