The phrase "auxiliary point" is correct and usable in written English.
It can be used in contexts where you want to refer to a secondary or supporting point in an argument or discussion.
Example: "While the main argument is compelling, the auxiliary point about economic implications cannot be overlooked."
Alternatives: "supporting point" or "secondary point".
For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.
Based on these auxiliary points, a series of auxiliary hyperbolas are constructed using the geometric characteristics of the hyperbola.
Through comparing, judging and changing the reference points, constructing new auxiliary points and auxiliary ellipses, forming new assumed ideal ellipses, the minimum zone evaluation for elliptical profile error is realized finally by using the iterative approximation method.
Finally, by comparing, determining, and changing the reference points, followed by constructing new auxiliary points and auxiliary hyperbolas, a minimum zone evaluation and fitting for the measured hyperbola profile are accomplished.
Second, two focal points of the least squares hyperbola are chosen as the initial reference points, and four auxiliary points are arranged (as square vertices) around each reference point.
As a consequence, the auxiliary points in step 2.3 of Table 4 can be deterministically set ([1], pp. 119-120), [37].
In this case, because the block center points are not in the same line, we utilize bilinear interpolation to obtain the concentration values C′ at the auxiliary points, e.g., i1 and i2.
Gerritsen and Lambers (2008) proposed in their anisotropic grid adaptivity method to use bilinear interpolation to obtain pressures of the auxiliary points (such as (P_{{left( {i1} right)}}) and (P_{{left( {i2} right)}}) in Fig. 6) for calculating the interfacial velocity using Darcy's law.
In the training phase, 30 landmarks are used to describe the pelvic ring; as with the femur model shape, these are a mixture of structural and auxiliary points.
