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Local geometric deviations of free-form surfaces are determined as normal deviations of measurement points from the nominal surface. Different sources of errors in the manufacturing process result in deviations of different character, deterministic and random. The different nature of geometric deviations may be the basis for decomposing the random and deterministic components in order to compute deterministic geometric deviations and further to introduce corrections to the processing program. Local geometric deviations constitute a spatial process. The article suggests applying the methods of spatial statistics to research on geometric deviations of free-form surfaces in order to test the existence of spatial autocorrelation. Identifying spatial correlation of measurement data proves the existence of a systematic, repetitive processing error. In such a case, the spatial modelling methods may be applied to fitting a surface regression model representing the deterministic deviations. The first step in model diagnosing is to examine the model residuals for the probability distribution and then the existence of spatial autocorrelation.

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The digit ratio (2D:4D) is said to be a potential marker of exposure to prenatal sex steroids. Some studies suggest that the 2D:4D is also linked with the testosterone response to challenging situations due to organizational effect of prenatal hormonal milieu on adult endocrine functioning. However, up to date, there were only four studies (conducted on small samples) that examined the 2D:4D and the testosterone response to a challenging situation (i.e. physical exertion or aggressive context). Here, we examined the relationship between the 2D:4D and the testosterone change under an acute exercise among 97 men. We found that the digit ratios (the right 2D:4D, the left 2D:4D, and the right minus left 2D:4D) were neither predictors of pre-exercise testosterone, nor the change in testosterone level after a cycling task. Our results add a contradictory to previous studies evidence in a discussion on the links of the 2D:4D and the testosterone change. More than 100 years ago, a difference in the length of the 2 nd , index finger (2D) and the 4 th , ring finger (4D) has been described 1. Further studies provided evidence that men and women vary when it comes to the magnitude of this difference 2. The ratio between the length of the 2 nd and the 4 th finger (2D:4D) has been reported to be smaller among men compared to women (men have longer the 4 th finger than the 2 nd finger) (but see also: 3,4). Since then, researchers have been interested in the origins and implications of the 2D:4D sexual dimorphism. Manning and colleagues 5 suggested that the difference between the 2D:4D among men and women develops during gestation under prenatal sex steroids control. The 2D:4D is said to be directly connected with the exposure to androgens in the uterus (with the lower digit ratios associated with the exposure to higher levels of testosterone, and higher digit ratios associated with the exposure to lower levels of testosterone). Hence, the 2D:4D is perceived as an index of prenatal testosterone level. However, correlational studies on the relationship between the 2D:4D and the prenatal testosterone level conducted on human fetuses brought conflicting results 6-11. Similar, mixed results have been found in experimental studies on animals 12,13 , thus, it is not surprising that such links are perceived as questionable and unclear 14-16. Even more speculative is that some researchers presume that the low 2D:4D may reflect higher adult testosterone 17-27. Interestingly, only a few studies reported a negative link between the 2D:4D and adult sex hormone levels 5,18-21,23 , whereas a meta-analysis conducted by Hönekopp et al. 28 and Zhang et al. 15 found no such association. Because there are many mixed findings on the mechanism of the observed differences in digit ratios 12-14,28 , and at the same time, there is a constantly growing body of literature showing positive associations between the 2D:4D and, for instance, psychological or physiological 29,30 characteristics, new hypotheses explaining the potential relationship between the...

Geometric deviations of free-form surfaces are attributed to many phenomena that occur during machining, both systematic (deterministic) and random in character. Measurements of free-form surfaces are performed with the use of numerically controlled CMMs on the basis of a CAD model, which results in obtaining coordinates of discrete measurement points. The spatial coordinates assigned at each measurement point include both a deterministic component and a random component at different proportions. The deterministic component of deviations is in fact the systematic component of processing errors, which is repetitive in nature. A CAD representation of deterministic geometric deviations might constitute the basis for completing a number of tasks connected with measurement and processing of free-form surfaces. The paper presents the results of testing a methodology of determining CAD models by estimating deterministic geometric deviations. The research was performed on simulated deviations superimposed on the CAD model of a nominal surface. Regression analysis, an iterative procedure, spatial statistics methods, and NURBS modelling were used for establishing the model.

The presented method is introduced to simulate and predict the accuracy of fitting two freeform surfaces. For this purpose, the CAD models of both actual surfaces should be determined on the basis of coordinate measurement data obtained in measurements along regular grids of points in the UV space. The NURBS regression surfaces are modeled on the measurement data. Adequate regression models are sought with the iterative procedure. In the following steps of the procedure, the number of control points and/or the degree of the surface is/are changed, and the autocorrelation of residuals from the models is tested using the spatial statistics methods. The designated models are optimal CAD representations of the actual surfaces. Tests of the accuracy of fitting the surfaces are carried out virtually by fitting together both models in the CAD software. The outcome of the study is a spatial model of the gap between the studied surfaces. The obtained model was verified experimentally by measuring the dimensions of the actual gap between the surfaces, applying a measuring microscope. The proposed method is a useful tool in analyzing and improving the accuracy of injection molds machining.

Obtaining discrete data is inseparably connected with losing information on surface properties. In contact measurements, the ball tip functions as a mechanical-geometrical filter. In coordinate measurements the coordinates of the measurement points of a discrete distribution on the measured surface are obtained. Surface geometric deviations are represented by a set of local deviations, i.e. deviations of measurement points from the nominal surface (the CAD model), determined in a direction normal to this surface. The results of measurements depend both on the ball tip diameter and the grid size of measurement points. This article presents findings on the influence of the ball tip diameter and the grid size on coordinate measurement results along with the experimental results of measurement of a free-form milled surface, in order to determine its local geometric deviations. One section of the surface under research was measured using different measurement parameters. The whole surface was also scanned with different parameters, observing the rule of selecting the tip diameter d and the sampling interval T in the ratio of 2:1.