A Comparison of Three Curve Intersection Algorithms

An empirical comparison is made between three algorithms for computing the points of intersection of two planar Bezier curves. The algorithms compared are: the well known Bezier subdivision algorithm, which is discussed in Lane 80; a subdivision algorithm based on interval analysis due to Koparkar and Mudur; and an algorithm due to Sederberg, Anderson and Goldman which reduces the problem to one of finding the roots of a univariate polynomial. The details of these three algorithms are presented in their respective references

Isogeometric boundary element analysis using unstructured T-splines

We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bézier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method. © 2012 Elsevier B.V

Evidence for Human Fronto-Central Gamma Activity during Long-Term Memory Encoding of Word Sequences

Although human gamma activity (30–80 Hz) associated with visual processing is often reported, it is not clear to what extend gamma activity can be reliably detected non-invasively from frontal areas during complex cognitive tasks such as long term memory (LTM) formation. We conducted a memory experiment composed of 35 blocks each having three parts: LTM encoding, working memory (WM) maintenance and LTM retrieval. In the LTM encoding and WM maintenance parts, participants had to respectively encode or maintain the order of three sequentially presented words. During LTM retrieval subjects had to reproduce these sequences. Using magnetoencephalography (MEG) we identified significant differences in the gamma and beta activity. Robust gamma activity (55–65 Hz) in left BA6 (supplementary motor area (SMA)/pre-SMA) was stronger during LTM rehearsal than during WM maintenance. The gamma activity was sustained throughout the 3.4 s rehearsal period during which a fixation cross was presented. Importantly, the difference in gamma band activity correlated with memory performance over subjects. Further we observed a weak gamma power difference in left BA6 during the first half of the LTM rehearsal interval larger for successfully than unsuccessfully reproduced word triplets. In the beta band, we found a power decrease in left anterior regions during LTM rehearsal compared to WM maintenance. Also this suppression of beta power correlated with memory performance over subjects. Our findings show that an extended network of brain areas, characterized by oscillatory activity in different frequency bands, supports the encoding of word sequences in LTM. Gamma band activity in BA6 possibly reflects memory processes associated with language and timing, and suppression of beta activity at left frontal sensors is likely to reflect the release of inhibition directly associated with the engagement of language functions

Attention Enhances the Retrieval and Stability of Visuospatial and Olfactory Representations in the Dorsal Hippocampus

Attention enhances the encoding and retrieval of olfactory and visuospatial representations by modulating place field stability, firing rate, and neuronal synchronization of pyramidal cells in the hippocampus