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A peculiar definition of the saw-tooth approximation of the softening branch is presented, which allows for a straightforward discretization of the softening branch in the case of snap-back on a constitutive level.
An additional detrimental factor for the development of root resorption might be the iatrogenous approximation of anterior tooth roots towards the palatal cortical plate [24, 25].
The actual hob tooth profile is a certain linear approximation of the desired profile.
An additional detrimental factor for the development of root resorption might be the iatrogenic approximation of the anterior tooth roots towards the cortical plate, which has been found to be significantly associated with the amount of resorption [16, 31].
Correspondingly, a Fresnel lens with linear saw-tooth grooves is equivalent to a piecewise linear approximation of a conical surface.
Thus, the solution in the form of (11) can be used as a sufficiently good approximation of the vertical movement of the tooth root.
In addition, results of a study by Bourauel et al. (2000) demonstrated that approximation of the actual geometry of the tooth with a paraboloid having an elliptical cross-section allows modelling the short-term and orthodontic tooth movements with high accuracy.
Limitations of this study involve the approximation of the material behavior of the tooth model.
(Their approximation: "mischievous mating").
(That is an approximation).
To a first approximation, yes.
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