With Cinderella[12], you can easily create constructions, figures consisting of points, lines, circles, conics and other geometric elements, together with relations that describe the mathematical connections between the elements.[5] A standard example is a triangle, consisting of three points and three segments connecting each pair of points, and the altitudes in that triangle. The representati...

Image analysis (IA) was used to determine the areas and circumferences of clusters of early somatic embryos (ESEs) of the Norway spruce (Picea abies /L./Karst.). Results obtained from IA were compared with the fresh weights of the ESE clusters and their esterase activities. The areas of the ESE clusters correlated well with both the increases in fresh weight (R=0.99) of the ESEs and their ester...

This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled in order to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compar...

We report the detection of multi-periodic oscillations of the cool evolved star α Hya (HD 81797, K3II-III). Two-hundred and forty-three high-resolution spectra (R = 48 000) of this star have been obtained in March and April 2005 with FEROS at the 2.2 m-MPG/ESO telescope in La Silla Observatory, Chile. We observed oscillations in the stellar radial velocity and the asymmetry of the spectral line...

In this rst installment of a two-part paper, the underlying theory for an algorithm that computes the Voronoi diagram and medial axis of a planar domain bounded by free-form (polynomial or rational) curve segments is presented. An incremental approach to computing the Voronoi diagram is used, wherein a single boundary segment is added to an existing boundary-segment set at each step. The introd...

Two years ago a new benchmark for the planetary survey was set with the discoveries of three extrasolar planets with masses below 20M⊕. In particular, the serendipitous discovery of the 14M⊕ planet around µ Ara found with HARPS with a semi-amplitude of only 4 m s −1 put in evidence the tremendous potential of HARPS for the search of this class of very low-mass planets. Aiming to discovering new...

In our recent paper [de Lacy Costello et al. 2010] we described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported previously were ca...

Clarkson recently introduced the o-smoothed distance do(p,q) = 2d(p,q)/(d(o, p)+d(o,q)+d(p,q)) (where d denotes the Euclidean distance in the plane) as a geometric analogue of the Jaccard distance; its Voronoi diagrams can be used to determine for a query point q the site p maximizing the dilation (d(p,o)+d(o,q))/d(p,q) of p and q in a star network centered at o. Although smoothed distance is n...

In the authors’ recent paper (de Lacy Costello et al., 2010) the authors described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported...

An offset algorithm is important to the contour-parallel tool path generation process. Usually, it is necessary to offset with islands. In this paper a new offset algorithm for a 2D point-sequence curve (PS-curve) with multiple islands is presented. The algorithm consists of three sub-processes, the islands bridging process, the raw offset curve generation and the global invalid loops removal. ...