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A Bézier curve is defined by a set of control points P 0 through P n, where n is called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the curve; however, the intermediate control points generally do not lie on the curve.
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value.
Laboratory quality control is designed to detect, reduce, and correct deficiencies in a laboratory's internal analytical process prior to the release of patient results, in order to improve the quality of the results reported by the laboratory.
All analytical procedures should be validated. Identification tests are conducted to ensure the identity of an analyte in a sample through comparison of the sample to a reference standard through methods such as spectrum, chromatographic behavior, and chemical reactivity. [5] Impurity testing can either be a quantitative test or a limit test.
The geometry of a single bicubic patch is thus completely defined by a set of 16 control points. These are typically linked up to form a B-spline surface in a similar way as Bézier curves are linked up to form a B-spline curve. Simpler Bézier surfaces are formed from biquadratic patches (m = n = 2), or Bézier triangles.
The variation diminishing property of Bézier curves is that they are smoother than the polygon formed by their control points. If a line is drawn through the curve, the number of intersections with the curve will be less than or equal to the number of intersections with the control polygon.
Paul de Casteljau (19 November 1930 – 24 March 2022) was a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, leading to the curves widely known as Bézier curves.
Once the calibration curve is obtained, the gel permeation chromatogram of any other polymer can be obtained in the same solvent and the molecular weights (usually M n and M w) and the complete molecular weight distribution for the polymer can be determined. A typical calibration curve is shown to the right and the molecular weight from an ...