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Unformatted text preview: que is employed to estimate density function of geometric deviations. Geometric deviations are calculated after each iterative fitting of substitute geometry to the updated set of samples using the least square function. The substitute geometry is defined as: S G = T (t ) × DG (3) where SG is the substitute geometry and DG is the desired or nominal geometry. T(t) is the rigid body transformation matrix defined by vector variables t, which consists of three rotation and three transformation parameters [ElMaraghy et al., 2004]. Using The L2-norm equation for least square fitting, the objective function of the optimization problem can be written as follows: n 1 Obj = min n t i ∑ P − T (t )× D i 1/ 2 2 G (4) Evaluation of Geometric Deviations in Sculptured Surfaces 139 where the statement inside the norm sign indicates the Euclidian distance of any sample point, Pi, from the temporary substitute geometry. By utilizing a direct search method, the optimum vector variable t* can be found...
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