Degree Elevation of B-spline Curves and Its Matrix Form

An algorithmic approach to degree elevation of B--spline curves is presented. The new algorithms are based on the blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (a) decompose the B--spline curveinto piecewise B'ezier curves, (b) degree elevate eachB'ezier piece, and (c) compose the piecewise B'ezier curves into B--spline curve. Key words: Degree Elevation, B--spline, Blossoming

best weighted Euclidean

www.elsevier.com/locate/cagd Constrained polynomial degree reduction in the L2-norm equal

Evaluation of the imaging properties of Microwave Imaging Reflectometry

Microwave Imaging Reflectometry (MIR) has been developed for unambiguous measurement of electron density fluctuations in fusion plasmas. The loss of phase information limiting the use of conventional reflectometry can be minimized by a large aperture imaging optics and an array of detectors in the MIR embodiment. The evaluation of the optical system is critical for precise reconstruction of the fluctuations. The optical systems of the prototype TEXTOR MIR [2] and newly-designed KSTARMIR [5] systems have been tested with a corrugated target simulating density fluctuations at the cut-off surface. The reconstructed phase from the MIR system has been compared to the directly measured phase of corrugations taking into account the rotational speed of the target. The effects of optical aberrations and interference between lenses on the phase reconstruction have been investigated by the 2D amplitude measurement of the reflected waves and the diffraction-based optical simulations. (CODE V) A preliminary design of the KSTAR MIR optics has been suggested which can minimize the aberration and interference effects.X112sciescopu

Direct Observation of a Transiently Formed Isomer During Iodoform Photolysis in Solution by Time-Resolved X-ray Liquidography

Photolysis of iodoform (CHI3) in solution has been extensively studied, but its reaction mechanism remains elusive. In particular, iso-iodoform (iso-CHI2-I) is formed as a product of the photolysis reaction, but its detailed structure is not known, and whether it is a major intermediate species has been controversial. Here, by using time-resolved X-ray liquidography, we determined the reaction mechanism of CHI3 photodissociation in cyclohexane as well as the structure of iso-CHI2-I. Both iso-CHI2-I and CHI2 radical were found to be formed within 100 ps with a branching ratio of 40:60. Iodine radicals (I), formed during the course of CHI3 photolysis, recombine nongeminately with either CHI2 or I. Based on our structural analysis, the I-I distance and the C-I-I angle of iso-CHI2-I were determined to be 2.922 +/- 0.004 angstrom and 133.9 +/- 0.8 degrees, respectively.111sciescopu