Epigeic spiders of the pastures of northern Wielkopolska

The fauna of epigeic spiders (Araneae) occurring on three different types of pastures in northern Wielkopolska was analysed. Studies were conducted from May 1992 to October 1993. The 18,995 specimens collected were classified as belonging to 137 species and 17 families. The family Linyphiidae proved the richest in species while Lycosidae was the most abundantly in terms of number of specimens. Zoocenological analysis of spider communities showed their differentiation testifying to differences in the sites studied. The dominants were: 1) Osowo Stare (Site 1): Pardosa palustris, 2) Sycyn Dolny (Site 2): Xerolycosa miniata, P. palustris, Xysticus kochi, 3) Brqczewo (Site 3): Erigone dentipalpis, P. palustris. Seasonal changes of dominance of the species at each site were established. A comparison of changes of the species' dominances in the years 1992 and 1993 disclosed similar values of the individual dominance coefficient at the sites in Osowo Stare and Brqczewo. This result indicates the occurrence of the process of stabilization of these biocenoses and a tendency to equilibrium in the environment. The least stable proved to be the site at Sycyn Dolny. Analysis of the seasonal dynamics of epigeic spider communities was also made by determining the mean number of species at each site in the two years of study. The highest number of species was noted in spring. It is interesting to note the appearance of species which are rare or very rare in Poland such as: Lepthyphantes insignis, Ostearius melanopygius, Enoplogriatha mordax and Enoplognatha oelandica

Efficient merging of multiple segments of B\'ezier curves

This paper deals with the merging problem of segments of a composite B\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P. Wo\'zny, S. Lewanowicz, Comput. Aided Geom. Design 26 (2009), 566--579) to compute the control points of the merged curve. Thanks to using fast schemes of evaluation of certain connections involving Bernstein and dual Bernstein polynomials, the complexity of our algorithm is significantly less than complexity of other merging methods

Fast evaluation of derivatives of B\'{e}zier curves

New geometric methods for fast evaluation of derivatives of polynomial and rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating polynomial or rational B\'{e}zier curves, which was recently given by the authors. Numerical tests show that the new approach is more efficient than the methods which use the famous de Casteljau algorithm. The algorithms work well even for high-order derivatives of rational B\'{e}zier curves of high degrees