144156 1995 carrino et al 2002 carrino l giorleo g

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Unformatted text preview: G. Giorleo 1 and 2. The last column, sixth, of Table 1 and 2, entitled Form deviation (proposed algorithm) tp, reports the form error of the tested datasets calculated using the proposed algorithm. Comparison of column sixth with column fifth gives the assessment capability of the proposed algorithm. For the conical frustum the datasets were extracted by the parametric equation of the corresponding cone, see figure 2 below. Figure 2: Representation of a cone used to generate the conical frustrum The set of parametric equations, explicating equation (6) for a cone and used to generate the conical frustum, is: h−u ⎧ ⎪ x = h r ⋅ cos ν ⎪ h−u ⎪ r ⋅ sin ν , (7) ⎨y = h ⎪ ⎪z = u ⎪ ⎩ where h and r are cone height and base radius, respectively. The cone base radius corresponds to the base radius of the truncated cone and it is reported in Table 1. The height of the conical frustum, reported in the forth column of Table 1, is the height of the original cone truncated by a given quantity: h − diff . This difference represents one of the two limits of the definition interval of u: u ∈ [0, h − diff ] . The “o...
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