The measurement model of OTHR involves the mapping from the ground coordinates ( left(rho, overset{rho },b,overset{b}right) ) to the slant coordinates (Rg, f d, Az).
At higher thresholds, this region had a more patchy topography, centered in the STS (Talairach coordinates left: −48, −52, 8; right: 46, −45, 11).
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In order to transform the element geometry from the global system coordinates (x, y, and z) to the local coordinates (left( {xi,eta,zeta } right)), the following equations were used as: left{ {left.
(64 Since ±CLVD corresponds to (epsilon = mp 1/2) in this diagram, we define the normalized coordinates (left( {tilde{epsilon },tilde{v}} right) = left( { - 2epsilon, v} right)).
Note that it is always possible to find ℓ coordinates (left {{i^{j}_{1}}, {i^{j}_{2}},ldots, i^{j}_{ell }right }phantom {dot {i}!}) at line 5.
(13 Considering that the horizontal coordinate takes values between −0.5 and 0.5, we use the normalized coordinates (left( {tilde{epsilon }, tilde{v}} right) = left( { - 2epsilon, v} right)) for comparison with other projections.
Since in this case the largest deformations occur near the alveolar crest, the deformations at the point with coordinates (left (x=frac {b}{sqrt {1-e^{2}}},0,hright)) are defined.
(47 Since ±CLVD is projected at (left( {p, q} right) = left( { mp left( {sqrt 6 - sqrt 2 } right)/2, 0} right)) and ±ISO is projected at (left( {p, q} right) = left( {0, pm sqrt 2 } right)) in this diagram, we define the normalized coordinates (left( {tilde{p}, tilde{q}} right) = left( { - p/left( {sqrt 6 - sqrt 2 } right),q/sqrt 2 } right)).
The minus signs in Eq. (9) are a consequence of the opposite directions of the local coordinates (left. n right|_{{varGamma (r_{i}^,left. s right|_{{varGamma (r_{i}^) and (left. n right|_{{varGamma (r_{i}^,left. s right|_{{varGamma (r_{i}^) along the interface.
